solution problem examples

Mixture Problems With Solutions

Mixture problems and their solutions are presented along with their solutions. Percentages are also used to solve these types of problems.

Problem 1: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?

Solution to Problem 1: Let x be the quantity of the 20% alcohol solution to be added to the 40 liters of a 50% alcohol. Let y be the quantity of the final 30% solution. Hence x + 40 = y We shall now express mathematically that the quantity of alcohol in x liters plus the quantity of alcohol in the 40 liters is equal to the quantity of alcohol in y liters. But remember the alcohol is measured in percentage term. 20% x + 50% * 40 = 30% y Substitute y by x + 40 in the last equation to obtain. 20% x + 50% * 40 = 30% (x + 40) Change percentages into fractions. 20 x / 100 + 50 * 40 / 100= 30 x / 100 + 30 * 40 / 100 Multiply all terms by 100 to simplify. 20 x + 50 * 40 = 30 x + 30 * 40 Solve for x. x = 80 liters 80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution.

Problem 2: John wants to make a 100 ml of 5% alcohol solution mixing a quantity of a 2% alcohol solution with a 7% alcohol solution. What are the quantities of each of the two solutions (2% and 7%) he has to use?

Solution to Problem 2: Let x and y be the quantities of the 2% and 7% alcohol solutions to be used to make 100 ml. Hence x + y = 100 We now write mathematically that the quantity of alcohol in x ml plus the quantity of alcohol in y ml is equal to the quantity of alcohol in 100 ml. 2% x + 7% y = 5% 100 The first equation gives y = 100 - x. Substitute in the last equation to obtain 2% x + 7% (100 - x) = 5% 100 Multiply by 100 and simplify 2 x + 700 - 7 x = 5 * 100 Solve for x x = 40 ml Substitute x by 40 in the first equation to find y y = 100 - x = 60 ml

Problem 3: Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy?

Solution to Problem 3: Let x and y be the weights, in grams, of sterling silver and of the 90% alloy to make the 500 grams at 91%. Hence x + y =500 The number of grams of pure silver in x plus the number of grams of pure silver in y is equal to the number of grams of pure silver in the 500 grams. The pure silver is given in percentage forms. Hence 92.5% x + 90% y = 91% 500 Substitute y by 500 - x in the last equation to write 92.5% x + 90% (500 - x) = 91% 500 Simplify and solve 92.5 x + 45000 - 90 x = 45500 x = 200 grams. 200 grams of Sterling Silver is needed to make the 91% alloy.

Problem 4: How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution.

Solution to Problem 4: Let x be the weights, in Kilograms, of pure water to be added. Let y be the weight, in Kilograms, of the 10% solution. Hence x + 100 = y Let us now express the fact that the amount of salt in the pure water (which 0) plus the amount of salt in the 30% solution is equal to the amount of salt in the final saline solution at 10%. 0 + 30% 100 = 10% y Substitute y by x + 100 in the last equation and solve. 30% 100 = 10% (x + 100) Solve for x. x = 200 Kilograms.

Problem 5: A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?

Solution to Problem 5: The amount of the final mixture is given by 50 ml + 30 ml = 80 ml The amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence 0 + 30% 50 ml = x (80) Solve for x x = 0.1817 = 18.75%

Problem 6: You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.

Solution to Problem 6: Let us first find the amount of alcohol in the 10% solution of 200 ml. 200 * 10% = 20 ml The amount of alcohol in the x ml of 25% solution is given by 25% x = 0.25 x The total amount of alcohol in the final solution is given by 20 + 0.25 x The ratio of alcohol in the final solution to the total amount of the solution is given by [ ( 20 + 0.25 x ) / (x + 200)] If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution. To have a percentage of 15%, we need to have [ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15 Solve the above equation for x 20 + 0.25 x = 0.15 * (x + 200) x = 100 ml

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Chapter 6: Polynomials

6.8 Mixture and Solution Word Problems

Solving mixture problems generally involves solving systems of equations. Mixture problems are ones in which two different solutions are mixed together, resulting in a new, final solution. Using a table will help to set up and solve these problems. The basic structure of this table is shown below:

The first column in the table (Name) is used to identify the fluids or objects being mixed in the problem. The second column (Amount) identifies the amounts of each of the fluids or objects. The third column (Value) is used for the value of each object or the percentage of concentration of each fluid. The last column (Equation) contains the product of the Amount times the Value or Concentration.

Example 6.8.1

Jasnah has 70 mL of a 50% methane solution. How much of a 80% solution must she add so the final solution is 60% methane? Find the equation.

The solution names are 50% (S 50 ), 60% (S 60 ), and 80% (S 80 ).
The amounts are S 50 = 70 mL, S 80 , and S 60 = 70 mL + S 80 .
The concentrations are S 50 = 0.50, S 60 = 0.60, and S 80 = 0.80.

The equation derived from this data is 0.50 (70 mL) + 0.80 (S 80 ) = 0.60 (70 mL + S 80 ).

Example 6.8.2

Sally and Terry blended a coffee mix that sells for [latex]\$2.50[/latex] by mixing two types of coffee. If they used 40 mL of a coffee that costs [latex]\$3.00,[/latex] how much of another coffee costing [latex]\$1.50[/latex] did they mix with the first?

The equation derived from this data is:

[latex]\begin{array}{ccccccc} 1.50(C_{1.50})&+&3.00(40)&=&2.50(40&+&C_{1.50}) \\ 1.50(C_{1.50})&+&120&=&100&+&2.50(C_{1.50}) \\ -2.50(C_{1.50})&-&120&=&-120&-&2.50(C_{1.50}) \\ \hline &&-1.00(C_{1.50})&=&-20&& \\ \\ &&(C_{1.50})&=&\dfrac{-20}{-1}&& \\ \\ &&C_{1.50}&=&20&& \end{array}[/latex]

This means 20 mL of the coffee selling for [latex]\$1.50[/latex] is needed for the mix.

Example 6.8.3

Nick and Chloe have two grades of milk from their small dairy herd: one that is 24% butterfat and another that is 18% butterfat. How much of each should they use to end up with 42 litres of 20% butterfat?

The equation derived from this data is:

[latex]\begin{array}{rrrrrrr} 0.24(B_{24})&+&0.18(42&- &B_{24})&=&0.20(42) \\ 0.24(B_{24})&+&7.56&-&0.18(B_{24})&=&8.4 \\ &-&7.56&&&&-7.56 \\ \hline &&&&0.06(B_{24})&=&0.84 \\ \\ &&&&B_{24}&=&\dfrac{0.84}{0.06} \\ \\ &&&&B_{24}&=&14 \end{array}[/latex]

This means 14 litres of the 24% buttermilk, and 28 litres of the 18% buttermilk is needed.

Example 6.8.4

In Natasha’s candy shop, chocolate, which sells for [latex]\$4[/latex] a kilogram, is mixed with nuts, which are sold for [latex]\$2.50[/latex] a kilogram. Chocolate and nuts are combined to form a chocolate-nut candy, which sells for [latex]\$3.50[/latex] a kilogram. How much of each are used to make 30 kilograms of the mixture?

[latex]\begin{array}{rrrrrrl} 4.00(C)&+&2.50(30&-&C)&=&3.50(30) \\ 4.00(C)&+&75&-&2.50(C)&=&105 \\ &-&75&&&&-75 \\ \hline &&&&1.50(C)&=&30 \\ \\ &&&&C&=&\dfrac{30}{1.50} \\ \\ &&&&C&=&20 \end{array}[/latex]

Therefore, 20 kg of chocolate is needed for the mixture.

With mixture problems, there is often mixing with a pure solution or using water, which contains none of the chemical of interest. For pure solutions, the concentration is 100%. For water, the concentration is 0%. This is shown in the following example.

Example 6.8.5

Joey is making a a 65% antifreeze solution using pure antifreeze mixed with water. How much of each should be used to make 70 litres?

[latex]\begin{array}{rrrrl} 1.00(A)&+&0.00(70-A)&=&0.65(0.70) \\ &&1.00A&=&45.5 \\ &&A&=&45.5 \\ \end{array}[/latex]

This means the amount of water added is 70 L − 45.5 L = 24.5 L.

For questions 1 to 9, write the equations that define the relationship.

A tank contains 8000 litres of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid?
How much pure antifreeze should be added to 5 litres of a 30% mixture of antifreeze to make a solution that is 50% antifreeze?
You have 12 kilograms of 10% saline solution and another solution of 3% strength. How many kilograms of the second should be added to the first in order to get a 5% solution?
How much pure alcohol must be added to 24 litres of a 14% solution of alcohol in order to produce a 20% solution?
How many litres of a blue dye that costs [latex]\$1.60[/latex] per litre must be mixed with 18 litres of magenta dye that costs [latex]\$2.50[/latex] per litre to make a mixture that costs [latex]\$1.90[/latex] per litre?
How many grams of pure acid must be added to 40 grams of a 20% acid solution to make a solution which is 36% acid?
A 100-kg bag of animal feed is 40% oats. How many kilograms of pure oats must be added to this feed to produce a blend of 50% oats?
A 20-gram alloy of platinum that costs [latex]\$220[/latex] per gram is mixed with an alloy that costs [latex]\$400[/latex] per gram. How many grams of the [latex]\$400[/latex] alloy should be used to make an alloy that costs [latex]\$300[/latex] per gram?
How many kilograms of tea that cost [latex]\$4.20[/latex] per kilogram must be mixed with 12 kilograms of tea that cost [latex]\$2.25[/latex] per kilogram to make a mixture that costs [latex]\$3.40[/latex] per kilogram?

Solve questions 10 to 21.

How many litres of a solvent that costs [latex]\$80[/latex] per litre must be mixed with 6 litres of a solvent that costs [latex]\$25[/latex] per litre to make a solvent that costs [latex]\$36[/latex] per litre?
How many kilograms of hard candy that cost [latex]\$7.50[/latex] per kg must be mixed with 24 kg of jelly beans that cost [latex]\$3.25[/latex] per kg to make a mixture that sells for [latex]\$4.50[/latex] per kg?
How many kilograms of soil supplement that costs [latex]\$7.00[/latex] per kg must be mixed with 20 kg of aluminum nitrate that costs [latex]\$3.50[/latex] per kg to make a fertilizer that costs [latex]\$4.50[/latex] per kg?
A candy mix sells for [latex]\$2.20[/latex] per kg. It contains chocolates worth [latex]\$1.80[/latex] per kg and other candy worth [latex]\$3.00[/latex] per kg. How much of each are in 15 kg of the mixture?
A certain grade of milk contains 10% butterfat and a certain grade of cream 60% butterfat. How many litres of each must be taken so as to obtain a mixture of 100 litres that will be 45% butterfat?
Solution A is 50% acid and solution B is 80% acid. How much of each should be used to make 100 cc of a solution that is 68% acid?
A paint that contains 21% green dye is mixed with a paint that contains 15% green dye. How many litres of each must be used to make 600 litres of paint that is 19% green dye?
How many kilograms of coffee that is 40% java beans must be mixed with coffee that is 30% java beans to make an 80-kg coffee blend that is 32% java beans?
A caterer needs to make a slightly alcoholic fruit punch that has a strength of 6% alcohol. How many litres of fruit juice must be added to 3.75 litres of 40% alcohol?
A mechanic needs to dilute a 70% antifreeze solution to make 20 litres of 18% strength. How many litres of water must be added?
How many millilitres of water must be added to 50 millilitres of 100% acid to make a 40% solution?
How many litres of water need to be evaporated from 50 litres of a 12% salt solution to produce a 15% salt solution?

Answer Key 6.8

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6.1.1: Practice Problems- Solution Concentration

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PROBLEM $\PageIndex{1}$

Explain what changes and what stays the same when 1.00 L of a solution of NaCl is diluted to 1.80 L.

The number of moles always stays the same in a dilution.

The concentration and the volumes change in a dilution.

PROBLEM $\PageIndex{2}$

What does it mean when we say that a 200-mL sample and a 400-mL sample of a solution of salt have the same molarity? In what ways are the two samples identical? In what ways are these two samples different?

The two samples contain the same proportion of moles of salt to liters of solution, but have different numbers of actual moles.

PROBLEM $\PageIndex{3}$

Determine the molarity for each of the following solutions:

0.444 mol of CoCl 2 in 0.654 L of solution
98.0 g of phosphoric acid, H 3 PO 4 , in 1.00 L of solution
0.2074 g of calcium hydroxide, Ca(OH) 2 , in 40.00 mL of solution
10.5 kg of Na 2 SO 4 ·10H 2 O in 18.60 L of solution
7.0 × 10 −3 mol of I 2 in 100.0 mL of solution
1.8 × 10 4 mg of HCl in 0.075 L of solution

PROBLEM $\PageIndex{4}$

Determine the molarity of each of the following solutions:

1.457 mol KCl in 1.500 L of solution
0.515 g of H 2 SO 4 in 1.00 L of solution
20.54 g of Al(NO 3 ) 3 in 1575 mL of solution
2.76 kg of CuSO 4 ·5H 2 O in 1.45 L of solution
0.005653 mol of Br 2 in 10.00 mL of solution
0.000889 g of glycine, C 2 H 5 NO 2 , in 1.05 mL of solution

5.25 × 10 -3 M

6.122 × 10 -2 M

1.13 × 10 -2 M

PROBLEM $\PageIndex{5}$

Calculate the number of moles and the mass of the solute in each of the following solutions:

(a) 2.00 L of 18.5 M H 2 SO 4 , concentrated sulfuric acid (b) 100.0 mL of 3.8 × 10 −5 M NaCN, the minimum lethal concentration of sodium cyanide in blood serum (c) 5.50 L of 13.3 M H 2 CO, the formaldehyde used to “fix” tissue samples (d) 325 mL of 1.8 × 10 −6 M FeSO 4 , the minimum concentration of iron sulfate detectable by taste in drinking water

37.0 mol H 2 SO 4

3.63 × 10 3 g H 2 SO 4

3.8 × 10 −6 mol NaCN

1.9 × 10 −4 g NaCN

73.2 mol H 2 CO

2.20 kg H 2 CO

5.9 × 10 −7 mol FeSO 4

8.9 × 10 −5 g FeSO 4

PROBLEM $\PageIndex{6}$

Calculate the molarity of each of the following solutions:

(a) 0.195 g of cholesterol, C 27 H 46 O, in 0.100 L of serum, the average concentration of cholesterol in human serum (b) 4.25 g of NH 3 in 0.500 L of solution, the concentration of NH 3 in household ammonia (c) 1.49 kg of isopropyl alcohol, C 3 H 7 OH, in 2.50 L of solution, the concentration of isopropyl alcohol in rubbing alcohol (d) 0.029 g of I 2 in 0.100 L of solution, the solubility of I 2 in water at 20 °C

5.04 × 10 −3 M

1.1 × 10 −3 M

PROBLEM $\PageIndex{7}$

There is about 1.0 g of calcium, as Ca 2+ , in 1.0 L of milk. What is the molarity of Ca 2+ in milk?

PROBLEM $\PageIndex{8}$

What volume of a 1.00- M Fe(NO 3 ) 3 solution can be diluted to prepare 1.00 L of a solution with a concentration of 0.250 M ?

PROBLEM $\PageIndex{9}$

If 0.1718 L of a 0.3556- M C 3 H 7 OH solution is diluted to a concentration of 0.1222 M , what is the volume of the resulting solution?

PROBLEM $\PageIndex{10}$

What volume of a 0.33- M C 12 H 22 O 11 solution can be diluted to prepare 25 mL of a solution with a concentration of 0.025 M ?

PROBLEM $\PageIndex{11}$

What is the concentration of the NaCl solution that results when 0.150 L of a 0.556- M solution is allowed to evaporate until the volume is reduced to 0.105 L?

PROBLEM $\PageIndex{12}$

What is the molarity of the diluted solution when each of the following solutions is diluted to the given final volume?

1.00 L of a 0.250- M solution of Fe(NO 3 ) 3 is diluted to a final volume of 2.00 L
0.5000 L of a 0.1222- M solution of C 3 H 7 OH is diluted to a final volume of 1.250 L
2.35 L of a 0.350- M solution of H 3 PO 4 is diluted to a final volume of 4.00 L
22.50 mL of a 0.025- M solution of C 12 H 22 O 11 is diluted to 100.0 mL

PROBLEM $\PageIndex{13}$

What is the final concentration of the solution produced when 225.5 mL of a 0.09988- M solution of Na 2 CO 3 is allowed to evaporate until the solution volume is reduced to 45.00 mL?

PROBLEM $\PageIndex{14}$

A 2.00-L bottle of a solution of concentrated HCl was purchased for the general chemistry laboratory. The solution contained 868.8 g of HCl. What is the molarity of the solution?

PROBLEM $\PageIndex{15}$

An experiment in a general chemistry laboratory calls for a 2.00- M solution of HCl. How many mL of 11.9 M HCl would be required to make 250 mL of 2.00 M HCl?

PROBLEM $\PageIndex{16}$

What volume of a 0.20- M K 2 SO 4 solution contains 57 g of K 2 SO 4 ?

PROBLEM $\PageIndex{17}$

The US Environmental Protection Agency (EPA) places limits on the quantities of toxic substances that may be discharged into the sewer system. Limits have been established for a variety of substances, including hexavalent chromium , which is limited to 0.50 mg/L. If an industry is discharging hexavalent chromium as potassium dichromate (K 2 Cr 2 O 7 ), what is the maximum permissible molarity of that substance?

4.8 × 10 −6 M

Contributors

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] ).

Adelaide Clark, Oregon Institute of Technology

Solving Equations

What is an equation.

An equation says that two things are equal. It will have an equals sign "=" like this:

That equations says:

what is on the left (x − 2) equals what is on the right (4)

So an equation is like a statement " this equals that "

What is a Solution?

A Solution is a value we can put in place of a variable (such as x ) that makes the equation true .

Example: x − 2 = 4

When we put 6 in place of x we get:

which is true

So x = 6 is a solution.

How about other values for x ?

For x=5 we get "5−2=4" which is not true , so x=5 is not a solution .
For x=9 we get "9−2=4" which is not true , so x=9 is not a solution .

In this case x = 6 is the only solution.

You might like to practice solving some animated equations .

Example: (x−3)(x−2) = 0

When x is 3 we get:

(3−3)(3−2) = 0 × 1 = 0

And when x is 2 we get:

(2−3)(2−2) = (−1) × 0 = 0

which is also true

So the solutions are:

x = 3 , or x = 2

When we gather all solutions together it is called a Solution Set

The above solution set is: {2, 3}

Solutions Everywhere!

Some equations are true for all allowed values and are then called Identities

Example: sin(−θ) = −sin(θ) is one of the Trigonometric Identities

Let's try θ = 30°:

sin(−30°) = −0.5 and

−sin(30°) = −0.5

So it is true for θ = 30°

Let's try θ = 90°:

sin(−90°) = −1 and

−sin(90°) = −1

So it is also true for θ = 90°

Is it true for all values of θ ? Try some values for yourself!

How to Solve an Equation

There is no "one perfect way" to solve all equations.

A Useful Goal

But we often get success when our goal is to end up with:

x = something

In other words, we want to move everything except "x" (or whatever name the variable has) over to the right hand side.

Example: Solve 3x−6 = 9

Now we have x = something ,

and a short calculation reveals that x = 5

Like a Puzzle

In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can (and cannot) do.

Here are some things we can do:

Add or Subtract the same value from both sides
Clear out any fractions by Multiplying every term by the bottom parts
Divide every term by the same nonzero value
Combine Like Terms
Expanding (the opposite of factoring) may also help
Recognizing a pattern, such as the difference of squares
Sometimes we can apply a function to both sides (e.g. square both sides)

Example: Solve √(x/2) = 3

And the more "tricks" and techniques you learn the better you will get.

Special Equations

There are special ways of solving some types of equations. Learn how to ...

solve Quadratic Equations
solve Radical Equations
solve Equations with Sine, Cosine and Tangent

Check Your Solutions

You should always check that your "solution" really is a solution.

How To Check

Take the solution(s) and put them in the original equation to see if they really work.

Example: solve for x:

2x x − 3 + 3 = 6 x − 3 (x≠3)

We have said x≠3 to avoid a division by zero.

Let's multiply through by (x − 3) :

2x + 3(x−3) = 6

Bring the 6 to the left:

2x + 3(x−3) − 6 = 0

Expand and solve:

2x + 3x − 9 − 6 = 0

5x − 15 = 0

5(x − 3) = 0

Which can be solved by having x=3

Let us check x=3 using the original question:

2 × 3 3 − 3 + 3 = 6 3 − 3

Hang On: 3 − 3 = 0 That means dividing by Zero!

