problem solving grid puzzles

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Logic puzzles with grids

Begin with our free grid puzzles, starting from easy to hard. Some puzzles go with answers, others only with hints.

We created 2500+ puzzles, math and logic games, and brain exercises. LogicLike educational platform helps children to build critical thinking skills. Adults improve mental abilities and develop ingenuity.

How to solve grid logic puzzles?

In a grid-based problem, there is a set of sections and matching options. Read the clues and remember: you can choose each option only once. The puzzle is guessed as soon as you connect the appropriate options.

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Easy logic puzzles with grids (for kids)

The flask with the red liquid is not the second. The flask with the blue liquid is neither the first one nor the second one. Choose the correct table.

The right one.

The third flask is with the blue liquid. The second one is not with the red liquid. Choose the correct table.

Which flask belongs to the Professor?

The blue one.

The Professor's flask is neither with blue nor with red liquid. Steam's flask has blue liquid inside. Use the "+" sign to mark to whom the flasks belong.

Annie, Martha, and Olive use the player names Tetris, Moon, and Oxie. Only Martha's player name has the same first letter as her real name. Use the "+" symbol to mark each girl's player name.

Solving puzzles improves ability to think outside the box. More than 2500 brain challenging logic puzzles , easy and tricky riddles , and brainteasers are waiting for you!

Hard logic grid puzzles (for kids and parents)

Three people met: - "We all have different-colored hair, but none of us has hair color matching our pet's fur color," said the brunette. - "You're right," said the orange cat's owner. Use the "+" sign to mark each cat's owner.

Each line and each column has only one "+" sign.

Ango, Kidd, and Tew buried some treasure. One pirate buried his under an orange tree, another buried his under a grapevine, while the third pirate buried his under a banana tree. Ango didn't use the seashell to bury his treasure. Tew buried a treasure chest, but not underneath the orange tree. The sack is buried under the grapevine. Use the "+" sign to mark each pirate's choice.

Want to learn how to solve any logic grid puzzle? Start your Logiclike adventure right now!

Each of three friends — Alex, Bill, and Phil — attend two classes for the following activities: soccer, tennis, chess, music school, karate, and basketball. Phil, a musician, and a karate kid study in one group. A basketball player, tennis player, and Alex walk to school together. The karate kid and soccer player are neighbors. The musician and basketball player go to Alex's house very often.

Start learning on Logiclike and you will be able to solve any grid puzzle!

Solving puzzles every day helps improve your thinking skills and keep your mind healthy. Get smart with LogicLike!

More than 550,000 kids and adults from all over the world are already improving mental skills with Logiclike.com.

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How to Solve Logic Puzzles

Last Updated: October 8, 2023

This article was reviewed by Timothy Huynh . Timothy Huynh is a Rubik’s Cube Artist based in Tampa, Florida. Timothy has been solving Rubik's Cubes professionally since 2016 and became a Guinness World Record Holder with advanced Rubik's cube-solving skills. Timothy has a follower base of over 8.6 million YouTube subscribers and 124k followers on Instagram. Internet celebrities including David Dobrik and Simu Liu have sung his praises, and Pixar has deemed his work "incredible." This article has been viewed 297,994 times.

This article includes general advice for logical reasoning problems, as well as thorough instructions for solving the most common type of logic puzzle. This type of puzzle provides a list or paragraph of clues, then asks you a question that requires you to use the clues to answer. Many books and websites that contain these logic puzzles come with a grid to help you solve them, but this article also includes instructions for making your own.

Setting up a Grid

• Here's an example problem: Three friends named Anna, Brad, and Caroline agree to bring one dessert each to a birthday party. Each friend is wearing a different color shirt. Anna wears a blue shirt. The person who brought brownies couldn't find her red shirt today. Brad didn't bring any dessert at all, which made the person wearing a yellow shirt irritated. Which person brought the ice cream?
• The example question, like all logic puzzles of this type, asks you to match two categories together. You start out knowing the names of several people and the names of several desserts, but you don't know who brought which dessert. Using the clues in the description, you need to figure out how to match each person to a dessert until you know who brought the ice cream. There's