And anyway, we said at the top that x≠3 , so ...

x = 3 does not actually work, and so:

There is No Solution!

That was interesting ... we thought we had found a solution, but when we looked back at the question we found it wasn't allowed!

This gives us a moral lesson:

"Solving" only gives us possible solutions, they need to be checked!

Note down where an expression is not defined (due to a division by zero, the square root of a negative number, or some other reason)
Show all the steps , so it can be checked later (by you or someone else)

35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Join the 150,000+ facilitators  using SessionLab.

How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

Problem-solving techniques to identify and analyze problems
Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve.

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward.

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats
Lightning Decision Jam
Problem Definition Process
Discovery & Action Dialogue

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

The Creativity Dice
Fishbone Analysis
Problem Tree
SWOT Analysis
Agreement-Certainty Matrix
The Journalistic Six
LEGO Challenge
What, So What, Now What?
Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

Improved Solutions
Four-Step Sketch
15% Solutions
How-Now-Wow matrix
Impact Effort Matrix

21. Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in/Check-out
Doodling Together
Show and Tell
Constellations
Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space.

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

Identify the issue : Recognize the problem that needs to be solved.
Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

Brainstorming with others
Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
Analyzing cause and effect
Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

Creating a list of potential ideas to solve the problem
Grouping and categorizing similar solutions
Prioritizing potential solutions based on feasibility, cost, and resources required
Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
Decision-making matrices
Pros and cons lists
Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

Communicating the solution to relevant parties
Setting timelines and milestones
Assigning tasks and responsibilities
Monitoring the solution and making adjustments as necessary
Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

Generate a diverse range of solutions
Encourage all team members to participate
Foster creative thinking

When brainstorming, remember to:

Reserve judgment until the session is over
Encourage wild ideas
Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

5 Whys : Ask “why” five times to get to the underlying cause.
Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

List your problem’s strengths, such as relevant resources or strong partnerships.
Identify its weaknesses, such as knowledge gaps or limited resources.
Explore opportunities, like trends or new technologies, that could help solve the problem.
Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

Write the problem in the center of a blank page.
Draw branches from the central problem to related sub-problems or contributing factors.
Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge.

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem .

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high.

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one.

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions.

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving.

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem.

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions.

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down

Identifying the problem allows you to see which steps need to be taken to solve it.

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible.

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist.

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

Will my team be on board with the proposition?
Does the solution align with organizational goals ?
Is the solution likely to achieve the desired outcomes?
Is the solution realistic and possible with current resources and constraints?
Will the solution solve the problem without causing additional unintended problems?

woman-helping-her-colleague-problem-solving-strategies

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it.

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem.

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems.

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

Use a solution that worked before
Brainstorming
Work backward
Use the Kipling method
Draw the problem
Use trial and error
Sleep on it
Get advice from your peers
Use the Pareto principle
Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .”

What is the problem?
Why is the problem important?
When did the problem arise, and when does it need to be solved?
How did the problem happen?
Where is the problem occurring?
Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

woman-drawing-mind-map-problem-solving-strategies

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level.

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own.

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group.

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone.

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales.

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit.

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

three-colleagues-looking-at-computer-problem-solving-strategies

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

Critical thinking and analytical skills
Communication skills , including active listening
Decision-making
Planning and prioritization
Emotional intelligence , including empathy and emotional regulation
Time management
Data analysis
Research skills
Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life.

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking.

two-colleagues-talking-at-corporate-event-problem-solving-strategies

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve.

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject.

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman.

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches.

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem.

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster.

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007.

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution.

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

Boost your productivity

Maximize your time and productivity with strategies from our expert coaches.

Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

5 problem-solving questions to prepare you for your next interview, what are metacognitive skills examples in everyday life, what is lateral thinking 7 techniques to encourage creative ideas, 31 examples of problem solving performance review phrases, learn what process mapping is and how to create one (+ examples), leadership activities that encourage employee engagement, can dreams help you solve problems 6 ways to try, how much do distractions cost 8 effects of lack of focus, similar articles, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, experimentation brings innovation: create an experimental workplace, 3 problem statement examples and steps to write your own, contingency planning: 4 steps to prepare for the unexpected, stay connected with betterup, get our newsletter, event invites, plus product insights and research..

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></center></p><h2>17 Smart Problem-Solving Strategies: Master Complex Problems</h2><ul><li>March 3, 2024</li><li>Productivity</li><li>25 min read</li></ul><p><center><img style=

Struggling to overcome challenges in your life? We all face problems, big and small, on a regular basis.

So how do you tackle them effectively? What are some key problem-solving strategies and skills that can guide you?

Effective problem-solving requires breaking issues down logically, generating solutions creatively, weighing choices critically, and adapting plans flexibly based on outcomes. Useful strategies range from leveraging past solutions that have worked to visualizing problems through diagrams. Core skills include analytical abilities, innovative thinking, and collaboration.

Want to improve your problem-solving skills? Keep reading to find out 17 effective problem-solving strategies, key skills, common obstacles to watch for, and tips on improving your overall problem-solving skills.

Key Takeaways:

Effective problem-solving requires breaking down issues logically, generating multiple solutions creatively, weighing choices critically, and adapting plans based on outcomes.
Useful problem-solving strategies range from leveraging past solutions to brainstorming with groups to visualizing problems through diagrams and models.
Core skills include analytical abilities, innovative thinking, decision-making, and team collaboration to solve problems.
Common obstacles include fear of failure, information gaps, fixed mindsets, confirmation bias, and groupthink.
Boosting problem-solving skills involves learning from experts, actively practicing, soliciting feedback, and analyzing others’ success.
Onethread’s project management capabilities align with effective problem-solving tenets – facilitating structured solutions, tracking progress, and capturing lessons learned.

What Is Problem-Solving?

Problem-solving is the process of understanding an issue, situation, or challenge that needs to be addressed and then systematically working through possible solutions to arrive at the best outcome.

It involves critical thinking, analysis, logic, creativity, research, planning, reflection, and patience in order to overcome obstacles and find effective answers to complex questions or problems.

The ultimate goal is to implement the chosen solution successfully.

What Are Problem-Solving Strategies?

Problem-solving strategies are like frameworks or methodologies that help us solve tricky puzzles or problems we face in the workplace, at home, or with friends.

Imagine you have a big jigsaw puzzle. One strategy might be to start with the corner pieces. Another could be looking for pieces with the same colors.

Just like in puzzles, in real life, we use different plans or steps to find solutions to problems. These strategies help us think clearly, make good choices, and find the best answers without getting too stressed or giving up.

Why Is It Important To Know Different Problem-Solving Strategies?

Knowing different problem-solving strategies is important because different types of problems often require different approaches to solve them effectively. Having a variety of strategies to choose from allows you to select the best method for the specific problem you are trying to solve.

This improves your ability to analyze issues thoroughly, develop solutions creatively, and tackle problems from multiple angles. Knowing multiple strategies also aids in overcoming roadblocks if your initial approach is not working.

Here are some reasons why you need to know different problem-solving strategies:

Different Problems Require Different Tools: Just like you can’t use a hammer to fix everything, some problems need specific strategies to solve them.
Improves Creativity: Knowing various strategies helps you think outside the box and come up with creative solutions.
Saves Time: With the right strategy, you can solve problems faster instead of trying things that don’t work.
Reduces Stress: When you know how to tackle a problem, it feels less scary and you feel more confident.
Better Outcomes: Using the right strategy can lead to better solutions, making things work out better in the end.
Learning and Growth: Each time you solve a problem, you learn something new, which makes you smarter and better at solving future problems.

Knowing different ways to solve problems helps you tackle anything that comes your way, making life a bit easier and more fun!

17 Effective Problem-Solving Strategies

Effective problem-solving strategies include breaking the problem into smaller parts, brainstorming multiple solutions, evaluating the pros and cons of each, and choosing the most viable option.

Critical thinking and creativity are essential in developing innovative solutions. Collaboration with others can also provide diverse perspectives and ideas.

By applying these strategies, you can tackle complex issues more effectively.

Now, consider a challenge you’re dealing with. Which strategy could help you find a solution? Here we will discuss key problem strategies in detail.

1. Use a Past Solution That Worked

This strategy involves looking back at previous similar problems you have faced and the solutions that were effective in solving them.

It is useful when you are facing a problem that is very similar to something you have already solved. The main benefit is that you don’t have to come up with a brand new solution – you already know the method that worked before will likely work again.

However, the limitation is that the current problem may have some unique aspects or differences that mean your old solution is not fully applicable.

The ideal process is to thoroughly analyze the new challenge, identify the key similarities and differences versus the past case, adapt the old solution as needed to align with the current context, and then pilot it carefully before full implementation.

An example is using the same negotiation tactics from purchasing your previous home when putting in an offer on a new house. Key terms would be adjusted but overall it can save significant time versus developing a brand new strategy.

2. Brainstorm Solutions

This involves gathering a group of people together to generate as many potential solutions to a problem as possible.

It is effective when you need creative ideas to solve a complex or challenging issue. By getting input from multiple people with diverse perspectives, you increase the likelihood of finding an innovative solution.

The main limitation is that brainstorming sessions can sometimes turn into unproductive gripe sessions or discussions rather than focusing on productive ideation —so they need to be properly facilitated.

The key to an effective brainstorming session is setting some basic ground rules upfront and having an experienced facilitator guide the discussion. Rules often include encouraging wild ideas, avoiding criticism of ideas during the ideation phase, and building on others’ ideas.

For instance, a struggling startup might hold a session where ideas for turnaround plans are generated and then formalized with financials and metrics.

3. Work Backward from the Solution

This technique involves envisioning that the problem has already been solved and then working step-by-step backward toward the current state.

This strategy is particularly helpful for long-term, multi-step problems. By starting from the imagined solution and identifying all the steps required to reach it, you can systematically determine the actions needed. It lets you tackle a big hairy problem through smaller, reversible steps.

A limitation is that this approach may not be possible if you cannot accurately envision the solution state to start with.

The approach helps drive logical systematic thinking for complex problem-solving, but should still be combined with creative brainstorming of alternative scenarios and solutions.

An example is planning for an event – you would imagine the successful event occurring, then determine the tasks needed the week before, two weeks before, etc. all the way back to the present.

4. Use the Kipling Method

This method, named after author Rudyard Kipling, provides a framework for thoroughly analyzing a problem before jumping into solutions.

It consists of answering six fundamental questions: What, Where, When, How, Who, and Why about the challenge. Clearly defining these core elements of the problem sets the stage for generating targeted solutions.

The Kipling method enables a deep understanding of problem parameters and root causes before solution identification. By jumping to brainstorm solutions too early, critical information can be missed or the problem is loosely defined, reducing solution quality.

Answering the six fundamental questions illuminates all angles of the issue. This takes time but pays dividends in generating optimal solutions later tuned precisely to the true underlying problem.

The limitation is that meticulously working through numerous questions before addressing solutions can slow progress.

The best approach blends structured problem decomposition techniques like the Kipling method with spurring innovative solution ideation from a diverse team.

An example is using this technique after a technical process failure – the team would systematically detail What failed, Where/When did it fail, How it failed (sequence of events), Who was involved, and Why it likely failed before exploring preventative solutions.

5. Try Different Solutions Until One Works (Trial and Error)

This technique involves attempting various potential solutions sequentially until finding one that successfully solves the problem.

Trial and error works best when facing a concrete, bounded challenge with clear solution criteria and a small number of discrete options to try. By methodically testing solutions, you can determine the faulty component.

A limitation is that it can be time-intensive if the working solution set is large.

The key is limiting the variable set first. For technical problems, this boundary is inherent and each element can be iteratively tested. But for business issues, artificial constraints may be required – setting decision rules upfront to reduce options before testing.

Furthermore, hypothesis-driven experimentation is far superior to blind trial and error – have logic for why Option A may outperform Option B.

Examples include fixing printer jams by testing different paper tray and cable configurations or resolving website errors by tweaking CSS/HTML line-by-line until the code functions properly.

6. Use Proven Formulas or Frameworks (Heuristics)

Heuristics refers to applying existing problem-solving formulas or frameworks rather than addressing issues completely from scratch.

This allows leveraging established best practices rather than reinventing the wheel each time.

It is effective when facing recurrent, common challenges where proven structured approaches exist.

However, heuristics may force-fit solutions to non-standard problems.

For example, a cost-benefit analysis can be used instead of custom weighting schemes to analyze potential process improvements.

Onethread allows teams to define, save, and replicate configurable project templates so proven workflows can be reliably applied across problems with some consistency rather than fully custom one-off approaches each time.

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7. Trust Your Instincts (Insight Problem-Solving)

Insight is a problem-solving technique that involves waiting patiently for an unexpected “aha moment” when the solution pops into your mind.

It works well for personal challenges that require intuitive realizations over calculated logic. The unconscious mind makes connections leading to flashes of insight when relaxing or doing mundane tasks unrelated to the actual problem.

Benefits include out-of-the-box creative solutions. However, the limitations are that insights can’t be forced and may never come at all if too complex. Critical analysis is still required after initial insights.

A real-life example would be a writer struggling with how to end a novel. Despite extensive brainstorming, they feel stuck. Eventually while gardening one day, a perfect unexpected plot twist sparks an ideal conclusion. However, once written they still carefully review if the ending flows logically from the rest of the story.

8. Reverse Engineer the Problem

This approach involves deconstructing a problem in reverse sequential order from the current undesirable outcome back to the initial root causes.

By mapping the chain of events backward, you can identify the origin of where things went wrong and establish the critical junctures for solving it moving ahead. Reverse engineering provides diagnostic clarity on multi-step problems.

However, the limitation is that it focuses heavily on autopsying the past versus innovating improved future solutions.

An example is tracing back from a server outage, through the cascade of infrastructure failures that led to it finally terminating at the initial script error that triggered the crisis. This root cause would then inform the preventative measure.

9. Break Down Obstacles Between Current and Goal State (Means-End Analysis)

This technique defines the current problem state and the desired end goal state, then systematically identifies obstacles in the way of getting from one to the other.

By mapping the barriers or gaps, you can then develop solutions to address each one. This methodically connects the problem to solutions.

A limitation is that some obstacles may be unknown upfront and only emerge later.

For example, you can list down all the steps required for a new product launch – current state through production, marketing, sales, distribution, etc. to full launch (goal state) – to highlight where resource constraints or other blocks exist so they can be addressed.

Onethread allows dividing big-picture projects into discrete, manageable phases, milestones, and tasks to simplify execution just as problems can be decomposed into more achievable components. Features like dependency mapping further reinforce interconnections.

Using Onethread’s issues and subtasks feature, messy problems can be decomposed into manageable chunks.

10. Ask “Why” Five Times to Identify the Root Cause (The 5 Whys)

This technique involves asking “Why did this problem occur?” and then responding with an answer that is again met with asking “Why?” This process repeats five times until the root cause is revealed.

Continually asking why digs deeper from surface symptoms to underlying systemic issues.

It is effective for getting to the source of problems originating from human error or process breakdowns.

However, some complex issues may have multiple tangled root causes not solvable through this approach alone.

An example is a retail store experiencing a sudden decline in customers. Successively asking why five times may trace an initial drop to parking challenges, stemming from a city construction project – the true starting point to address.

11. Evaluate Strengths, Weaknesses, Opportunities, and Threats (SWOT Analysis)

This involves analyzing a problem or proposed solution by categorizing internal and external factors into a 2×2 matrix: Strengths, Weaknesses as the internal rows; Opportunities and Threats as the external columns.

Systematically identifying these elements provides balanced insight to evaluate options and risks. It is impactful when evaluating alternative solutions or developing strategy amid complexity or uncertainty.

The key benefit of SWOT analysis is enabling multi-dimensional thinking when rationally evaluating options. Rather than getting anchored on just the upsides or the existing way of operating, it urges a systematic assessment through four different lenses:

Internal Strengths: Our core competencies/advantages able to deliver success
Internal Weaknesses: Gaps/vulnerabilities we need to manage
External Opportunities: Ways we can differentiate/drive additional value
External Threats: Risks we must navigate or mitigate

Multiperspective analysis provides the needed holistic view of the balanced risk vs. reward equation for strategic decision making amid uncertainty.

However, SWOT can feel restrictive if not tailored and evolved for different issue types.

Teams should view SWOT analysis as a starting point, augmenting it further for distinct scenarios.

An example is performing a SWOT analysis on whether a small business should expand into a new market – evaluating internal capabilities to execute vs. risks in the external competitive and demand environment to inform the growth decision with eyes wide open.

12. Compare Current vs Expected Performance (Gap Analysis)

This technique involves comparing the current state of performance, output, or results to the desired or expected levels to highlight shortfalls.

By quantifying the gaps, you can identify problem areas and prioritize address solutions.

Gap analysis is based on the simple principle – “you can’t improve what you don’t measure.” It enables facts-driven problem diagnosis by highlighting delta to goals, not just vague dissatisfaction that something seems wrong. And measurement immediately suggests improvement opportunities – address the biggest gaps first.

This data orientation also supports ROI analysis on fixing issues – the return from closing larger gaps outweighs narrowly targeting smaller performance deficiencies.

However, the approach is only effective if robust standards and metrics exist as the benchmark to evaluate against. Organizations should invest upfront in establishing performance frameworks.

Furthermore, while numbers are invaluable, the human context behind problems should not be ignored – quantitative versus qualitative gap assessment is optimally blended.

For example, if usage declines are noted during software gap analysis, this could be used as a signal to improve user experience through design.

13. Observe Processes from the Frontline (Gemba Walk)

A Gemba walk involves going to the actual place where work is done, directly observing the process, engaging with employees, and finding areas for improvement.

By experiencing firsthand rather than solely reviewing abstract reports, practical problems and ideas emerge.

The limitation is Gemba walks provide anecdotes not statistically significant data. It complements but does not replace comprehensive performance measurement.

An example is a factory manager inspecting the production line to spot jam areas based on direct reality rather than relying on throughput dashboards alone back in her office. Frontline insights prove invaluable.

14. Analyze Competitive Forces (Porter’s Five Forces)

This involves assessing the marketplace around a problem or business situation via five key factors: competitors, new entrants, substitute offerings, suppliers, and customer power.

Evaluating these forces illuminates risks and opportunities for strategy development and issue resolution. It is effective for understanding dynamic external threats and opportunities when operating in a contested space.

However, over-indexing on only external factors can overlook the internal capabilities needed to execute solutions.

A startup CEO, for example, may analyze market entry barriers, whitespace opportunities, and disruption risks across these five forces to shape new product rollout strategies and marketing approaches.

15. Think from Different Perspectives (Six Thinking Hats)

The Six Thinking Hats is a technique developed by Edward de Bono that encourages people to think about a problem from six different perspectives, each represented by a colored “thinking hat.”

The key benefit of this strategy is that it pushes team members to move outside their usual thinking style and consider new angles. This brings more diverse ideas and solutions to the table.

It works best for complex problems that require innovative solutions and when a team is stuck in an unproductive debate. The structured framework keeps the conversation flowing in a positive direction.

Limitations are that it requires training on the method itself and may feel unnatural at first. Team dynamics can also influence success – some members may dominate certain “hats” while others remain quiet.

A real-life example is a software company debating whether to build a new feature. The white hat focuses on facts, red on gut feelings, black on potential risks, yellow on benefits, green on new ideas, and blue on process. This exposes more balanced perspectives before deciding.

Onethread centralizes diverse stakeholder communication onto one platform, ensuring all voices are incorporated when evaluating project tradeoffs, just as problem-solving should consider multifaceted solutions.

16. Visualize the Problem (Draw it Out)

Drawing out a problem involves creating visual representations like diagrams, flowcharts, and maps to work through challenging issues.

This strategy is helpful when dealing with complex situations with lots of interconnected components. The visuals simplify the complexity so you can thoroughly understand the problem and all its nuances.

Key benefits are that it allows more stakeholders to get on the same page regarding root causes and it sparks new creative solutions as connections are made visually.

However, simple problems with few variables don’t require extensive diagrams. Additionally, some challenges are so multidimensional that fully capturing every aspect is difficult.

A real-life example would be mapping out all the possible causes leading to decreased client satisfaction at a law firm. An intricate fishbone diagram with branches for issues like service delivery, technology, facilities, culture, and vendor partnerships allows the team to trace problems back to their origins and brainstorm targeted fixes.

17. Follow a Step-by-Step Procedure (Algorithms)

An algorithm is a predefined step-by-step process that is guaranteed to produce the correct solution if implemented properly.

Using algorithms is effective when facing problems that have clear, binary right and wrong answers. Algorithms work for mathematical calculations, computer code, manufacturing assembly lines, and scientific experiments.

Key benefits are consistency, accuracy, and efficiency. However, they require extensive upfront development and only apply to scenarios with strict parameters. Additionally, human error can lead to mistakes.

For example, crew members of fast food chains like McDonald’s follow specific algorithms for food prep – from grill times to ingredient amounts in sandwiches, to order fulfillment procedures. This ensures uniform quality and service across all locations. However, if a step is missed, errors occur.

The Problem-Solving Process

The problem-solving process typically includes defining the issue, analyzing details, creating solutions, weighing choices, acting, and reviewing results.

In the above, we have discussed several problem-solving strategies. For every problem-solving strategy, you have to follow these processes. Here’s a detailed step-by-step process of effective problem-solving:

Step 1: Identify the Problem

The problem-solving process starts with identifying the problem. This step involves understanding the issue’s nature, its scope, and its impact. Once the problem is clearly defined, it sets the foundation for finding effective solutions.

Identifying the problem is crucial. It means figuring out exactly what needs fixing. This involves looking at the situation closely, understanding what’s wrong, and knowing how it affects things. It’s about asking the right questions to get a clear picture of the issue.

This step is important because it guides the rest of the problem-solving process. Without a clear understanding of the problem, finding a solution is much harder. It’s like diagnosing an illness before treating it. Once the problem is identified accurately, you can move on to exploring possible solutions and deciding on the best course of action.

Step 2: Break Down the Problem

Breaking down the problem is a key step in the problem-solving process. It involves dividing the main issue into smaller, more manageable parts. This makes it easier to understand and tackle each component one by one.

After identifying the problem, the next step is to break it down. This means splitting the big issue into smaller pieces. It’s like solving a puzzle by handling one piece at a time.

By doing this, you can focus on each part without feeling overwhelmed. It also helps in identifying the root causes of the problem. Breaking down the problem allows for a clearer analysis and makes finding solutions more straightforward.

Each smaller problem can be addressed individually, leading to an effective resolution of the overall issue. This approach not only simplifies complex problems but also aids in developing a systematic plan to solve them.

Step 3: Come up with potential solutions

Coming up with potential solutions is the third step in the problem-solving process. It involves brainstorming various options to address the problem, considering creativity and feasibility to find the best approach.

After breaking down the problem, it’s time to think of ways to solve it. This stage is about brainstorming different solutions. You look at the smaller issues you’ve identified and start thinking of ways to fix them. This is where creativity comes in.

You want to come up with as many ideas as possible, no matter how out-of-the-box they seem. It’s important to consider all options and evaluate their pros and cons. This process allows you to gather a range of possible solutions.

Later, you can narrow these down to the most practical and effective ones. This step is crucial because it sets the stage for deciding on the best solution to implement. It’s about being open-minded and innovative to tackle the problem effectively.

Step 4: Analyze the possible solutions

Analyzing the possible solutions is the fourth step in the problem-solving process. It involves evaluating each proposed solution’s advantages and disadvantages to determine the most effective and feasible option.

After coming up with potential solutions, the next step is to analyze them. This means looking closely at each idea to see how well it solves the problem. You weigh the pros and cons of every solution.

Consider factors like cost, time, resources, and potential outcomes. This analysis helps in understanding the implications of each option. It’s about being critical and objective, ensuring that the chosen solution is not only effective but also practical.

This step is vital because it guides you towards making an informed decision. It involves comparing the solutions against each other and selecting the one that best addresses the problem.

By thoroughly analyzing the options, you can move forward with confidence, knowing you’ve chosen the best path to solve the issue.

Step 5: Implement and Monitor the Solutions

Implementing and monitoring the solutions is the final step in the problem-solving process. It involves putting the chosen solution into action and observing its effectiveness, making adjustments as necessary.

Once you’ve selected the best solution, it’s time to put it into practice. This step is about action. You implement the chosen solution and then keep an eye on how it works. Monitoring is crucial because it tells you if the solution is solving the problem as expected.

If things don’t go as planned, you may need to make some changes. This could mean tweaking the current solution or trying a different one. The goal is to ensure the problem is fully resolved.

This step is critical because it involves real-world application. It’s not just about planning; it’s about doing and adjusting based on results. By effectively implementing and monitoring the solutions, you can achieve the desired outcome and solve the problem successfully.

Why This Process is Important

Following a defined process to solve problems is important because it provides a systematic, structured approach instead of a haphazard one. Having clear steps guides logical thinking, analysis, and decision-making to increase effectiveness. Key reasons it helps are:

Clear Direction: This process gives you a clear path to follow, which can make solving problems less overwhelming.
Better Solutions: Thoughtful analysis of root causes, iterative testing of solutions, and learning orientation lead to addressing the heart of issues rather than just symptoms.
Saves Time and Energy: Instead of guessing or trying random things, this process helps you find a solution more efficiently.
Improves Skills: The more you use this process, the better you get at solving problems. It’s like practicing a sport. The more you practice, the better you play.
Maximizes collaboration: Involving various stakeholders in the process enables broader inputs. Their communication and coordination are streamlined through organized brainstorming and evaluation.
Provides consistency: Standard methodology across problems enables building institutional problem-solving capabilities over time. Patterns emerge on effective techniques to apply to different situations.

The problem-solving process is a powerful tool that can help us tackle any challenge we face. By following these steps, we can find solutions that work and learn important skills along the way.

Key Skills for Efficient Problem Solving

Efficient problem-solving requires breaking down issues logically, evaluating options, and implementing practical solutions.

Key skills include critical thinking to understand root causes, creativity to brainstorm innovative ideas, communication abilities to collaborate with others, and decision-making to select the best way forward. Staying adaptable, reflecting on outcomes, and applying lessons learned are also essential.

With practice, these capacities will lead to increased personal and team effectiveness in systematically addressing any problem.

Let’s explore the powers you need to become a problem-solving hero!

Critical Thinking and Analytical Skills

Critical thinking and analytical skills are vital for efficient problem-solving as they enable individuals to objectively evaluate information, identify key issues, and generate effective solutions.

These skills facilitate a deeper understanding of problems, leading to logical, well-reasoned decisions. By systematically breaking down complex issues and considering various perspectives, individuals can develop more innovative and practical solutions, enhancing their problem-solving effectiveness.

Communication Skills

Effective communication skills are essential for efficient problem-solving as they facilitate clear sharing of information, ensuring all team members understand the problem and proposed solutions.

These skills enable individuals to articulate issues, listen actively, and collaborate effectively, fostering a productive environment where diverse ideas can be exchanged and refined. By enhancing mutual understanding, communication skills contribute significantly to identifying and implementing the most viable solutions.

Decision-Making

Strong decision-making skills are crucial for efficient problem-solving, as they enable individuals to choose the best course of action from multiple alternatives.

These skills involve evaluating the potential outcomes of different solutions, considering the risks and benefits, and making informed choices. Effective decision-making leads to the implementation of solutions that are likely to resolve problems effectively, ensuring resources are used efficiently and goals are achieved.

Planning and Prioritization

Planning and prioritization are key for efficient problem-solving, ensuring resources are allocated effectively to address the most critical issues first. This approach helps in organizing tasks according to their urgency and impact, streamlining efforts towards achieving the desired outcome efficiently.

Emotional Intelligence

Emotional intelligence enhances problem-solving by allowing individuals to manage emotions, understand others, and navigate social complexities. It fosters a positive, collaborative environment, essential for generating creative solutions and making informed, empathetic decisions.

Leadership skills drive efficient problem-solving by inspiring and guiding teams toward common goals. Effective leaders motivate their teams, foster innovation, and navigate challenges, ensuring collective efforts are focused and productive in addressing problems.

Time Management

Time management is crucial in problem-solving, enabling individuals to allocate appropriate time to each task. By efficiently managing time, one can ensure that critical problems are addressed promptly without neglecting other responsibilities.

Data Analysis

Data analysis skills are essential for problem-solving, as they enable individuals to sift through data, identify trends, and extract actionable insights. This analytical approach supports evidence-based decision-making, leading to more accurate and effective solutions.

Research Skills

Research skills are vital for efficient problem-solving, allowing individuals to gather relevant information, explore various solutions, and understand the problem’s context. This thorough exploration aids in developing well-informed, innovative solutions.

Becoming a great problem solver takes practice, but with these skills, you’re on your way to becoming a problem-solving hero.

How to Improve Your Problem-Solving Skills?

Improving your problem-solving skills can make you a master at overcoming challenges. Learn from experts, practice regularly, welcome feedback, try new methods, experiment, and study others’ success to become better.

Learning from Experts

Improving problem-solving skills by learning from experts involves seeking mentorship, attending workshops, and studying case studies. Experts provide insights and techniques that refine your approach, enhancing your ability to tackle complex problems effectively.

To enhance your problem-solving skills, learning from experts can be incredibly beneficial. Engaging with mentors, participating in specialized workshops, and analyzing case studies from seasoned professionals can offer valuable perspectives and strategies.

Experts share their experiences, mistakes, and successes, providing practical knowledge that can be applied to your own problem-solving process. This exposure not only broadens your understanding but also introduces you to diverse methods and approaches, enabling you to tackle challenges more efficiently and creatively.

Improving problem-solving skills through practice involves tackling a variety of challenges regularly. This hands-on approach helps in refining techniques and strategies, making you more adept at identifying and solving problems efficiently.

One of the most effective ways to enhance your problem-solving skills is through consistent practice. By engaging with different types of problems on a regular basis, you develop a deeper understanding of various strategies and how they can be applied.

This hands-on experience allows you to experiment with different approaches, learn from mistakes, and build confidence in your ability to tackle challenges.

Regular practice not only sharpens your analytical and critical thinking skills but also encourages adaptability and innovation, key components of effective problem-solving.

Openness to Feedback

Being open to feedback is like unlocking a secret level in a game. It helps you boost your problem-solving skills. Improving problem-solving skills through openness to feedback involves actively seeking and constructively responding to critiques.

This receptivity enables you to refine your strategies and approaches based on insights from others, leading to more effective solutions.

Learning New Approaches and Methodologies

Learning new approaches and methodologies is like adding new tools to your toolbox. It makes you a smarter problem-solver. Enhancing problem-solving skills by learning new approaches and methodologies involves staying updated with the latest trends and techniques in your field.

This continuous learning expands your toolkit, enabling innovative solutions and a fresh perspective on challenges.

Experimentation

Experimentation is like being a scientist of your own problems. It’s a powerful way to improve your problem-solving skills. Boosting problem-solving skills through experimentation means trying out different solutions to see what works best. This trial-and-error approach fosters creativity and can lead to unique solutions that wouldn’t have been considered otherwise.

Analyzing Competitors’ Success

Analyzing competitors’ success is like being a detective. It’s a smart way to boost your problem-solving skills. Improving problem-solving skills by analyzing competitors’ success involves studying their strategies and outcomes. Understanding what worked for them can provide valuable insights and inspire effective solutions for your own challenges.

Challenges in Problem-Solving

Facing obstacles when solving problems is common. Recognizing these barriers, like fear of failure or lack of information, helps us find ways around them for better solutions.

Fear of Failure

Fear of failure is like a big, scary monster that stops us from solving problems. It’s a challenge many face. Because being afraid of making mistakes can make us too scared to try new solutions.

How can we overcome this? First, understand that it’s okay to fail. Failure is not the opposite of success; it’s part of learning. Every time we fail, we discover one more way not to solve a problem, getting us closer to the right solution. Treat each attempt like an experiment. It’s not about failing; it’s about testing and learning.

Lack of Information

Lack of information is like trying to solve a puzzle with missing pieces. It’s a big challenge in problem-solving. Because without all the necessary details, finding a solution is much harder.

How can we fix this? Start by gathering as much information as you can. Ask questions, do research, or talk to experts. Think of yourself as a detective looking for clues. The more information you collect, the clearer the picture becomes. Then, use what you’ve learned to think of solutions.

Fixed Mindset

A fixed mindset is like being stuck in quicksand; it makes solving problems harder. It means thinking you can’t improve or learn new ways to solve issues.

How can we change this? First, believe that you can grow and learn from challenges. Think of your brain as a muscle that gets stronger every time you use it. When you face a problem, instead of saying “I can’t do this,” try thinking, “I can’t do this yet.” Look for lessons in every challenge and celebrate small wins.

Everyone starts somewhere, and mistakes are just steps on the path to getting better. By shifting to a growth mindset, you’ll see problems as opportunities to grow. Keep trying, keep learning, and your problem-solving skills will soar!

Jumping to Conclusions

Jumping to conclusions is like trying to finish a race before it starts. It’s a challenge in problem-solving. That means making a decision too quickly without looking at all the facts.

How can we avoid this? First, take a deep breath and slow down. Think about the problem like a puzzle. You need to see all the pieces before you know where they go. Ask questions, gather information, and consider different possibilities. Don’t choose the first solution that comes to mind. Instead, compare a few options.

Feeling Overwhelmed

Feeling overwhelmed is like being buried under a mountain of puzzles. It’s a big challenge in problem-solving. When we’re overwhelmed, everything seems too hard to handle.

How can we deal with this? Start by taking a step back. Breathe deeply and focus on one thing at a time. Break the big problem into smaller pieces, like sorting puzzle pieces by color. Tackle each small piece one by one. It’s also okay to ask for help. Sometimes, talking to someone else can give you a new perspective.

Confirmation Bias

Confirmation bias is like wearing glasses that only let you see what you want to see. It’s a challenge in problem-solving. Because it makes us focus only on information that agrees with what we already believe, ignoring anything that doesn’t.

How can we overcome this? First, be aware that you might be doing it. It’s like checking if your glasses are on right. Then, purposely look for information that challenges your views. It’s like trying on a different pair of glasses to see a new perspective. Ask questions and listen to answers, even if they don’t fit what you thought before.

Groupthink is like everyone in a group deciding to wear the same outfit without asking why. It’s a challenge in problem-solving. It means making decisions just because everyone else agrees, without really thinking it through.

How can we avoid this? First, encourage everyone in the group to share their ideas, even if they’re different. It’s like inviting everyone to show their unique style of clothes.

Listen to all opinions and discuss them. It’s okay to disagree; it helps us think of better solutions. Also, sometimes, ask someone outside the group for their thoughts. They might see something everyone in the group missed.

Overcoming obstacles in problem-solving requires patience, openness, and a willingness to learn from mistakes. By recognizing these barriers, we can develop strategies to navigate around them, leading to more effective and creative solutions.

What are the most common problem-solving techniques?

The most common techniques include brainstorming, the 5 Whys, mind mapping, SWOT analysis, and using algorithms or heuristics. Each approach has its strengths, suitable for different types of problems.

What’s the best problem-solving strategy for every situation?

There’s no one-size-fits-all strategy. The best approach depends on the problem’s complexity, available resources, and time constraints. Combining multiple techniques often yields the best results.

How can I improve my problem-solving skills?

Improve your problem-solving skills by practicing regularly, learning from experts, staying open to feedback, and continuously updating your knowledge on new approaches and methodologies.

Are there any tools or resources to help with problem-solving?

Yes, tools like mind mapping software, online courses on critical thinking, and books on problem-solving techniques can be very helpful. Joining forums or groups focused on problem-solving can also provide support and insights.

What are some common mistakes people make when solving problems?

Common mistakes include jumping to conclusions without fully understanding the problem, ignoring valuable feedback, sticking to familiar solutions without considering alternatives, and not breaking down complex problems into manageable parts.

Final Words

Mastering problem-solving strategies equips us with the tools to tackle challenges across all areas of life. By understanding and applying these techniques, embracing a growth mindset, and learning from both successes and obstacles, we can transform problems into opportunities for growth. Continuously improving these skills ensures we’re prepared to face and solve future challenges more effectively.

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Spencer Greenberg
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Problem-Solving Techniques That Work For All Types of Challenges

Essay by Spencer Greenberg, Clearer Thinking founder

A lot of people don’t realize that there are general purpose problem solving techniques that cut across domains. They can help you deal with thorny challenges in work, your personal life, startups, or even if you’re trying to prove a new theorem in math.

Below are the 26 general purpose problem solving techniques that I like best, along with a one-word name I picked for each, and hypothetical examples to illustrate what sort of strategy I’m referring to.

Consider opening up this list whenever you’re stuck solving a challenging problem. It’s likely that one or more of these techniques can help!

1. Clarifying

Try to define the problem you are facing as precisely as you can, maybe by writing down a detailed description of exactly what the problem is and what constraints exist for a solution, or by describing it in detail to another person. This may lead to you realizing the problem is not quite what you had thought, or that it has a more obvious solution than you thought.

Life Example

“I thought that I needed to find a new job, but when I thought really carefully about what I don’t like about my current job, I realized that I could likely fix those things by talking to my boss or even, potentially, just by thinking about them differently.”

Startup Example

“we thought we had a problem with users not wanting to sign up for the product, but when we carefully investigated what the problem really was, we discovered it was actually more of a problem of users wanting the product but then growing frustrated because of bad interface design.”

2. Subdividing

Break the problem down into smaller problems in such a way that if you solve each of the small problems, you will have solved the entire problem. Once a problem is subdivided it can also sometimes be parallelized (e.g., by involving different people to work on the different components).

“My goal is to get company Z to become a partner with my company, and that seems hard, so let me break that goal into the steps of (a) listing the ways that company Z would benefit from becoming a partner with us, (b) finding an employee at company Z who would be responsive to hearing about these benefits, and (c) tracking down someone who can introduce me to that employee.”

Math Example

“I want to prove that a certain property applies to all functions of a specific type, so I start by (a) showing that every function of that type can be written as a sum of a more specific type of function, then I show that (b) the property applies to each function of the more specific type, and finally I show that (c) if the property applies to each function in a set of functions then it applies to arbitrary sums of those functions as well.”

3. Simplifying

Think of the simplest variation of the problem that you expect you can solve that shares important features in common with your problem, and see if solving this simpler problem gives you ideas for how to solve the more difficult version.

“I don’t know how to hire a CTO, but I do know how to hire a software engineer because I’ve done it many times, and good CTOs will often themselves be good software engineers, so how can I tweak my software engineer hiring to make it appropriate for hiring a CTO?”

“I don’t know how to calculate this integral as it is, but if I remove one of the free parameters, I actually do know how to calculate it, and maybe doing that calculation will give me insight into the solution of the more complex integral.”

4. Crowd-sourcing

Use suggestions from multiple people to gain insight into how to solve the problem, for instance by posting on Facebook or Twitter requesting people’s help, or by posting to a Q&A site like Quora, or by sending emails to 10 people you know explaining the problem and requesting assistance.

Business Example

“Do you have experience outsourcing manufacturing to China? If so, I’d appreciate hearing your thoughts about how to approach choosing a vendor.”

Health Example

“I have trouble getting myself to stick to doing exercise daily. If you also used to have trouble getting yourself to exercise but don’t anymore, I’d love to know what worked to make it easier for you.”

5. Splintering

If the problem you are trying to solve has special cases that a solution to the general problem would also apply to, consider just one or two of these special cases as examples and solve the problem just for those cases first. Then see if a solution to one of those special cases helps you solve the problem in general.

“I want to figure out how to improve employee retention in general, let me examine how I could have improved retention in the case of the last three people that quit.”

“I want to figure out how to convince a large number of people to become customers, let me first figure out how to convince just Bill and John to become customers since they seem like the sort of customer I want to attract, and see what general lessons I learn from doing that.”

Read the books or textbooks that seem most related to the topic, and see whether they provide a solution to the problem, or teach you enough related information that you can now solve it yourself.

Economics Example

“Economists probably have already figured out reasonable ways to estimate demand elasticity, let’s see what an econometrics textbook says rather than trying to invent a technique from scratch.”

Mental Health Example

“I’ve been feeling depressed for a long time, maybe I should read some well-liked books about depression.”

7. Searching

Think of a similar problem that you think practitioners, bloggers or academics might have already solved and search online (e.g., via google, Q&A sites, or google scholar academic paper search) to see if anyone has done a write-up about how they solved it.

Advertising Example

“I’m having trouble figuring out the right advertising keywords to bid on for my specific product, I bet someone has a blog post describing how to approach choosing keywords for other related products.”

Machine Learning Example

“I can’t get this neural network to train properly in my specific case, I wonder if someone has written a tutorial about how to apply neural networks to related problems.”

8. Unconstraining

List all the constraints of the problem, then temporarily ignore one or more of the constraints that make the problem especially hard, and try to solve it without those constraints. If you can, then see if you can modify that unconstrained solution until it becomes a solution for the fully constrained problem.

“I need to hire someone who can do work at the intersection of machine learning and cryptography, let me drop the constraint of having cryptography experience and recruit machine learning people, then pick from among them a person that seems both generally capable and well positioned to learn the necessary cryptography.”

Computer Science Example

“I need to implement a certain algorithm, and it needs to be efficient, but that seems very difficult, so let me first figure out how to implement an inefficient version of the algorithm (i.e., drop the efficiency constraint), then at the end I will try to figure out how to optimize that algorithm for efficiency.”

9. Distracting

Fill your mind with everything you know about the problem, including facts, constraints, challenges, considerations, etc. and then stop thinking about the problem, and go and do a relaxing activity that requires little focus, such as walking, swimming, cooking, napping or taking a bath to see if new ideas or potential solutions pop into your mind unexpectedly as your subconscious continues to work on the problem without your attention.

“For three days, I’ve been trying to solve this problem at work, but the solution only came to me when I was strolling in the woods and not even thinking about it.”

Example from mathematician Henri Poincaré

“The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go someplace or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.”

10. Reexamining

Write down all the assumptions you’ve been making about the problem or about what a solution should I look like (yes – make an actual list). Then start challenging them one by one to see if they are actually needed or whether some may be unnecessary or mistaken.

Psychology Example

“We were assuming in our lab experiments that when people get angry they have some underlying reason behind it, but there may be some anger that is better modeled as a chemical fluctuation that is only loosely related to what happens in the lab, such as when people are quick to anger because they are hungry.”

“I need to construct a function that has this strange property, and so far I’ve assumed that the function must be smooth, but if it doesn’t actually need to be then perhaps I can construct just such a function out of simple linear pieces that are glued together.”

11. Reframing

Try to see the problem differently. For instance, by flipping the default, analyzing the inverse of the problem instead, thinking about how you would achieve the opposite of what you want, or shifting to an opposing perspective.

If we were building this company over again completely from scratch, what would we do differently in the design of our product, and can we pivot the product in that direction right now?”

“Should move to New York to take a job that pays $20,000 more per year? Well, if I already lived in New York, the decision to stay there rather than taking a $20,000 pay cut to move here would be an easy one. So maybe I’m overly focused on the current default of not being in New York and the short term unpleasantness of relocating.”

Marketing Example

“If I were one of our typical potential customers, what would I do to try to find a product like ours?”

12. Brainstorming

Set a timer for at least 5 minutes, and generate as many plausible solutions or ideas that you can without worrying about quality at all. Evaluate the ideas only at the end after the timer goes off.

“I’m going to set a timer for 5 minutes and come up with at least three new ways I could go about looking for a co-founder.”

“I’m going to set a timer for 20 minutes and come up with at least five possible explanations for why I’ve been feeling so anxious lately.”

13. Experting

Find an expert (or someone highly knowledgeable) in the topic area and ask their opinion about the best way to solve the problem.

“Why do you think most attempts at creating digital medical records failed, and what would someone have to do differently to have a reasonable chance at success?”

“What sort of optimization algorithm would be most efficient for minimizing the objective functions of this type?”

14. Eggheading

Ask the smartest person you know how they would solve the problem. Be sure to send an email in advance, describing the details so that this person has time to deeply consider the problem before you discuss it.

“Given the information I sent you about our competitors and the interviews we’ve done with potential customers, in which direction would you pivot our product if you were me (and why)?”

Research Example

“Given the information I sent you about our goals and the fact that our previous research attempts have gotten nowhere, how would you approach researching this topic to find the answer we need?”

15. Guessing

Start with a guess for what the solution could be, now check if it actually works and if not, start tweaking that guess to see if you can morph it into something that could work.

“I don’t know what price to use for the product we’re selling, so let me start with an initial guess and then begin trying to sell the thing, and tweak the price down if it seems to be a sticking point for customers, and tweak the price up if the customers don’t seem to pay much attention to the price.”

“My off the cuff intuition says that this differential equation might have a solution of the form x^a * e^(b x)for some a or b, let me plug it into the equation to see if indeed it satisfies the equation for any choice of a and b, and if not, let me see if I can tweak it to make something similar work.”

“I don’t know what the most effective diet for me would be, so I’ll just use my intuition to ban from my diet some foods that seem both unhealthy and addictive, and see if that helps.”

16. Comparing

Think of similar domains you already understand or similar problems you have already solved in the past, and see whether your knowledge of those domains or solutions to those similar problems may work as a complete or partial solution here.

“I don’t know how to find someone to fix things in my apartment, but I have found a good house cleaner before by asking a few friends who they use, so maybe I can simply use the same approach for finding a person to fix things.”

“This equation I’m trying to simplify reminds me of work I’m familiar with related to Kullback-Leibler divergence, I wonder if results from information theory could be applied in this case.”

17. Outsourcing

Consider whether you can hire someone to solve this problem, instead of figuring out how to solve it yourself.

“I don’t really understand how to get media attention for my company, so let me hire a public relations firm and let them handle the process.”

“I have no fashion sense, but I’d like to look better. Maybe I should hire someone fashionable who works in apparel to go shopping with me and help me choose what I should wear.”

18. Experimenting

Rapidly develop possible solutions and test them out (in sequence, or in parallel) by applying cheap and fast experiments. Discard those that don’t work, or iterate on them to improve them based on what you learn from the experiments.

“We don’t know if people will like a product like the one we have in mind, but we can put together a functioning prototype quickly, show five people that seem like they could be potential users, and iterate or create an entirely new design based on how they respond.”

“I don’t know if cutting out sugar will help improve my energy levels, but I can try it for two weeks and see if I notice any differences.”

19. Generalizing

Consider the more general case of the specific problem you are trying to solve, and then work on solving the general version instead. Paradoxically, it is sometimes easier to make progress on the general case rather than a specific one because it increases your focus on the structure of the problem rather than unimportant details.

“I want to figure out how to get this particular key employee more motivated to do good work, let me construct a model of what makes employees motivated to do good work in general, then I’ll apply it to this case.”

“I want to solve this specific differential equation, but it’s clearly a special case of a more general class of differential equations, let me study the general class and see what I can learn about them first and then apply what I learn to the specific case.”

20. Approximating

Consider whether a partial or approximate solution would be acceptable and, if so, aim for that instead of a full or exact solution.

“Our goal is to figure out which truck to send out for which delivery, which theoretically depends on many factors such as current location, traffic conditions, truck capacity, fuel efficiency, how many hours the driver has been on duty, the number of people manning each truck, the hourly rate we pay each driver, etc. etc. Maybe if we focus on just the three variables that we think are most important, we can find a good enough solution.”

“Finding a solution to this equation seems difficult, but if I approximate one of the terms linearly it becomes much easier, and maybe for the range of values we’re interested in, that’s close enough to an exact solution!”

21. Annihilating

Try to prove that the problem you are attempting to solve is actually impossible. If you succeed, you may save yourself a lot of time working on something impossible. Furthermore, in attempting to prove that the problem is impossible, you may gain insight into what makes it actually possible to solve, or if it turns out to truly be impossible, figure out how you could tweak the problem to make it solvable.

“I’m struggling to find a design for a theoretical voting system that has properties X, Y, and Z, let me see if I can instead prove that no such voting system with these three properties could possibly exist.”

“My goal has been to prove that this property always applies to this class of functions, let me see if I can generate a counterexample to prove that this goal is actually impossible.”

Physics Example

“I was trying to design a physical system with certain properties, but I now realize that if such a system could be realized, then it would allow for perpetual motion, and therefore it is impossible to build the sort of system I had in mind.”

22. Modeling

Try to build an explicit model of the situation, including what elements there are and how they related to each other. For instance, try drawing a diagram or flow chart that encapsulates your understanding of all the important information that relates to the problem.

“I’ve noticed that there are certain situations that cause me to freak out that would not bother other people. So what are the common elements when this happens, and how do they seem to relate to each other and to the way I end up feeling? Let me see if I can draw a diagram of this on paper.”

“What are all the different groups (e.g., providers, payers, patients) involved in the healthcare system, and if we diagram how they interact with each other, will that give us ideas for how we can sell our healthcare product?”

23. Brute forcing

One-by-one, consider every possible solution to the problem until you’ve found a good one or exhausted them all.

Startup example

“We’re not sure the order that these four parts of the user registration process should go in, so let’s make a list of all 24 possible orderings, and examine them one by one to see which makes the most sense.”

“It’s not clear how to pick which of these machine learning methods to use on this problem, but since we have lots of data, we can just try each of the algorithms and see which makes the most accurate predictions on data we’ve held to the side for testing.”

24. Refocusing

Forget about trying to solve the problem, and instead consider why you are trying to solve it. Then consider if there is a different problem you can work on that is aimed at producing the same sort of value in a different way.

Startup Example 1

“Maybe instead of trying increasingly hard to figure out how to get this type of consumer to buy, we need to switch our focus to the problem of how to sell to businesses, since what we actually care about is selling it, not selling it to one particular group.”

Startup Example 2

“I’ve been banging my head against the wall trying to implement this extremely complex feature, but there are lots of features that users would find just as valuable that are much easier to implement, maybe I should focus on those instead.”

25. Sidestepping

Consider whether you really want to spend more time trying to solve this problem and whether you can avoid the problem by instead working on totally different problems that you also care about.

“We’ve tried selling our solution to replace Excel for 12 months without much success, maybe we should go back to the drawing board and consider designing a totally new product. Our assumptions about customer needs seem to simply have been wrong.”

“I’ve spent six months on this math problem with little progress, but there are two other math problems I’m equally excited about, so maybe I should spend some time investigating whether one of those may be more tractable.”

26. Aggregating

Consider whether multiple problems you’re now experiencing might, in fact, be caused by the same source of difficulty, rather than being independent problems.

“I seem to be having conflict with a few different friends right now – could it be that I’m doing something without realizing it that is increasing my chance of conflict with all of them?”

“Three employees have quit in the last month. Perhaps the primary problem isn’t really about convincing this one important employee to stay, which is how I was framing it, but rather, about identifying why people keep leaving more generally.”

26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter.

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
Tailor your interview answer with the specific skills and qualifications outlined in the job description.
Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills?

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation.

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

Critical thinking
Analytical skills
Decision making
Research skills
Technical skills
Communication skills
Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow.

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve.

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams.

Examples of Problem-Solving in the Workplace

Correcting a mistake at work, whether it was made by you or someone else
Overcoming a delay at work through problem solving and communication
Resolving an issue with a difficult or upset customer
Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
Troubleshooting and resolving technical issues
Handling and resolving a conflict with a coworker
Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
Taking initiative when another team member overlooked or missed something important
Taking initiative to meet with your superior to discuss a problem before it became potentially worse
Solving a safety issue at work or reporting the issue to those who could solve it
Using problem solving abilities to reduce/eliminate a company expense
Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
Changing how a process, team, or task is organized to make it more efficient
Using creative thinking to come up with a solution that the company hasn’t used before
Performing research to collect data and information to find a new solution to a problem
Boosting a company or team’s performance by improving some aspect of communication among employees
Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

Coordinating work between team members in a class project
Reassigning a missing team member’s work to other group members in a class project
Adjusting your workflow on a project to accommodate a tight deadline
Speaking to your professor to get help when you were struggling or unsure about a project
Asking classmates, peers, or professors for help in an area of struggle
Talking to your academic advisor to brainstorm solutions to a problem you were facing
Researching solutions to an academic problem online, via Google or other methods
Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them.

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description.

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities.

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution.

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce.

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

3 Answers to “How Do You Handle Stress?”
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100 Problem and Solution Examples for a Smoother Life

Life is full of challenges, but with the right tips and tricks, solving problems can become much easier.

Here’s a big list of 100 problem and solution examples to show you that with a little bit of creativity, hard work, and smart thinking, you can figure out how to fix everyday issues.

From making your day-to-day tasks easier, keeping yourself healthy, to fixing things around the house, there’s an answer for almost everything here. Think of this list as your go-to guide for solving problems. It’s here to help you find ways to deal with your challenges in ways that work best for you.

See also: Into in Tagalog: Best translation of the English word ‘Into’ in Tagalog

100 Problem and Solution Examples

Problem: There’s a leak in the kitchen sink. Solution: Tighten the pipes or call a plumber to fix the leak.
Problem: My phone’s storage is full. Solution: Delete unnecessary files or transfer them to cloud storage.
Problem: I’m not getting enough exercise. Solution: Create a regular workout schedule or join a fitness class.
Problem: The garden is overrun with weeds. Solution: Dedicate time to weed regularly or hire a gardening service.
Problem: I’m struggling to understand a new topic in class. Solution: Seek extra help from the teacher, hire a tutor, or use online resources.
Problem: The house feels cluttered and disorganized. Solution: Implement a decluttering strategy and organize items using storage solutions.
Problem: Grocery bills are too high. Solution: Plan meals, buy in bulk, and look for discounts and coupons.
Problem: I keep forgetting important tasks. Solution: Use a planner or digital reminders to keep track of tasks.
Problem: There’s a constant argument over household chores. Solution: Create a chore schedule and divide tasks fairly among family members.
Problem: My computer is running slow. Solution: Clear cache, uninstall unnecessary programs, or upgrade hardware.
Problem: I’m feeling stressed and overwhelmed. Solution: Practice stress-relief techniques like meditation or seek professional help.
Problem: The room is too bright for sleeping. Solution: Install blackout curtains or use a sleep mask.
Problem: The Wi-Fi connection is weak in some parts of the house. Solution: Use a Wi-Fi extender or upgrade to a mesh network system.
Problem: I have a hard time waking up early. Solution: Set multiple alarms, adjust your sleep schedule gradually, or use a sunrise alarm clock.
Problem: The air in the room is dry. Solution: Use a humidifier to add moisture to the air.
Problem: I’m running out of ideas for meals. Solution: Use meal planning apps or websites for inspiration.
Problem: The paint on the walls is peeling. Solution: Repaint the walls or hire a professional to address the issue.
Problem: I’m spending too much time on social media. Solution: Use app blockers or set specific times for social media use.
Problem: My energy bills are too high. Solution: Implement energy-saving practices like using LED bulbs and reducing heating.
Problem: I can’t find my keys. Solution: Use a key finder gadget or establish a dedicated spot for keys.
Problem: I feel lonely working from home. Solution: Join online communities, schedule social activities, or work from co-working spaces.
Problem: There’s an unpleasant odor in the fridge. Solution: Clean the fridge thoroughly and use baking soda to absorb odors.
Problem: I need to improve my language skills for a job. Solution: Use language learning apps, take courses, or practice with native speakers.
Problem: The shower drain is clogged. Solution: Use a plunger or a chemical drain cleaner to clear the blockage.
Problem: I’m having difficulty managing my budget. Solution: Use budgeting apps or consult a financial advisor to create a budget plan.
Problem: I keep missing appointments. Solution: Use a digital calendar with alerts for appointments.
Problem: My clothes are fading after washing. Solution: Use cold water and gentle detergents or sort clothes by color.
Problem: The neighborhood is noisy at night. Solution: Use earplugs or soundproof windows to reduce noise.
Problem: I need to increase my reading speed. Solution: Practice speed reading techniques or use speed reading apps.
Problem: My laptop battery drains quickly. Solution: Adjust power settings for efficiency or replace the battery.
Problem: I have difficulty staying hydrated. Solution: Carry a water bottle or set reminders to drink water.
Problem: I’m not confident in public speaking. Solution: Join a public speaking club or take classes to improve skills.
Problem: The room feels stale and musty. Solution: Increase ventilation or use air purifiers and dehumidifiers.
Problem: I struggle with morning routine efficiency. Solution: Plan and prepare the night before and establish a consistent routine.
Problem: My bicycle tire is flat. Solution: Learn to patch or replace the tire or take it to a repair shop.
Problem: I’m experiencing burnout from work. Solution: Take time off, set boundaries for work, and engage in relaxing activities.
Problem: My plants keep dying. Solution: Research plant needs, adjust watering/light, or choose low-maintenance plants.
Problem: I’m anxious about an upcoming exam. Solution: Create a study plan, practice relaxation techniques, and seek support from peers.
Problem: It’s hard to find parking near work. Solution: Arrive earlier, use public transportation, or find a nearby parking garage.
Problem: I want to reduce my environmental impact. Solution: Adopt sustainable practices like recycling, using public transport, and reducing waste.
Problem: I have a toothache . Solution: Practice good oral hygiene and visit the dentist for a check-up.
Problem: I need to make a decision but feel indecisive. Solution: Create a pros and cons list or seek advice from trusted individuals.
Problem: The car won’t start in the morning. Solution: Check the battery and ignition system or call for roadside assistance.
Problem: My child is struggling with homework. Solution: Help them organize their work, provide assistance, or seek a tutor.
Problem: I want to learn a new skill but lack resources. Solution: Utilize free online courses or exchange skills with friends.
Problem: The coffee maker is not working. Solution: Troubleshoot common issues or consider a repair or replacement.
Problem: I need to improve my relationship with a colleague. Solution: Communicate openly, seek common ground, or involve a mediator if necessary.
Problem: My suitcase is over the weight limit for a flight. Solution: Repack to prioritize essentials or pay for additional baggage allowance.
Problem: I’m not meeting my fitness goals. Solution: Adjust goals to be more realistic, vary routines, or get a fitness buddy.
Problem: I feel disconnected from my community. Solution: Volunteer, join local clubs or groups, or attend community events.
Problem: My pet is shedding fur all over the house. Solution: Regular grooming, invest in a good vacuum cleaner, or consult a vet for advice.
Problem: I procrastinate on important tasks. Solution: Break tasks into smaller steps, use a timer, or eliminate distractions.
Problem: The basement is prone to flooding. Solution: Install a sump pump, improve drainage, or consult with waterproofing experts.
Problem: I’m not getting along with my roommate. Solution: Set clear house rules, communicate openly, or consider mediation.
Problem: My computer keeps overheating. Solution: Clean out dust from the vents, use a cooling pad, or check for software issues.
Problem: I struggle with learning a new language. Solution: Immerse yourself in the language, practice daily, or use language exchange partners.
Problem: My energy levels dip in the afternoon. Solution: Eat a balanced diet, maintain a regular sleep schedule, or take short breaks.
Problem: I have a hard time saving money. Solution: Set automatic transfers to savings, track spending, or set financial goals.
Problem: The wallpaper is peeling off the walls. Solution: Reapply or replace wallpaper, or switch to paint for a more durable solution.
Problem: I need to find a new job but feel overwhelmed. Solution: Update your resume, use job search platforms, or network in your industry.
Problem: The air quality in my city is poor. Solution: Use air purifiers at home, wear masks outdoors, or advocate for environmental policies.
Problem: I feel isolated working remotely. Solution: Schedule regular check-ins with colleagues, or join virtual coworking spaces.
Problem: My child is being bullied at school. Solution: Talk to the school authorities, provide emotional support, or involve a counselor.
Problem: I have difficulty remembering passwords. Solution: Use a password manager or develop a system for creating and remembering passwords.
Problem: The hot water runs out too quickly. Solution: Install a more efficient water heater or limit shower times.
Problem: I’m struggling to stay motivated to exercise. Solution: Set achievable goals, find a workout buddy, or try new activities.
Problem: My email inbox is overwhelming. Solution: Unsubscribe from unnecessary lists, use email sorting rules, or set aside time for email management.
Problem: I can’t concentrate on work from home. Solution: Designate a specific workspace, establish a routine, or use noise-cancelling headphones.
Problem: My credit card debt is too high. Solution: Create a payment plan, consider consolidating debt, or seek financial counseling.
Problem: I’m experiencing writer’s block. Solution: Take a break, seek inspiration from other works, or try free writing exercises.
Problem: My smartphone battery dies quickly. Solution: Adjust screen brightness, close unused apps, or replace the battery.
Problem: I feel bored with my daily routine. Solution: Introduce new hobbies, change your routine, or plan something to look forward to.
Problem: The kitchen is always messy. Solution: Implement a cleaning schedule, organize kitchen tools, or declutter countertops.
Problem: I’m worried about retirement savings. Solution: Start or increase contributions to a retirement account, or consult a financial planner.
Problem: I get anxious before public speaking. Solution: Practice regularly, visualize success, or attend a public speaking workshop.
Problem: My digital files are disorganized. Solution: Create a file organization system, regularly clean up files, or use cloud storage efficiently.
Problem: I struggle to keep plants alive. Solution: Choose low-maintenance plants, research plant care, or use plant care apps.
Problem: My child resists bedtime. Solution: Establish a bedtime routine, ensure a comfortable sleep environment, or limit screen time before bed.
Problem: I have a long commute to work. Solution: Listen to audiobooks/podcasts, consider telecommuting, or explore alternate routes.
Problem: My home has poor natural lighting. Solution: Use mirrors to reflect light, choose light wall colors, or install additional lighting.
Problem: I feel unproductive working from home. Solution: Set daily goals, eliminate distractions, or schedule work during peak productivity times.
Problem: My social media posts aren’t engaging. Solution: Research your audience, improve content quality, or use analytics for insights.
Problem: I struggle with acne. Solution: Follow a skincare routine, consult a dermatologist, or make dietary changes.
Problem: I need to improve my time management. Solution: Use time management tools, prioritize tasks, or learn to say no to non-essential tasks.
Problem: I’m having trouble sleeping. Solution: Establish a sleep schedule, create a relaxing bedtime routine, or avoid caffeine before bed.
Problem: The paint color in the living room feels outdated. Solution: Repaint with a modern, uplifting color or use decorative accents to refresh the space.
Problem: My car is consuming too much fuel. Solution: Regular maintenance checks, drive more efficiently, or consider a more fuel-efficient vehicle.
Problem: I find it hard to stay informed with current events. Solution: Subscribe to a news summary service, listen to news podcasts, or set aside time daily for news.
Problem: I’m not satisfied with my current career path. Solution: Explore new industries, consider additional training, or consult a career coach.
Problem: I struggle with managing my emails. Solution: Use email management tools, allocate specific times for email, or automate responses.
Problem: I want to make new friends but don’t know how. Solution: Join clubs or groups with similar interests, attend social events, or use social apps.
Problem: My shoes are uncomfortable for long walks. Solution: Invest in quality, supportive shoes or use orthotic insoles for additional support.
Problem: I’m not drinking enough water throughout the day. Solution: Carry a reusable water bottle, set reminders, or flavor your water for variety.
Problem: I need to reduce screen time before bed. Solution: Establish a no-screens rule an hour before bed, read, or do relaxation exercises instead.
Problem: I have a small closet and too many clothes. Solution: Declutter clothes, use space-saving organizers, or rotate clothes seasonally.
Problem: I want to eat healthier but lack cooking skills. Solution: Start with simple recipes, watch cooking tutorials, or attend a cooking class.
Problem: My home office is uncomfortable. Solution: Invest in ergonomic furniture, ensure proper lighting, or personalize your space.
Problem: I’m nervous about moving to a new city. Solution: Research the city, connect with local communities online, or visit before moving.
Problem: I have difficulty focusing on reading. Solution: Create a quiet, comfortable reading space, set reading goals, or use focus apps.
Problem: I want to reduce my carbon footprint. Solution: Use public transport, reduce energy consumption, or adopt a plant-based diet.

These are the 100 problem and solution examples that can help you solve many common problems in everyday life. Whether it’s something personal, about work, or issues at home, this list gives you simple and doable ways to make things better.

By using these tips, you can handle problems more easily, feel less stressed, and get through your day smoother. Remember, solving problems is about finding out what’s wrong, thinking of ways to fix it, and then doing something about it. With these examples, you now have a bunch of ideas on how to deal with different challenges, making life a bit easier and more enjoyable.

How to Write a Problem Solution Paper

Last Updated: July 22, 2023 Fact Checked

This article was co-authored by Stephanie Wong Ken, MFA . Stephanie Wong Ken is a writer based in Canada. Stephanie's writing has appeared in Joyland, Catapult, Pithead Chapel, Cosmonaut's Avenue, and other publications. She holds an MFA in Fiction and Creative Writing from Portland State University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 147,156 times.

A problem solution paper focuses on a particular problem or set of problems. As the essay writer, you will then need to come up with a solution or several solutions to the stated problem. Problem solution papers are common on exams, as they allow you to explore an issue and use critical thinking to respond with a solution. To write a problem solution paper, start by outlining the paper. Then, follow the structure of a problem solution paper and polish the paper so it is at its best when you turn it in.

Starting the Paper

For example, you may have a main situation like, “obesity and poor fitness,” or “trigger warnings on college campuses.”
If you get to choose the situation, make a list of groups you belong to, such as “school,” “family,” “race,” “culture”,” or “local community.” Then, identify a situation or issue you have encountered as a member of one of these groups.

Step 2 Determine the key components of the paper.

In the situation component, you will paraphrase the prompt of the paper in your own words.
In the problem component, you will state the problem or problems and explain what they are in your own words.
In the solution component, you will state your solution or solutions to the problem. You will also explain how it will address the problem.
In the evaluation component, you will list the main ideas in the paper and offer a prediction or recommendation based on your solution to the problem.
There will only be one situation presented to you in the prompt for the paper. You can then have multiple problems and multiple solutions that link back to the situation.

Step 3 Use the block structure for the outline.

Introduction section, where you discuss the situation
Transition sentence or paragraph
Conclusion section, where you discuss the evaluation

Step 4 Try the chain structure for the outline.

Problem 1 and Solution to Problem 1
Problem 2 and Solution to Problem 2
Problem 3 and Solution to Problem 3

Writing the Paper

Step 1 State the situation in your own words.

For example, if the situation in the paper prompt is “obesity and poor fitness,” you may focus on specific aspects of the situation in the introduction. You may look at how the consumption of unhealthy food and the overuse of cars plays into obesity and poor fitness in society.

Step 2 Research the problem or problems.

If you cannot find a lot of outside material on the problem, you can collect your own data for the paper. Do this by making a survey that you give to people who are affected by the problem. You can also interview people associated with the problem, or with possible solutions.
For example, if you were researching the problem “trigger warnings on college campuses,” you may interview college representatives at your university or college. You may also talk to students on campus.
Most problem solution papers written for exams do not require you to cite any outside sources. You may need to cite your sources if you are writing the problem solution paper for a class.

For example, if you were writing about the situation “obesity and poor fitness,” you may have the following thesis statement: “Obesity and poor fitness can lead to a decrease in life expectancy, and it is essential that individuals and governments work together to tackle this issue by improving their citizen's diet and fitness.”

For example, you may come up with a solution that addresses a lack of resources by adding support, money, or more staff. Or you may come up with a solution that addresses the problem by changing an existing practice or habit.

Step 5 Support your solutions with specific examples.

For example, if one of your solutions to the problem of obesity and poor fitness is to encourage people to cook at home, you may list a few specific ways people can do this. You may suggest that national eating healthy at home campaign is created, offering recipes online that take less than 30 minutes to prepare at home.

Step 6 Wrap up the paper with an evaluation.

For example, you may end up a call to action like, “With rising levels of obesity in our country, it is essential that we take action now to address this serious issue.”

Polishing the Paper

Step 1 Confirm the paper follows a clear structure or outline.

You can create a reverse outline using your paper as a guide, where you go through each section and confirm it follows the outline you started with.

Step 2 Check for spelling, grammar, and punctuation.

You can also show the paper to a peer, friend, or family member and get them to proofread it for you.

Step 3 Revise the paper to fit the word count.

If you are writing the problem solution paper for a class assignment, you may still have a set word count. Check that your paper falls within this word count.
↑ https://www.jccc.edu/student-resources/academic-resource-center/writing-center/files/problem-solution-paper.pdf
↑ http://www.eapfoundation.com/writing/essays/problemsolution/
↑ https://grammar.yourdictionary.com/grammar/writing/how-to-write-a-problem-solution-essay.html
↑ https://www.shsu.edu/centers/academic-success-center/writing/handouts/modes/essays/9.-.Problem.Solution.Essay.pdf
↑ https://clt.library.jwu.edu/c.php?g=1028305&p=7459493
↑ https://clt.library.jwu.edu/c.php?g=1028305&p=7459493#s-lg-box-wrapper-27749528

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About This Article

A problem solution paper focuses on a particular issue and should include one or more solutions to it. You’ll need to begin the paper by stating the situation in your own words. For example, the situation could be “obesity and core fitness.” Include a thesis statement at the end of your introduction, which could be something like, “Obesity can lead to decreased life expectancy, making it imperative for governments and people to tackle this issue by improving diet and fitness.” The following sections should deal with identifying all of the problems arising from the situation and proposing solutions to them. Try to give examples to explain each solution. For instance, if you say the growth of obesity can be stopped by improving people’s diets, you could propose a national healthy eating campaign. Finally, you should conclude by evaluating the whole paper and making recommendations about how to implement your solutions. For tips from our Writing co-author on how to plan an outline for your problem solving paper, read on! Did this summary help you? Yes No

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39 Best Problem-Solving Examples

problem-solving examples and definition, explained below

Problem-solving is a process where you’re tasked with identifying an issue and coming up with the most practical and effective solution.

This indispensable skill is necessary in several aspects of life, from personal relationships to education to business decisions.

Problem-solving aptitude boosts rational thinking, creativity, and the ability to cooperate with others. It’s also considered essential in 21st Century workplaces.

If explaining your problem-solving skills in an interview, remember that the employer is trying to determine your ability to handle difficulties. Focus on explaining exactly how you solve problems, including by introducing your thoughts on some of the following frameworks and how you’ve applied them in the past.

Problem-Solving Examples

1. divergent thinking.

Divergent thinking refers to the process of coming up with multiple different answers to a single problem. It’s the opposite of convergent thinking, which would involve coming up with a singular answer .

The benefit of a divergent thinking approach is that it can help us achieve blue skies thinking – it lets us generate several possible solutions that we can then critique and analyze .

In the realm of problem-solving, divergent thinking acts as the initial spark. You’re working to create an array of potential solutions, even those that seem outwardly unrelated or unconventional, to get your brain turning and unlock out-of-the-box ideas.

This process paves the way for the decision-making stage, where the most promising ideas are selected and refined.

Go Deeper: Divervent Thinking Examples

2. Convergent Thinking

Next comes convergent thinking, the process of narrowing down multiple possibilities to arrive at a single solution.

This involves using your analytical skills to identify the best, most practical, or most economical solution from the pool of ideas that you generated in the divergent thinking stage.

In a way, convergent thinking shapes the “roadmap” to solve a problem after divergent thinking has supplied the “destinations.”

Have a think about which of these problem-solving skills you’re more adept at: divergent or convergent thinking?

Go Deeper: Convergent Thinking Examples

3. Brainstorming

Brainstorming is a group activity designed to generate a multitude of ideas regarding a specific problem. It’s divergent thinking as a group , which helps unlock even more possibilities.

A typical brainstorming session involves uninhibited and spontaneous ideation, encouraging participants to voice any possible solutions, no matter how unconventional they might appear.

It’s important in a brainstorming session to suspend judgment and be as inclusive as possible, allowing all participants to get involved.

By widening the scope of potential solutions, brainstorming allows better problem definition, more creative solutions, and helps to avoid thinking “traps” that might limit your perspective.

Go Deeper: Brainstorming Examples

4. Thinking Outside the Box

The concept of “thinking outside the box” encourages a shift in perspective, urging you to approach problems from an entirely new angle.

Rather than sticking to traditional methods and processes, it involves breaking away from conventional norms to cultivate unique solutions.

In problem-solving, this mindset can bypass established hurdles and bring you to fresh ideas that might otherwise remain undiscovered.

Think of it as going off the beaten track when regular routes present roadblocks to effective resolution.

5. Case Study Analysis

Analyzing case studies involves a detailed examination of real-life situations that bear relevance to the current problem at hand.

For example, if you’re facing a problem, you could go to another environment that has faced a similar problem and examine how they solved it. You’d then bring the insights from that case study back to your own problem.

This approach provides a practical backdrop against which theories and assumptions can be tested, offering valuable insights into how similar problems have been approached and resolved in the past.

See a Broader Range of Analysis Examples Here

6. Action Research

Action research involves a repetitive process of identifying a problem, formulating a plan to address it, implementing the plan, and then analyzing the results. It’s common in educational research contexts.

The objective is to promote continuous learning and improvement through reflection and action. You conduct research into your problem, attempt to apply a solution, then assess how well the solution worked. This becomes an iterative process of continual improvement over time.

For problem-solving, this method offers a way to test solutions in real-time and allows for changes and refinements along the way, based on feedback or observed outcomes. It’s a form of active problem-solving that integrates lessons learned into the next cycle of action.

Go Deeper: Action Research Examples

7. Information Gathering

Fundamental to solving any problem is the process of information gathering.

This involves collecting relevant data , facts, and details about the issue at hand, significantly aiding in the understanding and conceptualization of the problem.

In problem-solving, information gathering underpins every decision you make.

This process ensures your actions are based on concrete information and evidence, allowing for an informed approach to tackle the problem effectively.

8. Seeking Advice

Seeking advice implies turning to knowledgeable and experienced individuals or entities to gain insights on problem-solving.

It could include mentors, industry experts, peers, or even specialized literature.

The value in this process lies in leveraging different perspectives and proven strategies when dealing with a problem. Moreover, it aids you in avoiding pitfalls, saving time, and learning from others’ experiences.

9. Creative Thinking

Creative thinking refers to the ability to perceive a problem in a new way, identify unconventional patterns, or produce original solutions.

It encourages innovation and uniqueness, often leading to the most effective results.

When applied to problem-solving, creative thinking can help you break free from traditional constraints, ideal for potentially complex or unusual problems.

Go Deeper: Creative Thinking Examples

10. Conflict Resolution

Conflict resolution is a strategy developed to resolve disagreements and arguments, often involving communication, negotiation, and compromise.

When employed as a problem-solving technique, it can diffuse tension, clear bottlenecks, and create a collaborative environment.

Effective conflict resolution ensures that differing views or disagreements do not become roadblocks in the process of problem-solving.

Go Deeper: Conflict Resolution Examples

11. Addressing Bottlenecks

Bottlenecks refer to obstacles or hindrances that slow down or even halt a process.

In problem-solving, addressing bottlenecks involves identifying these impediments and finding ways to eliminate them.

This effort not only smooths the path to resolution but also enhances the overall efficiency of the problem-solving process.

For example, if your workflow is not working well, you’d go to the bottleneck – that one point that is most time consuming – and focus on that. Once you ‘break’ this bottleneck, the entire process will run more smoothly.

12. Market Research

Market research involves gathering and analyzing information about target markets, consumers, and competitors.

In sales and marketing, this is one of the most effective problem-solving methods. The research collected from your market (e.g. from consumer surveys) generates data that can help identify market trends, customer preferences, and competitor strategies.

In this sense, it allows a company to make informed decisions, solve existing problems, and even predict and prevent future ones.

13. Root Cause Analysis

Root cause analysis is a method used to identify the origin or the fundamental reason for a problem.

Once the root cause is determined, you can implement corrective actions to prevent the problem from recurring.

As a problem-solving procedure, root cause analysis helps you to tackle the problem at its source, rather than dealing with its surface symptoms.

Go Deeper: Root Cause Analysis Examples

14. Mind Mapping

Mind mapping is a visual tool used to structure information, helping you better analyze, comprehend and generate new ideas.

By laying out your thoughts visually, it can lead you to solutions that might not have been apparent with linear thinking.

In problem-solving, mind mapping helps in organizing ideas and identifying connections between them, providing a holistic view of the situation and potential solutions.

15. Trial and Error

The trial and error method involves attempting various solutions until you find one that resolves the problem.

It’s an empirical technique that relies on practical actions instead of theories or rules.

In the context of problem-solving, trial and error allows you the flexibility to test different strategies in real situations, gaining insights about what works and what doesn’t.

16. SWOT Analysis

SWOT is an acronym standing for Strengths, Weaknesses, Opportunities, and Threats.

It’s an analytic framework used to evaluate these aspects in relation to a particular objective or problem.

In problem-solving, SWOT Analysis helps you to identify favorable and unfavorable internal and external factors. It helps to craft strategies that make best use of your strengths and opportunities, whilst addressing weaknesses and threats.

Go Deeper: SWOT Analysis Examples

17. Scenario Planning

Scenario planning is a strategic planning method used to make flexible long-term plans.

It involves imagining, and then planning for, multiple likely future scenarios.

By forecasting various directions a problem could take, scenario planning helps manage uncertainty and is an effective tool for problem-solving in volatile conditions.

18. Six Thinking Hats

The Six Thinking Hats is a concept devised by Edward de Bono that proposes six different directions or modes of thinking, symbolized by six different hat colors.

Each hat signifies a different perspective, encouraging you to switch ‘thinking modes’ as you switch hats. This method can help remove bias and broaden perspectives when dealing with a problem.

19. Decision Matrix Analysis

Decision Matrix Analysis is a technique that allows you to weigh different factors when faced with several possible solutions.

After listing down the options and determining the factors of importance, each option is scored based on each factor.

Revealing a clear winner that both serves your objectives and reflects your values, Decision Matrix Analysis grounds your problem-solving process in objectivity and comprehensiveness.

20. Pareto Analysis

Also known as the 80/20 rule, Pareto Analysis is a decision-making technique.

It’s based on the principle that 80% of problems are typically caused by 20% of the causes, making it a handy tool for identifying the most significant issues in a situation.

Using this analysis, you’re likely to direct your problem-solving efforts more effectively, tackling the root causes producing most of the problem’s impact.

21. Critical Thinking

Critical thinking refers to the ability to analyze facts to form a judgment objectively.

It involves logical, disciplined thinking that is clear, rational, open-minded, and informed by evidence.

For problem-solving, critical thinking helps evaluate options and decide the most effective solution. It ensures your decisions are grounded in reason and facts, and not biased or irrational assumptions.

Go Deeper: Critical Thinking Examples

22. Hypothesis Testing

Hypothesis testing usually involves formulating a claim, testing it against actual data, and deciding whether to accept or reject the claim based on the results.

In problem-solving, hypotheses often represent potential solutions. Hypothesis testing provides verification, giving a statistical basis for decision-making and problem resolution.

Usually, this will require research methods and a scientific approach to see whether the hypothesis stands up or not.

Go Deeper: Types of Hypothesis Testing

23. Cost-Benefit Analysis

A cost-benefit analysis (CBA) is a systematic process of weighing the pros and cons of different solutions in terms of their potential costs and benefits.

It allows you to measure the positive effects against the negatives and informs your problem-solving strategy.

By using CBA, you can identify which solution offers the greatest benefit for the least cost, significantly improving efficacy and efficiency in your problem-solving process.

Go Deeper: Cost-Benefit Analysis Examples

24. Simulation and Modeling

Simulations and models allow you to create a simplified replica of real-world systems to test outcomes under controlled conditions.

In problem-solving, you can broadly understand potential repercussions of different solutions before implementation.

It offers a cost-effective way to predict the impacts of your decisions, minimizing potential risks associated with various solutions.

25. Delphi Method

The Delphi Method is a structured communication technique used to gather expert opinions.

The method involves a group of experts who respond to questionnaires about a problem. The responses are aggregated and shared with the group, and the process repeats until a consensus is reached.

This method of problem solving can provide a diverse range of insights and solutions, shaped by the wisdom of a collective expert group.

26. Cross-functional Team Collaboration

Cross-functional team collaboration involves individuals from different departments or areas of expertise coming together to solve a common problem or achieve a shared goal.

When you bring diverse skills, knowledge, and perspectives to a problem, it can lead to a more comprehensive and innovative solution.

In problem-solving, this promotes communal thinking and ensures that solutions are inclusive and holistic, with various aspects of the problem being addressed.

27. Benchmarking

Benchmarking involves comparing one’s business processes and performance metrics to the best practices from other companies or industries.

In problem-solving, it allows you to identify gaps in your own processes, determine how others have solved similar problems, and apply those solutions that have proven to be successful.

It also allows you to compare yourself to the best (the benchmark) and assess where you’re not as good.

28. Pros-Cons Lists

A pro-con analysis aids in problem-solving by weighing the advantages (pros) and disadvantages (cons) of various possible solutions.

This simple but powerful tool helps in making a balanced, informed decision.

When confronted with a problem, a pro-con analysis can guide you through the decision-making process, ensuring all possible outcomes and implications are scrutinized before arriving at the optimal solution. Thus, it helps to make the problem-solving process both methodical and comprehensive.

29. 5 Whys Analysis

The 5 Whys Analysis involves repeatedly asking the question ‘why’ (around five times) to peel away the layers of an issue and discover the root cause of a problem.

As a problem-solving technique, it enables you to delve into details that you might otherwise overlook and offers a simple, yet powerful, approach to uncover the origin of a problem.

For example, if your task is to find out why a product isn’t selling your first answer might be: “because customers don’t want it”, then you ask why again – “they don’t want it because it doesn’t solve their problem”, then why again – “because the product is missing a certain feature” … and so on, until you get to the root “why”.

30. Gap Analysis

Gap analysis entails comparing current performance with potential or desired performance.

You’re identifying the ‘gaps’, or the differences, between where you are and where you want to be.

In terms of problem-solving, a Gap Analysis can help identify key areas for improvement and design a roadmap of how to get from the current state to the desired one.

31. Design Thinking

Design thinking is a problem-solving approach that involves empathy, experimentation, and iteration.

The process focuses on understanding user needs, challenging assumptions , and redefining problems from a user-centric perspective.

In problem-solving, design thinking uncovers innovative solutions that may not have been initially apparent and ensures the solution is tailored to the needs of those affected by the issue.

32. Analogical Thinking

Analogical thinking involves the transfer of information from a particular subject (the analogue or source) to another particular subject (the target).

In problem-solving, you’re drawing parallels between similar situations and applying the problem-solving techniques used in one situation to the other.

Thus, it allows you to apply proven strategies to new, but related problems.

33. Lateral Thinking

Lateral thinking requires looking at a situation or problem from a unique, sometimes abstract, often non-sequential viewpoint.

Unlike traditional logical thinking methods, lateral thinking encourages you to employ creative and out-of-the-box techniques.

In solving problems, this type of thinking boosts ingenuity and drives innovation, often leading to novel and effective solutions.

Go Deeper: Lateral Thinking Examples

34. Flowcharting

Flowcharting is the process of visually mapping a process or procedure.

This form of diagram can show every step of a system, process, or workflow, enabling an easy tracking of the progress.

As a problem-solving tool, flowcharts help identify bottlenecks or inefficiencies in a process, guiding improved strategies and providing clarity on task ownership and process outcomes.

35. Multivoting

Multivoting, or N/3 voting, is a method where participants reduce a large list of ideas to a prioritized shortlist by casting multiple votes.

This voting system elevates the most preferred options for further consideration and decision-making.

As a problem-solving technique, multivoting allows a group to narrow options and focus on the most promising solutions, ensuring more effective and democratic decision-making.

36. Force Field Analysis

Force Field Analysis is a decision-making technique that identifies the forces for and against change when contemplating a decision.

The ‘forces’ represent the differing factors that can drive or hinder change.

In problem-solving, Force Field Analysis allows you to understand the entirety of the context, favoring a balanced view over a one-sided perspective. A comprehensive view of all the forces at play can lead to better-informed problem-solving decisions.

TRIZ, which stands for “The Theory of Inventive Problem Solving,” is a problem-solving, analysis, and forecasting methodology.

It focuses on finding contradictions inherent in a scenario. Then, you work toward eliminating the contraditions through finding innovative solutions.

So, when you’re tackling a problem, TRIZ provides a disciplined, systematic approach that aims for ideal solutions and not just acceptable ones. Using TRIZ, you can leverage patterns of problem-solving that have proven effective in different cases, pivoting them to solve the problem at hand.

38. A3 Problem Solving

A3 Problem Solving, derived from Lean Management, is a structured method that uses a single sheet of A3-sized paper to document knowledge from a problem-solving process.

Named after the international paper size standard of A3 (or 11-inch by 17-inch paper), it succinctly records all key details of the problem-solving process from problem description to the root cause and corrective actions.

Used in problem-solving, this provides a straightforward and logical structure for addressing the problem, facilitating communication between team members, ensuring all critical details are included, and providing a record of decisions made.

39. Scenario Analysis

Scenario Analysis is all about predicting different possible future events depending upon your decision.

To do this, you look at each course of action and try to identify the most likely outcomes or scenarios down the track if you take that course of action.

This technique helps forecast the impacts of various strategies, playing each out to their (logical or potential) end. It’s a good strategy for project managers who need to keep a firm eye on the horizon at all times.

When solving problems, Scenario Analysis assists in preparing for uncertainties, making sure your solution remains viable, regardless of changes in circumstances.

How to Answer “Demonstrate Problem-Solving Skills” in an Interview

When asked to demonstrate your problem-solving skills in an interview, the STAR method often proves useful. STAR stands for Situation, Task, Action, and Result.

Situation: Begin by describing a specific circumstance or challenge you encountered. Make sure to provide enough detail to allow the interviewer a clear understanding. You should select an event that adequately showcases your problem-solving abilities.

For instance, “In my previous role as a project manager, we faced a significant issue when our key supplier abruptly went out of business.”

Task: Explain what your responsibilities were in that situation. This serves to provide context, allowing the interviewer to understand your role and the expectations placed upon you.

For instance, “It was my task to ensure the project remained on track despite this setback. Alternative suppliers needed to be found without sacrificing quality or significantly increasing costs.”

Action: Describe the steps you took to manage the problem. Highlight your problem-solving process. Mention any creative approaches or techniques that you used.

For instance, “I conducted thorough research to identify potential new suppliers. After creating a shortlist, I initiated contact, negotiated terms, assessed samples for quality and made a selection. I also worked closely with the team to re-adjust the project timeline.”

Result: Share the outcomes of your actions. How did the situation end? Did your actions lead to success? It’s particularly effective if you can quantify these results.

For instance, “As a result of my active problem solving, we were able to secure a new supplier whose costs were actually 10% cheaper and whose quality was comparable. We adjusted the project plan and managed to complete the project just two weeks later than originally planned, despite the major vendor setback.”

Remember, when you’re explaining your problem-solving skills to an interviewer, what they’re really interested in is your approach to handling difficulties, your creativity and persistence in seeking a resolution, and your ability to carry your solution through to fruition. Tailoring your story to highlight these aspects will help exemplify your problem-solving prowess.

Go Deeper: STAR Interview Method Examples

Benefits of Problem-Solving

Problem-solving is beneficial for the following reasons (among others):

It can help you to overcome challenges, roadblocks, and bottlenecks in your life.
It can save a company money.
It can help you to achieve clarity in your thinking.
It can make procedures more efficient and save time.
It can strengthen your decision-making capacities.
It can lead to better risk management.

Whether for a job interview or school, problem-solving helps you to become a better thinking, solve your problems more effectively, and achieve your goals. Build up your problem-solving frameworks (I presented over 40 in this piece for you!) and work on applying them in real-life situations.

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Animism Examples
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 10 Magical Thinking Examples
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ Social-Emotional Learning (Definition, Examples, Pros & Cons)
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ What is Educational Psychology?

From Dilemmas to Solutions: Problem-Solving Examples to Learn From

By Daria Burnett
May 21, 2023

Introduction to Problem-Solving

Life is full of challenges and dilemmas, both big and small.

But if there’s one skill that can help you navigate these, it’s problem-solving .

So, what exactly is problem-solving? And why is it such a crucial skill in daily life?

Understanding the Concept of Problem-Solving

Problem-solving is a mental process that involves identifying, analyzing, and resolving challenges or difficulties.

It’s like a journey that starts with a problem and ends with a solution.

It’s a skill that’s not just used in the field of psychology but in all aspects of life.

Whether you’re trying to decide on the best route to work, dealing with a disagreement with a friend, or figuring out how to fix a leaky faucet, you’re using your problem-solving skills.

When you’re faced with a problem, your brain goes through a series of steps to find a solution.

This process can be conscious or unconscious and can involve logical thinking, creativity, and prior knowledge.

Effective problem-solving can lead to better decisions and outcomes, making it a valuable tool in your personal and professional life.

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Importance of Problem-Solving in Daily Life

Why is problem-solving so important in daily life? Well, it’s simple.

Problems are a part of life.

They arise in different shapes and sizes, and in different areas of life, including work, relationships, health, and personal growth.

Having strong problem-solving skills can help you navigate these challenges effectively and efficiently.

In your personal life, problem-solving can help you manage stress and conflict, make better decisions, and achieve your goals.

In the workplace, it can help you navigate complex projects, improve processes, and foster innovation.

Problem-solving is also a key skill in many professions and industries, from engineering and science to healthcare and customer service.

Moreover, problem-solving can contribute to your overall mental well-being.

It can give you a sense of control and agency, reduce feelings of stress and anxiety, and foster a positive attitude.

It’s also a key component of resilience, the ability to bounce back from adversity.

In conclusion, problem-solving is a fundamental skill in life.

It’s a tool you can use to tackle challenges, make informed decisions, and drive change.

By understanding the concept of problem-solving and recognizing its importance in daily life, you’re taking the first step toward becoming a more effective problem solver.

As we delve deeper into this topic, you’ll discover practical problem-solving examples, learn about different problem-solving techniques, and gain insights on how to improve your own problem-solving skills.

So, stay tuned and continue your exploration of introduction to psychology with us.

Stages of Problem-Solving

The process of problem-solving can be broken down into three key stages: identifying the problem , developing possible solutions , and implementing the best solution .

Each stage requires a different set of skills and strategies.

By understanding these stages, you can enhance your problem-solving abilities and tackle various challenges more effectively.

Identifying the Problem

The first step in problem-solving is recognizing that a problem exists.

This involves defining the issue clearly and understanding its root cause.

You might need to gather information, ask questions, and analyze the situation from multiple perspectives.

It can be helpful to write down the problem and think about how it impacts you or others involved.

For instance, if you’re struggling with time management, the problem might be that you have too many obligations and not enough time.

Or perhaps your methods of organizing your tasks aren’t effective.

It’s important to be as specific as possible when identifying the problem, as this will guide the rest of the problem-solving process.

Developing Possible Solutions

Once you’ve identified the problem, the next step is to brainstorm possible solutions.

This is where creativity comes into play.

Don’t limit yourself; even ideas that seem unrealistic or out of the box can lead to effective solutions.

Consider different strategies and approaches.

You could try using techniques like mind mapping, listing pros and cons, or consulting with others for fresh perspectives.

Remember, the goal is to generate a variety of options, not to choose a solution at this stage.

Implementing the Best Solution

The final stage of problem-solving is to select the best solution and put it into action.

Review the options you’ve developed, evaluate their potential effectiveness, and make a decision.

Keep in mind that the “best” solution isn’t necessarily the perfect one (as there might not be a perfect solution), but rather the one that seems most likely to achieve your desired outcome given the circumstances.

Once you’ve chosen a solution, plan out the steps needed to implement it and then take action.

Monitor the results and adjust your approach as necessary.

If the problem persists, don’t be discouraged; return to the previous stages, reassess the problem and your potential solutions, and try again.

Remember, problem-solving is a dynamic process that often involves trial and error.

It’s an essential skill in many areas of life, from everyday challenges to workplace dilemmas.

To learn more about the psychology behind problem-solving and decision-making, check out our introduction to psychology article.

Problem-Solving Examples

Understanding the concept of problem-solving is one thing, but seeing it in action is another.

To help you grasp the practical application of problem-solving strategies, let’s explore three different problem-solving examples from daily life, the workplace, and relationships.

Daily Life Problem-Solving Example

Imagine you’re trying to lose weight but struggle with late-night snacking.

The issue isn’t uncommon, but it’s hindering your progress towards your weight loss goal.

Identifying the Problem : Late-night snacking is causing you to consume extra calories, preventing weight loss.
Developing Possible Solutions : You could consider eating an earlier dinner, having a healthier snack option, or practicing mindful eating.
Implementing the Best Solution : After trying out different solutions, you find that preparing a healthy snack in advance minimizes your calorie intake and satisfies your late-night cravings, helping you stay on track with your weight loss goal.

Workplace Problem-Solving Example

Let’s consider a scenario where a team at work is failing to meet project deadlines consistently.

Identifying the Problem : The team is not completing projects on time, causing delays in the overall project timeline.
Developing Possible Solutions : The team could consider improving their time management skills, using project management tools, or redistributing tasks among team members.
Implementing the Best Solution : After trying out different strategies, the team finds that using a project management tool helps them stay organized, delegate tasks effectively, and complete projects within the given timeframe.

For more insights on effective management styles that can help in problem-solving at the workplace, check out our articles on autocratic leadership , democratic leadership style , and laissez faire leadership .

Relationship Problem-Solving Example

In a romantic relationship, conflicts can occasionally arise.

Let’s imagine a common issue where one partner feels the other isn’t spending enough quality time with them.

Identifying the Problem : One partner feels neglected due to a lack of quality time spent together.
Developing Possible Solutions : The couple could consider scheduling regular date nights, engaging in shared hobbies, or setting aside a specific time each day for undisturbed conversation.
Implementing the Best Solution : The couple decides to implement a daily “unplugged” hour where they focus solely on each other without distractions. This results in improved relationship satisfaction.

For more on navigating relationship challenges, check out our articles on anxious avoidant attachment and emotional awareness .

These problem-solving examples illustrate how the process of identifying a problem, developing possible solutions, and implementing the best solution can be applied to various situations.

By understanding and applying these strategies, you can improve your problem-solving skills and navigate challenges more effectively.

Techniques for Effective Problem-Solving

As you navigate the world of problem-solving, you’ll find that there are multiple techniques you can use to arrive at a solution.

Each technique offers a unique approach to identifying issues, generating potential solutions, and choosing the best course of action.

In this section, we’ll explore three common techniques: Brainstorming , Root Cause Analysis , and SWOT Analysis .

Brainstorming

Brainstorming is a free-thinking method used to generate a large number of ideas related to a specific problem.

You do this by suspending criticism and allowing your creativity to flow.

The aim is to produce as many ideas as possible, even if they seem far-fetched.

You then evaluate these ideas to identify the most beneficial solutions.

By using brainstorming, you can encourage out-of-the-box thinking and possibly discover innovative solutions to challenging problems.

Root Cause Analysis

Root Cause Analysis (RCA) is a method used to identify the underlying causes of a problem.

The goal is to address these root causes rather than the symptoms of the problem.

This technique helps to prevent the same issue from recurring in the future.

There are several RCA methods, such as the “5 Whys” technique, where you ask “why” multiple times until you uncover the root cause of the problem.

By identifying and addressing the root cause, you tackle the problem at its source, which can lead to more effective and long-lasting solutions.

SWOT Analysis

SWOT Analysis is a strategic planning technique that helps you identify your Strengths, Weaknesses, Opportunities, and Threats related to a problem.

This approach encourages you to examine the problem from different angles, helping you understand the resources you have at your disposal (Strengths), the areas where you could improve (Weaknesses), the external factors that could benefit you (Opportunities), and the external factors that could cause problems (Threats).

With this comprehensive understanding, you can develop a well-informed strategy to solve the problem.

Each of these problem-solving techniques provides a distinct approach to identifying and resolving issues.

By understanding and utilizing these methods, you can enhance your problem-solving skills and increase your effectiveness in dealing with challenges.

For more insights into effective problem-solving and other psychological topics, explore our introduction to psychology .

Improving Your Problem-Solving Skills

Learning to solve problems effectively is a skill that can be honed with time and practice.

The following are some ways to enhance your problem-solving capabilities.

Practice Makes Perfect

The saying “practice makes perfect” holds true when it comes to problem-solving.

The more problems you tackle, the better you’ll become at devising and implementing effective solutions.

Seek out opportunities to practice your problem-solving skills both in everyday life and in more complex situations.

This could involve resolving a dispute at work, figuring out a puzzle, or even strategizing in a board game.

Each problem you encounter is a new opportunity to apply and refine your skills.

Learning from Others’ Experiences

There’s much to be gained from observing how others approach problem-solving.

Whether it’s reading about problem solving examples from renowned psychologists or discussing strategies with colleagues, you can learn valuable techniques and perspectives from the experiences of others.

Consider participating in group activities that require problem-solving, such as escape rooms or team projects.

Observe how team members identify problems, brainstorm solutions, and decide on the best course of action.

Embracing a Growth Mindset

A key component of effective problem-solving is adopting a growth mindset.

This mindset, coined by psychologist Carol Dweck, is the belief that abilities and intelligence can be developed through dedication and hard work.

When you embrace a growth mindset, you view challenges as opportunities to learn and grow rather than as insurmountable obstacles.

Believing in your ability to develop and enhance your problem-solving skills over time can make the process less daunting and more rewarding.

So, when you encounter a problem, instead of thinking, “I can’t do this,” try thinking, “I can’t do this yet, but with effort and practice, I can learn.”

For more on the growth mindset, you might want to check out our article on what is intrinsic motivation which includes how a growth mindset can fuel your motivation to improve.

By practicing regularly, learning from others, and embracing a growth mindset, you can continually improve your problem-solving skills and become more adept at overcoming challenges you encounter.

Composition Type: Problem-Solution Essays

An Introduction to Punctuation
Ph.D., Rhetoric and English, University of Georgia
M.A., Modern English and American Literature, University of Leicester
B.A., English, State University of New York

In composition , using a problem-solution format is a method for analyzing and writing about a topic by identifying a problem and proposing one or more solutions. A problem-solution essay is a type of argument. "This sort of essay involves argumentation in that the writer seeks to convince the reader to take a particular course of action. In explaining the problem, it may also need to persuade the reader concerning specific causes" (Dave Kemper et al., "Fusion: Integrated Reading and Writing," 2016).

The Thesis Statement

In many types of report writing, the thesis statement is posed front and center, in one sentence. Author Derek Soles writes about how the thesis statement in a problem-solution paper differs from a straight "report of findings" type of text:

"[One] expository mode is the problem-solution essay, topics for which are typically framed in the form of questions. Why did fourth-graders from poor families score low on a nationwide math test, and how can educators improve math education for this group? Why is Iran a threat to our national security, and how can we reduce this threat? Why did it take the Democratic Party so long to select a candidate for the 2008 presidential election, and what can the party do to make the process more efficient in the future? These essays have two parts: a full explanation of the nature of the problem, followed by an analysis of solutions and their likelihood of success."

("The Essentials of Academic Writing," 2nd ed. Wadsworth, Cengage, 2010)

Readers need additional context before you get to your thesis, but that is not to say that the thesis has to be posed as a question in the introduction:

"In a problem-solution essay, the thesis statement usually proposes the solution. Because readers must first understand the problem, the thesis statement usually comes after a description of the problem. The thesis statement does not have to give details about the solution. Instead, it summarizes the solution. It should also lead naturally to the body of the essay, preparing your reader for a discussion of how your solution would work."

(Dorothy Zemach and Lynn Stafford-Yilmaz, "Writers at Work: The Essay." Cambridge University Press, 2008)

Sample Introductions

It can be helpful to see completed examples before writing in order to examine what makes for an effective piece. See how these introductions give some context before posing the topic and lead naturally into the body paragraphs, where the evidence will be listed. You can imagine how the author has organized the rest of the piece.

"We buried my cousin last summer. He was 32 when he hanged himself from a closet coat rack in the throes of alcoholism, the fourth of my blood relatives to die prematurely from this deadly disease. If America issued drinking licenses, those four men—including my father, who died at 54 of liver failure—might be alive today."

(Mike Brake, "Needed: A License to Drink." Newsweek , March 13, 1994)

"America is suffering from overwork. Too many of us are too busy, trying to squeeze more into each day while having less to show for it. Although our growing time crunch is often portrayed as a personal dilemma, it is, in fact, a major social problem that has reached crisis proportions over the past twenty years."

(Barbara Brandt, "Whole Life Economics: Revaluing Daily Life." New Society, 1995)

"The modern-day apartment dweller is faced with a most annoying problem: paper-thin walls and sound-amplifying ceilings. To live with this problem is to live with the invasion of privacy. There is nothing more distracting than to hear your neighbors' every function. Although the source of the noise cannot be eliminated, the problem can be solved."

(Maria B. Dunn, "One Man's Ceiling Is Another Man's Floor: The Problem of Noise")

Organization

In "Passages: A Writer's Guide, " how to organize a problem-solution paper is explained:

"Though to some extent [your organization of the paper] depends on your topic, do make sure that you include the following information:

Introduction: Identify the problem in a nutshell. Explain why this is a problem, and mention who should be concerned about it.

Problem Paragraph(s): Explain the problem clearly and specifically. Demonstrate that this is not just a personal complaint, but a genuine problem that affects many people.

"Solution Paragraph(s): Offer a concrete solution to the problem, and explain why this is the best one available. You may want to point out why other possible solutions are inferior to yours. If your solution calls for a series of steps or actions to be followed, present these steps in a logical order.

"Conclusion: Reemphasize the importance of the problem and the value of your solution. Choose a problem that you have experienced and thought about—one that you have solved or are in the process of solving. Then, in the essay itself, you may use your own experience to illustrate the problem. However, don't focus all the attention on yourself and on your troubles. Instead, direct the essay at others who are experiencing a similar problem. In other words, don't write an I essay ('How I Cure the Blues'); write a you essay ('How You Can Cure the Blues')."

(Richard Nordquist, Passages: A Writer's Guide , 3rd ed. St. Martin's Press, 1995)

What Is Expository Writing?
What an Essay Is and How to Write One
How to Teach Topic Sentences Using Models
Beef Up Critical Thinking and Writing Skills: Comparison Essays
Thesis: Definition and Examples in Composition
How to Write a Solid Thesis Statement
exploratory essay
Definition and Examples of Analysis in Composition
Definition and Examples of Body Paragraphs in Composition
An Introduction to Academic Writing
How to Write a Good Thesis Statement
The Ultimate Guide to the 5-Paragraph Essay
How to Structure an Essay
Understanding Organization in Composition and Speech
Topical Organization Essay
Examples of Great Introductory Paragraphs

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Video transcript

My Speech Class

Public Speaking Tips & Speech Topics

Problem-Solution Speech [Topics, Outline, Examples]

Jim Peterson has over 20 years experience on speech writing. He wrote over 300 free speech topic ideas and how-to guides for any kind of public speaking and speech writing assignments at My Speech Class.

In this article:

Problem-Solution Outline

Problem-solution examples, criminal justice, environment, relationships, teen issues.

What to include in your problem-solution speech or essay?

Problem-solution papers employ a nonfiction text structure, and typically contain the following elements:

Introduction: Introduce the problem and explain why the audience should be concerned about it.

Cause/Effect : Inform the audience on what causes the problem. In some cases, you may also need to take time to dispel common misconceptions people have about the real cause.

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Thesis Statement: The thesis typically lays out the problem and solution in the form of a question and answer. See examples below.

Solution : Explain the solution clearly and in detail, your problem-solving strategy, and reasons why your solution will work. In this section, be sure to answer common objections, such as “there is a better solution,” “your solution is too costly,” and “there are more important problems to solve.”

Call to Action: Summarize the problem and solution, and paint a picture of what will happen if your final solution is adopted. Also, let the reader know what steps they should take to help solve the problem.

These are the most used methods of developing and arranging:

Problem Solution Method Recommended if you have to argue that there is a social and current issue at stake and you have convince the listeners that you have the best solution. Introduce and provide background information to show what is wrong now.

List the best and ideal conditions and situations. Show the options. Analyze the proper criteria. And present your plan to solve the not wanted situation.

Problem Cause Solution Method Use this pattern for developing and identifying the source and its causes.

Analyze the causes and propose elucidations to the causes.

Problem Cause-Effect Method Use this method to outline the effects of the quandary and what causes it all. Prove the connection between financial, political, social causes and their effects.

Comparative Advantage Method Use this organizational public speaking pattern as recommendation in case everyone knows of the impasse and the different fixes and agrees that something has to be done.

Here are some examples of problems you could write about, with a couple of potential solutions for each one:

Marriage Problem: How do we reduce the divorce rate?

Solution 1: Change the laws to make it more difficult for couples to divorce.

Solution 2: Impose a mandatory waiting period on couples before they can get married.

Environmental Problem: What should we do to reduce the level of carbon dioxide in the atmosphere?

Solution 1: Use renewable energy to fuel your home and vehicles.

Solution 2: Make recycling within local communities mandatory.

Technical Problem: How do we reduce Windows error reporting issues on PCs?

Solution 1: Learn to use dialogue boxes and other command prompt functions to keep your computer system clean.

Solution 2: Disable error reporting by making changes to the registry.

Some of the best problems to write about are those you have personal experience with. Think about your own world; the town you live in, schools you’ve attended, sports you’ve played, places you’ve worked, etc. You may find that you love problem-solution papers if you write them on a topic you identify with. To get your creativity flowing, feel free to browse our comprehensive list of problem-solution essay and paper topics and see if you can find one that interests you.

Problem-Solution Topics for Essays and Papers

How do we reduce murder rates in the inner cities?
How do we stop police brutality?
How do we prevent those who are innocent from receiving the death penalty?
How do we deal with the problem of gun violence?
How do we stop people from driving while intoxicated?
How do we prevent people from texting while driving?
How do we stop the growing child trafficking problem?
What is the best way to deal with domestic violence?
What is the best way to rehabilitate ex-cons?
How do we deal with the problem of overcrowded prisons?
How do we reduce binge drinking on college campuses?
How do we prevent sexual assaults on college campuses?
How do we make college tuition affordable?
What can students do to get better grades in college?
What is the best way for students to effectively balance their classes, studies, work, and social life?
What is the best way for college students to deal with a problem roommate?
How can college students overcome the problem of being homesick?
How can college students manage their finances more effectively?
What is the best way for college students to decide on a major?
What should be done about the problem of massive student loan debts?
How do we solve the global debt crisis?
How do we keep countries from employing child labor?
How do we reduce long-term unemployment?
How do we stop businesses from exploiting consumers?
How do we reduce inflation and bring down the cost of living?
How do we reduce the home foreclosure rate?
What should we do to discourage consumer debt?
What is the best way to stimulate economic growth?
How do we lower the prime cost of manufacturing raw materials?
How can book retailers deal with rising bookseller inventory costs and stay competitive with online sellers?
How do we prevent kids from cheating on exams?
How do we reduce the illiteracy rate?
How do we successfully integrate English as a Second Language (ESL) students into public schools?
How do we put an end to the problem of bullying in schools?
How do we effectively teach students life management skills?
How do we give everyone access to a quality education?
How do we develop a system to increase pay for good teachers and get rid of bad ones?
How do we teach kids to problem solve?
How should schools deal with the problem of disruptive students?
What can schools do to improve reading comprehension on standardized test scores?
What is the best way to teach sex education in public schools?
How do we teach students to recognize a noun clause?
How do we teach students the difference between average speed and average velocity?
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1.3: Problem Solving Strategies

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Michelle Manes
University of Hawaii

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Think back to the first problem in this chapter, the ABC Problem. What did you do to solve it? Even if you did not figure it out completely by yourself, you probably worked towards a solution and figured out some things that did not work.

Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985. [1]

$George_Pólya_ca_1973.jpg$

George Pólya, circa 1973

Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY 2.0 ( http://creativecommons.org/licenses/by/2.0 )], via Wikimedia Commons ↵

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.
After understanding, then make a plan.
Carry out the plan.
Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

We have already seen one problem solving strategy, which we call “Wishful Thinking.” Do not be afraid to change the problem! Ask yourself “what if” questions:

What if the picture was different?
What if the numbers were simpler?
What if I just made up some numbers?

You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started.

This brings us to the most important problem solving strategy of all:

Problem Solving Strategy 2 (Try Something!).

If you are really trying to solve a problem, the whole point is that you do not know what to do right out of the starting gate. You need to just try something! Put pencil to paper (or stylus to screen or chalk to board or whatever!) and try something. This is often an important step in understanding the problem; just mess around with it a bit to understand the situation and figure out what is going on.

And equally important: If what you tried first does not work, try something else! Play around with the problem until you have a feel for what is going on.

Last week, Alex borrowed money from several of his friends. He finally got paid at work, so he brought cash to school to pay back his debts. First he saw Brianna, and he gave her 1/4 of the money he had brought to school. Then Alex saw Chris and gave him 1/3 of what he had left after paying Brianna. Finally, Alex saw David and gave him 1/2 of what he had remaining. Who got the most money from Alex?

Think/Pair/Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What did you figure out about the problem? This problem lends itself to two particular strategies. Did you try either of these as you worked on the problem? If not, read about the strategy and then try it out before watching the solution.

Problem Solving Strategy 3 (Draw a Picture).

Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric, like this one, thinking visually can help! Can you represent something in the situation by a picture?

Draw a square to represent all of Alex’s money. Then shade 1/4 of the square — that’s what he gave away to Brianna. How can the picture help you finish the problem?

After you have worked on the problem yourself using this strategy (or if you are completely stuck), you can watch someone else’s solution.

Problem Solving Strategy 4 (Make Up Numbers).

Part of what makes this problem difficult is that it is about money, but there are no numbers given. That means the numbers must not be important. So just make them up!

You can work forwards: Assume Alex had some specific amount of money when he showed up at school, say $100. Then figure out how much he gives to each person. Or you can work backwards: suppose he has some specific amount left at the end, like $10. Since he gave Chris half of what he had left, that means he had $20 before running into Chris. Now, work backwards and figure out how much each person got.

Watch the solution only after you tried this strategy for yourself.

If you use the “Make Up Numbers” strategy, it is really important to remember what the original problem was asking! You do not want to answer something like “Everyone got $10.” That is not true in the original problem; that is an artifact of the numbers you made up. So after you work everything out, be sure to re-read the problem and answer what was asked!

(Squares on a Chess Board)

How many squares, of any possible size, are on a 8 × 8 chess board? (The answer is not 64... It’s a lot bigger!)

Remember Pólya’s first step is to understand the problem. If you are not sure what is being asked, or why the answer is not just 64, be sure to ask someone!

Think / Pair / Share

It is clear that you want to draw a picture for this problem, but even with the picture it can be hard to know if you have found the correct answer. The numbers get big, and it can be hard to keep track of your work. Your goal at the end is to be absolutely positive that you found the right answer. You should never ask the teacher, “Is this right?” Instead, you should declare, “Here’s my answer, and here is why I know it is correct!”

Problem Solving Strategy 5 (Try a Simpler Problem).

Pólya suggested this strategy: “If you can’t solve a problem, then there is an easier problem you can solve: find it.” He also said: “If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?” In this case, an 8 × 8 chess board is pretty big. Can you solve the problem for smaller boards? Like 1 × 1? 2 × 2? 3 × 3?

Of course the ultimate goal is to solve the original problem. But working with smaller boards might give you some insight and help you devise your plan (that is Pólya’s step (2)).

Problem Solving Strategy 6 (Work Systematically).

If you are working on simpler problems, it is useful to keep track of what you have figured out and what changes as the problem gets more complicated.

For example, in this problem you might keep track of how many 1 × 1 squares are on each board, how many 2 × 2 squares on are each board, how many 3 × 3 squares are on each board, and so on. You could keep track of the information in a table:

Problem Solving Strategy 7 (Use Manipulatives to Help You Investigate).

Sometimes even drawing a picture may not be enough to help you investigate a problem. Having actual materials that you move around can sometimes help a lot!

For example, in this problem it can be difficult to keep track of which squares you have already counted. You might want to cut out 1 × 1 squares, 2 × 2 squares, 3 × 3 squares, and so on. You can actually move the smaller squares across the chess board in a systematic way, making sure that you count everything once and do not count anything twice.

Problem Solving Strategy 8 (Look for and Explain Patterns).

Sometimes the numbers in a problem are so big, there is no way you will actually count everything up by hand. For example, if the problem in this section were about a 100 × 100 chess board, you would not want to go through counting all the squares by hand! It would be much more appealing to find a pattern in the smaller boards and then extend that pattern to solve the problem for a 100 × 100 chess board just with a calculation.

If you have not done so already, extend the table above all the way to an 8 × 8 chess board, filling in all the rows and columns. Use your table to find the total number of squares in an 8 × 8 chess board. Then:

Describe all of the patterns you see in the table.
Can you explain and justify any of the patterns you see? How can you be sure they will continue?
What calculation would you do to find the total number of squares on a 100 × 100 chess board?

(We will come back to this question soon. So if you are not sure right now how to explain and justify the patterns you found, that is OK.)

(Broken Clock)

This clock has been broken into three pieces. If you add the numbers in each piece, the sums are consecutive numbers. ( Consecutive numbers are whole numbers that appear one after the other, such as 1, 2, 3, 4 or 13, 14, 15.)

$index-12_1-300x282-1.png$

Can you break another clock into a different number of pieces so that the sums are consecutive numbers? Assume that each piece has at least two numbers and that no number is damaged (e.g. 12 isn’t split into two digits 1 and 2.)

Remember that your first step is to understand the problem. Work out what is going on here. What are the sums of the numbers on each piece? Are they consecutive?

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What progress have you made?

Problem Solving Strategy 9 (Find the Math, Remove the Context).

Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

In this case, worrying about the clock and exactly how the pieces break is less important than worrying about finding consecutive numbers that sum to the correct total. Ask yourself:

What is the sum of all the numbers on the clock’s face?
Can I find two consecutive numbers that give the correct sum? Or four consecutive numbers? Or some other amount?
How do I know when I am done? When should I stop looking?

Of course, solving the question about consecutive numbers is not the same as solving the original problem. You have to go back and see if the clock can actually break apart so that each piece gives you one of those consecutive numbers. Maybe you can solve the math problem, but it does not translate into solving the clock problem.

Problem Solving Strategy 10 (Check Your Assumptions).

When solving problems, it is easy to limit your thinking by adding extra assumptions that are not in the problem. Be sure you ask yourself: Am I constraining my thinking too much?

In the clock problem, because the first solution has the clock broken radially (all three pieces meet at the center, so it looks like slicing a pie), many people assume that is how the clock must break. But the problem does not require the clock to break radially. It might break into pieces like this:

$index-13_1-300x296.png$

Were you assuming the clock would break in a specific way? Try to solve the problem now, if you have not already.

Magic Squares Questions

Ai generator.

Magic squares are captivating puzzles in mathematics , where the sum of numbers in each row, column, and diagonal of a square grid is equal, showcasing a perfect balance of integers . This concept intersects various mathematical disciplines, including Algebra for forming equations, and Statistics for analyzing numerical arrangements. Exploring rational and irrational numbers within these squares introduces complexity, especially when linked with square and square roots . The least squares method, often utilized in data fitting, parallels the optimization used in constructing magic squares, making it a rich topic for mathematical exploration and application.

Magic Squares Questions with Solution

Question 1: constructing a basic 3×3 magic square.

Problem: Construct a 3×3 magic square using the numbers 1 through 9.

Solution: A 3×3 magic square requires that the sum of the numbers in each row, column, and diagonal is equal. The traditional magic square solution for 3×3 is:

Question 2: Inserting Rational and Irrational Numbers

Problem: Create a 3×3 magic square using both rational and irrational numbers which sum up to an integer.

Solution: One way to approach this is by including the irrational numbers √2 and √3, and balancing them with their negatives and rational numbers:

Question 3: Algebraic Magic Square

Problem: Fill a 3×3 magic square where each cell contains a linear expression 𝑎𝑥+𝑏 a x + b and find the values of 𝑥 x that satisfy the magic square condition.

Solution: Let’s consider simple linear terms 𝑥,𝑥+1,𝑥−1,𝑒𝑡𝑐.

Setting up equations for the rows, we find 𝑥 = 0 which checks with the sums across the board.

Question 4: Least Squares in Magic Square

Problem: Apply the least squares method to find the best fitting 3×3 magic square for a given set of nine numbers: [1, 3, 5, 7, 9, 11, 13, 15, 17].

Solution: Using the least squares method, we calculate the expected value of each cell based on the mean of the given numbers and then adjust to get as close as possible to the mean while maintaining the magic square properties. This problem is complex and typically requires numerical or software-assisted solutions to minimize the squared differences from the mean (which is 9 in this case).

Question 5: Magic Square Using Integers

Problem: Create a 3×3 magic square that sums to 12 using negative integers.

Solution: A valid configuration can be:

Question 6: Magic Square Involving Square and Square Roots

Problem: Design a 3×3 magic square that incorporates both square numbers and their square roots.

Solution: We can use both perfect squares and their roots to fill the magic square, aiming for the sum in each row, column, and diagonal to be consistent. Consider:

Question 7: Magic Square with Statistics Concept

Problem: Construct a 3×3 magic square using the concept of mean, median, and mode.

Solution: We can set the magic square so that the mean, median, and mode of the numbers used are also consistent. Use:

In this magic square, the mean (5), median (6), and mode (8) of all numbers do not contribute directly to the properties of the magic square but show a well-rounded set of statistics. This square also aligns with the standard sum rule of 16 for a 3×3 magic square.

Question 8: Magic Square Using Least Squares Method for Error Minimization

Problem: Adjust a near-magic square [2, 7, 6; 9, 5, 1; 4, 3, 8] using the least squares method to correct one entry and achieve a magic square.

Solution: In the given array, the sums are slightly off for a magic square. Using the least squares method, we can adjust the middle cell from 5 to 5.1 to balance the sums:

Now each row, column, and diagonal approximates the sum closer to the desired magic constant. This solution uses numerical optimization to tweak the square to desired properties.

Question 9: Integer Magic Square with Specific Sum

Problem: Develop a 3×3 magic square where the sum of each row, column, and diagonal equals zero using integers.

Solution: A possible configuration using both positive and negative integers is:

This layout ensures that each line sums to zero, demonstrating the application of integer solutions in magic square construction, emphasizing balance among positive and negative values.

Question 10: Magic Square Using Only Prime Numbers

Problem: Create a 3×3 magic square using only prime numbers.

Solution: Consider using primes close in value to maintain balance:

This configuration ensures each row, column, and diagonal sums to 177, showcasing a unique challenge solved by prime number selection.

Question 11: Fibonacci Magic Square

Problem: Construct a 3×3 magic square using Fibonacci numbers.

Solution: Using Fibonacci numbers strategically:

Question 12: Rational and Irrational Number Mix

Problem: Fill a 3×3 magic square with a mix of rational and irrational numbers that sum to 10.

Question 13: Complex Numbers Magic Square

Problem: Develop a 3×3 magic square using complex numbers that sum to a real number.

Question 14: Negative Integers Magic Square

Create a 3×3 magic square using only negative integers that sum to -9.

Question 15: Algebraic Expressions Magic Square

Problem: Construct a 3×3 magic square where each cell contains a different algebraic expression of 𝑥.

Solving for 𝑥 = 1 will make each row, column, and diagonal sum to 9.

square root 1 to 100
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A magic square is a grid of numbers arranged such that the sum of every row, column, and diagonal is the same. This constant sum is known as the magic constant.

Yes, magic squares can be constructed using a combination of rational and irrational numbers. By carefully balancing these numbers, it’s possible to maintain the magic constant across all rows, columns, and diagonals.

Fibonacci numbers can be arranged into a magic square by selecting numbers from the sequence that, when arranged correctly, sum to a consistent magic constant in every row, column, and diagonal.

Yes, magic squares can be created exclusively with prime numbers. The challenge is to select primes that, when arranged, achieve the required magic constant.

Indeed, complex numbers can form magic squares. The sum of each row, column, and diagonal needs to be a real number to maintain traditional magic square properties, or it can be a complex number with consistent real and imaginary parts across the sums.

Absolutely. A magic square can be formed using negative integers, ensuring that the sums of the rows, columns, and diagonals reach a negative magic constant.

Algebraic expressions can be used in each cell of a magic square, where the expressions are crafted such that their evaluations lead to a consistent sum across the structure, given certain values of the variables involved.

The least squares method can be employed to adjust a nearly correct set of numbers in a magic square to minimize the sum of the squared differences from the intended magic constant, optimizing the arrangement for closer adherence to magic square conditions.

Yes, decimal numbers can be used in magic squares to finely adjust the sums to the desired magic constant, offering a precise approach to achieving balance in the grid.

Quadratic expressions can be placed in the cells of a magic square such that, for a given value of 𝑥 x , the sum of the expressions in each row, column, and diagonal equals a constant. This method combines higher-level algebra with the traditional magic square format.

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4 Common Types of Team Conflict — and How to Resolve Them

Randall S. Peterson,
Priti Pradhan Shah,
Amanda J. Ferguson,
Stephen L. Jones

Advice backed by three decades of research into thousands of team conflicts around the world.

Managers spend 20% of their time on average managing team conflict. Over the past three decades, the authors have studied thousands of team conflicts around the world and have identified four common patterns of team conflict. The first occurs when conflict revolves around a single member of a team (20-25% of team conflicts). The second is when two members of a team disagree (the most common team conflict at 35%). The third is when two subgroups in a team are at odds (20-25%). The fourth is when all members of a team are disagreeing in a whole-team conflict (less than 15%). The authors suggest strategies to tailor a conflict resolution approach for each type, so that managers can address conflict as close to its origin as possible.

If you have ever managed a team or worked on one, you know that conflict within a team is as inevitable as it is distracting. Many managers avoid dealing with conflict in their team where possible, hoping reasonable people can work it out. Despite this, research shows that managers spend upwards of 20% of their time on average managing conflict.

Randall S. Peterson is the academic director of the Leadership Institute and a professor of organizational behavior at London Business School. He teaches leadership on the School’s Senior Executive and Accelerated Development Program.
PS Priti Pradhan Shah is a professor in the Department of Work and Organization at the Carlson School of Management at the University of Minnesota. She teaches negotiation in the School’s Executive Education and MBA Programs.
AF Amanda J. Ferguson is an associate professor of Management at Northern Illinois University. She teaches Organizational Behavior and Leading Teams in the School’s MBA programs.
SJ Stephen L. Jones is an associate professor of Management at the University of Washington Bothell. He teaches Organizational and Strategic Management at the MBA level.

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How Rest of World is tracking AI use around elections worldwide

Rest of World's 2024 AI Elections Tracker.

As two billion people around the world head to the polls, a key concern for many has been the potential role new AI could play in election campaigns. This technology could worsen issues around disinformation or online harassment.

For now, and despite a few well-publicised instances, there isn’t yet a lot of evidence of AI playing a significant role in elections this year. But many news organisations will focus on votes in the US, the UK and the European Union, potentially leaving the Global South elections undercovered. Rest of World, a non-profit online publication covering technology’s impact outside of the West, is aiming to address this problem with a new project, the 2024 AI Elections Tracker , launched on 16 April.

The tracker is an ongoing log of examples of AI being used around elections. Examples are flagged to the team, verified and reported on before a summary is added to the tracker's timeline, with the context and links to the original image, video or post. I spoke to Victoria Turk , Features Director at Rest of World, who explains the project in her own words.

1. The project in a nutshell

Victoria Turk: “The idea is to gather examples of AI being used in the context of elections globally. To give a bit of background, 2024 is a massive year for elections: we've got more than two billion people globally eligible to vote this year. This comes after a big boom in generative AI tools which are very accessible, things like ChatGPT, AI image generators, and audio and video tools.

There's been a lot of discussion around what that could mean for democracy in terms of how these tools could be used or abused in campaigning and spreading misinformation and disinformation. We wanted to look at what's actually happening and go beyond those theoretical concerns to see what's happening on the ground. We are looking at how generative AI tools are being used around elections in countries worldwide.”

2. The problem they wanted to solve

V. T.: “Everyone knows from a top-level perspective that generative AI tools are being used around elections. What we want to find out are the genuine instances of this happening, especially outside of the West. I think a lot of focus is on English-language content, maybe around the US elections and the UK elections. Western outlets in particular are looking less at the elections in Latin America, Africa or Asia.

We're keeping this going throughout the year and we're hoping we'll end up with a database of content which we can then look at to see overarching trends in the future. That database will be open to be used also by other people who can come back and see what's happened in different places.

I should say we are not just focusing on the negative uses of these tools, so when people think about elections and generative AI, they think automatically about disinformation, misinformation, deepfakes, and intentionally misleading voters. We are seeing some of that, but there are also other creative uses of this technology. In some cases, we're seeing political parties and campaigns using this tech to better reach voters, spread their campaign materials, and provide information.

We saw this from Imran Khan , the former Prime Minister of Pakistan: his party was using AI to enable him to give a video speech to his supporters even though he was imprisoned. In Belarus, we saw the opposition create an AI candidate powered by ChatGPT that could answer people's questions in a way that might be dangerous for a real opponent in that political context.

We've also seen a lot of like fun stuff: memes and people either poking fun at the opposition or making celebratory memes around the candidates that they support and so we're not taking a view on whether this is good or bad, we want to capture what is happening.”

3. The problems they encountered

V. T.: “A lot of this content is in local languages, so having journalists who speak that language and are familiar with the context is critical. We wouldn't be able to do it without that knowledge. Verifying if something actually is AI is a big challenge and sometimes it is very obvious: often people will state that they have used AI to make something and they're quite upfront about it; sometimes they're even showing off that they're adept at using these new tools.

In other cases, maybe they don't admit to using AI or they're trying to, in the case of deepfakes, pass off content as being legitimate when actually it's falsified. In those cases, we have to do a bit of detective work to check if the content is AI-generated or not.”

4. How they found a solution

V. T.: “So far, we've found that there's no one-size-fits-all solution to do these checks. There are some tools out there that will give you a score as to how likely they think an image, a video or audio is to have been AI-generated, but I don't think any of them are foolproof , so we're using as many resources as we can.

We’ve been both using some of the online tools available, but also going directly to researchers in this space to get their view, and going to local fact-checking organisations to see what they think.

Sometimes that's about looking for digital clues. So maybe the mouth movements don't line up with the audio, which might suggest that the video has been tampered with. But it might be more contextual: if you know the local political situation, you know that it's probably very unlikely that a particular instance, for example, shown in a video, actually happened and so you do some more traditional reporting to find out if the people pictured were in that spot at that time.

Also, from the start we built into the tracker an update possibility. We are aware that there may be cases where the story changes or we get more information about an entry and we feel that we need to add that information for our readers.”

5. How they tested their tool

V. T.: “We've launched with the initial idea that this is something that's going to grow. We launched it with several incidents that took place from the beginning of January until the launch date on 16 April. Now we are planning to update with new entries as we come across them. We are trying to be as responsive as possible.

We're expecting to see the number of entries rise and fall in line with elections, so you'd expect to see a lot more content generated around a specific election when that occurs.

At the moment, most entries are about Indonesia, Pakistan and Bangladesh because they have already had their elections. We are expecting to see more around the elections in Mexico and South Africa as those elections get closer in time. It's a new format for us, it's unusual in that it is one project that we are consistently working on and changing through the year, so it'll be interesting to see how it develops.”

6. How the tool works in practice

V. T.: “One of the things we have at Rest of World which I think is a real advantage over a lot of publications is a global team and a global network of contributors, so we're leaning on that a lot to find and report on the entries for this tracker. We've got journalists in pretty much every region outside of the West. We don't cover North America and Western Europe. We've got a network of contributors in different countries who have been tasked with looking for examples of AI being used in or around elections in their country.

They are pitching those examples to us and then reporting them out, verifying that AI has been used, trying to find the details of who's doing it, why they are doing it, what tools they might be using, how the content is spreading, and they're all feeding into one tracker . That's important because a lot of this content might be in local languages, it might require knowledge of the local political context that one person sitting in one country is not going to have for everywhere around the world.

We are also working with other organisations in this space and we are encouraging people to share what they're seeing with us, and we're sharing back with them to make sure that we're covering as many bases as we can.

Finally, we are also asking readers to submit examples that they see on social media. We are trying to get as many examples our way as possible so that we can then look into them and verify if they meet the criteria to be included in the tracker.”

A screenshot of Rest of World's AI Elections Tracker.

7. How the tool can be improved

V. T.: “The first thing is just getting as many examples as we can, and we were really happy to see that even on the first day of launch we got a few reader-submitted entries to look into which is great because the more people are contributing, the more incidents we're going to see and so keeping up that momentum is important to make this as useful as possible.

We are interested to see how people end up using it and to see what kind of content we've got. At the moment, it's possible to filter content by month, by country and by the platform we're seeing it spread on. We are interested to see how useful that filtering technique is. Maybe that's something that we can develop in the future.

One part of this that we thought was quite important from the start is saving the content that we're talking about. A lot of this content may be removed either by the platforms or by the people who have put it out there in the first place. We think it's really important to preserve the content so that it makes sense when people come back to look at it in the future and that they're able to see exactly what it was. That's something that we're working on to include.

There may be cases where we decide not to show that content if we think it could cause particular damage. But in general, we want to build a library so that readers, researchers, and whoever might want to use this tool, have something to refer back to.

We're also interested in tracking how platforms approach AI content around elections. Some have developed specific rules for this. Others are still working on those or changing them as they go. We want to track how different platforms respond to this content in terms of, do they take it down, or label it? Are we seeing particular phenomena on particular platforms? That's something that we are trying to include in the entries as we go as well.”

8. How this can help newsrooms

V. T.: “We're just putting it all out so that people can see it all and use it for themselves. Other people who are writing about the phenomenon of AI around elections can have these examples to draw on. It could be a useful resource, with different publications focusing on different geographies or on specific technological trends who might want to look at the specific incidents that are relevant to them. The more entries we get, the more interesting data analysis might be possible by looking at the data en masse to see if particular trends reveal themselves.”

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Latest News

In the tech world and beyond, new 5G applications are being discovered every day. From driverless cars to smarter cities, farms, and even shopping experiences, the latest standard in wireless networks is poised to transform the way we interact with information, devices and each other. What better time to take a closer look at how humans are putting 5G to use to transform their world.

What is 5G?

5G (fifth-generation mobile technology is the newest standard for cellular networks. Like its predecessors, 3G, 4G and 4G LTE, 5G technology uses radio waves for data transmission. However, due to significant improvements in latency, throughput and bandwidth, 5G is capable of faster download and upload speeds than previous networks.

Since its release in 2019, 5G broadband technology has been hailed as a breakthrough technology with significant implications for both consumers and businesses. Primarily, this is due to its ability to handle large volumes of data that is generated by complex devices that use its networks.

As mobile technology has expanded over the years, the number of data users generate every day has increased exponentially. Currently, other transformational technologies like artificial intelligence (AI), the Internet of Things (IoT ) and machine learning (ML) require faster speeds to function than 3G and 4G networks offer. Enter 5G, with its lightning-fast data transfer capabilities that allow newer technologies to function in the way they were designed to.

Here are some of the biggest differences between 5G and previous wireless networks.

Physical footprint : The transmitters that are used in 5G technology are smaller than in predecessors’ networks, allowing for discrete placement in out-of-the-way places. Furthermore, “cells”—geographical areas that all wireless networks require for connectivity—in 5G networks are smaller and require less power to run than in previous generations.
Error rates : 5G’s adaptive Modulation and Coding Scheme (MCS), a schematic that wifi devices use to transmit data, is more powerful than ones in 3G and 4G networks. This makes 5G’s Block Error Rate (BER)—a metric of error frequency—much lower.
Bandwidth : By using a broader spectrum of radio frequencies than previous wireless networks, 5G networks can transmit on a wider range of bandwidths. This increases the number of devices that they can support at any given time.
Lower latency : 5G’s low latency , a measurement of the time it takes data to travel from one location to another, is a significant upgrade over previous generations. This means that routine activities like downloading a file or working in the cloud is going to be faster with a 5G connection than a connection on a different network.

Like all wireless networks, 5G networks are separated into geographical areas that are known as cells. Within each cell, wireless devices—such as smartphones, PCs, and IoT devices—connect to the internet via radio waves that are transmitted between an antenna and a base station. The technology that underpins 5G is essentially the same as in 3G and 4G networks. But due to its lower latency, 5G networks are capable of delivering faster download speeds—in some cases as high as 10 gigabits per second (Gbps).

As more and more devices are built for 5G speeds, demand for 5G connectivity is growing. Today, many popular Internet Service Providers (ISPs), such as Verizon, Google and AT&T, offer 5G networks to homes and businesses. According to Statista, more than 200 million homes and businesses have already purchased it with that number expected to at least double by 2028 (link resides outside ibm.com).

Let’s take a look at three areas of technological improvement that have made 5G so unique.

New telecom specifications

The 5G NR (New Radio) standard for cellular networks defines a new radio access technology (RAT) specification for all 5G mobile networks. The 5G rollout began in 2018 with a global initiative known as the 3rd Generation Partnership Project (3FPP). The initiative defined a new set of standards to steer the design of devices and applications for use on 5G networks.

The initiative was a success, and 5G networks grew swiftly in the ensuing years. Today, 45% of networks worldwide are 5G compatible, with that number forecasted to rise to 85% by the end of the decade according to a recent report by Ericsson (link resides outside ibm.com).

Independent virtual networks (network slicing)

On 5G networks, network operators can offer multiple independent virtual networks (in addition to public ones) on the same infrastructure. Unlike previous wireless networks, this new capability allows users to do more things remotely with greater security than ever before. For example, on a 5G network, enterprises can create use cases or business models and assign them their own independent virtual network. This dramatically improves the user experience for their employees by adding greater customizability and security.

Private networks

In addition to network slicing, creating a 5G private network can also enhance personalization and security features over those available on previous generations of wireless networks. Global businesses seeking more control and mobility for their employees increasingly turn to private 5G network architectures rather than public networks they’ve used in the past.

Now that we better understand how 5G technology works, let’s take a closer look at some of the exciting applications it’s enabling.

Autonomous vehicles

From taxi cabs to drones and beyond, 5G technology underpins most of the next-generation capabilities in autonomous vehicles. Until the 5G cellular standard came along, fully autonomous vehicles were a bit of a pipe dream due to the data transmission limitations of 3G and 4G technology. Now, 5G’s lightning-fast connection speeds have made transport systems for cars, trains and more, faster than previous generations, transforming the way systems and devices connect, communicate and collaborate.

Smart factories

5G, along with AI and ML, is poised to help factories become not only smarter but more automated, efficient, and resilient. Today, many mundane but necessary tasks that are associated with equipment repair and optimization are being turned over to machines thanks to 5G connectivity paired with AI and ML capabilities. This is one area where 5G is expected to be highly disruptive, impacting everything from fuel economy to the design of equipment lifecycles and how goods arrive at our homes.

For example, on a busy factory floor, drones and cameras that are connected to smart devices that use the IoT can help locate and transport something more efficiently than in the past and prevent theft. Not only is this better for the environment and consumers, but it also frees up employees to dedicate their time and energy to tasks that are more suited to their skill sets.

Smart cities

The idea of a hyper-connected urban environment that uses 5G network speeds to spur innovation in areas like law enforcement, waste disposal and disaster mitigation is fast becoming a reality. Some cities already use 5G-enabled sensors to track traffic patterns in real time and adjust signals, helping guide the flow of traffic, minimize congestion, and improve air quality.

In another example, 5G power grids monitor supply and demand across heavily populated areas and deploy AI and ML applications to “learn” what times energy is in high or low demand. This process has been shown to significantly impact energy conservation and waste, potentially reducing carbon emissions and helping cities reach sustainability goals.

Smart healthcare

Hospitals, doctors, and the healthcare industry as a whole already benefit from the speed and reliability of 5G networks every day. One example is the area of remote surgery that uses robotics and a high-definition live stream that is connected to the internet via a 5G network. Another is the field of mobile health, where 5G gives medical workers in the field quick access to patient data and medical history. This enables them to make smarter decisions, faster, and potentially save lives.

Lastly, as we saw during the pandemic, contact tracing and the mapping of outbreaks are critical to keeping populations safe. 5G’s ability to deliver of volumes of data swiftly and securely allows experts to make more informed decisions that have ramifications for everyone.

5G paired with new technological capabilities won’t just result in the automation of employee tasks, it will dramatically improve them and the overall employee experience . Take virtual reality (VR) and augmented reality (AR), for example. VR (digital environments that shut out the real world) and AR (digital content that augments the real world) are already used by stockroom employees, transportation drivers and many others. These employees rely on wearables that are connected to a 5G network capable of high-speed data transfer rates that improve several key capabilities, including the following:

Live views : 5G connectivity provides live, real-time views of equipment, events, and even people. One way in which this feature is being used in professional sports is to allow broadcasters to remotely call a sporting event from outside the stadium where the event is taking place.
Digital overlays : IoT applications in a warehouse or industrial setting allow workers that are equipped with smart glasses (or even just a smartphone) to obtain real-time insights from an application. This includes repair instructions or the name and location of a spare part.
Drone inspections : Right now, one of the leading causes of employee injury is inspection of equipment or project sites in remote and potentially dangerous areas. Drones, which are connected via 5G networks, can safely monitor equipment and project sites and even take readings from hard-to-reach gauges.

Edge computing , a computing framework that allows computations to be done closer to data sources, is fast becoming the standard for enterprises. According to this Gartner white paper (link resides outside ibm.com), by 2025, 75% of enterprise data will be processed at the edge (compared to only 10% today). This shift saves businesses time and money and enables better control over large volumes of data. It would be impossible without the new speed standards that are generated by 5G technology.

Ultra-reliable edge computing and 5G enable the enterprise to achieve faster transmission speeds, increased control and greater security over massive volumes of data. Together, these twin technologies will help reduce latency while increasing speed, reliability and bandwidth, resulting in faster, more comprehensive data analysis and insights for businesses everywhere.

5G solutions with IBM Cloud Satellite

5G presents significant opportunities for the enterprise, but first, you need a platform that can handle its speed. IBM Cloud Satellite® lets you deploy and run apps consistently across on-premises, edge computing and public cloud environments on a 5G network. And it’s all enabled by secure and auditable communications within the IBM Cloud®.

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39 Best Problem-Solving Examples (2024)
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Mixture Problems With Solutions
Change percentages into fractions. Multiply all terms by 100 to simplify. Solve for x. 80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution. Problem 2: John wants to make a 100 ml of 5% alcohol solution mixing a quantity of a 2% alcohol solution with a 7% alcohol solution.
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6.8 Mixture and Solution Word Problems. Solving mixture problems generally involves solving systems of equations. Mixture problems are ones in which two different solutions are mixed together, resulting in a new, final solution. Using a table will help to set up and solve these problems. The basic structure of this table is shown below: Example ...
6.1.1: Practice Problems- Solution Concentration
PROBLEM 6.1.1.6 6.1.1. 6. Calculate the molarity of each of the following solutions: (a) 0.195 g of cholesterol, C 27 H 46 O, in 0.100 L of serum, the average concentration of cholesterol in human serum. (b) 4.25 g of NH 3 in 0.500 L of solution, the concentration of NH 3 in household ammonia.
Solving equations & inequalities
Unit test. Level up on all the skills in this unit and collect up to 1,100 Mastery points! Start Unit test. There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
Mixture Problems
Here are some examples for solving mixture problems. Example 1. Coffee worth $1.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20 pounds of a mixture worth 90¢ per pound. How many pounds of each type are used? ... Example 2. Solution A is 50% hydrochloric acid, while solution B is 75% hydrochloric acid. How many liters of ...
Solving Equations
Example: x − 2 = 4. When we put 6 in place of x we get: 6 − 2 = 4. which is true. So x = 6 is a solution. How about other values for x? For x=5 we get "5−2=4" which is not true, so x=5 is not a solution. For x=9 we get "9−2=4" which is not true, so x=9 is not a solution. etc; In this case x = 6 is the only solution.
35 problem-solving techniques and methods for solving complex problems
15% Solutions. Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly.
What is Problem Solving? (Steps, Techniques, Examples)
The problem-solving process typically includes the following steps: Identify the issue: Recognize the problem that needs to be solved. Analyze the situation: Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present. Generate potential solutions: Brainstorm a list of possible ...
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One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training, shadowing a mentor, or working with a coach. 2. Practice. Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life.
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If the problem you are trying to solve has special cases that a solution to the general problem would also apply to, consider just one or two of these special cases as examples and solve the problem just for those cases first. Then see if a solution to one of those special cases helps you solve the problem in general.
26 Expert-Backed Problem Solving Examples
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100 Problem and Solution Examples. Problem: There's a leak in the kitchen sink. Solution: Tighten the pipes or call a plumber to fix the leak. Problem: My phone's storage is full. Solution: Delete unnecessary files or transfer them to cloud storage. Problem: I'm not getting enough exercise.
How to Write a Problem Solution Paper: 13 Steps (with Pictures)
1. Confirm the paper follows a clear structure or outline. Review the paper and confirm it covers the four components of a problem solution paper. Make sure it addresses the problem and the solution in detail. Check that your thesis statement appears in the introduction and in the conclusion sections of the paper.
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After you have chosen your topic, you can find instructions about how to develop your ideas, find a unique solution to the problem, and organize your essay in "How to Write Your Problem Solution Paper." 4 Parts of Problem Solution. Describe a problem vividly. Propose a solution. Argue that the solution is practical, feasible, cost-effective ...
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Problem-Solving Examples 1. Divergent Thinking. Divergent thinking refers to the process of coming up with multiple different answers to a single problem.It's the opposite of convergent thinking, which would involve coming up with a singular answer.. The benefit of a divergent thinking approach is that it can help us achieve blue skies thinking - it lets us generate several possible ...
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Moreover, problem-solving can contribute to your overall mental well-being. It can give you a sense of control and agency, reduce feelings of stress and anxiety, and foster a positive attitude. It's also a key component of resilience, the ability to bounce back from adversity. In conclusion, problem-solving is a fundamental skill in life.
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1.3: Problem Solving Strategies
For example, in this problem you might keep track of how many 1 × 1 squares are on each board, how many 2 × 2 squares on are each board, how many 3 × 3 squares are on each board, and so on. ... In the clock problem, because the first solution has the clock broken radially (all three pieces meet at the center, so it looks like slicing a pie ...
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35 problem-solving techniques and methods for solving complex problems

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Clearly define the problem

Don’t jump to conclusions

Try different approaches

Don’t take it personally

Get the right people in the room

Document everything

Bring a facilitator

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1. Six Thinking Hats

2. Lightning Decision Jam

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6. Discovery & Action Dialogue (DAD)

7. Design Sprint 2.0

8. Open space technology

Techniques to identify and analyze problems

10. The Creativity Dice

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13. SWOT Analysis

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16. Speed Boat

17. The Journalistic Six

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19. What, So What, Now What?

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Problem-solving techniques for developing solutions

21. Mindspin

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23. Four Step Sketch

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25. How-Now-Wow Matrix

26. Impact and Effort Matrix

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29. Doodling Together

30. Show and Tell

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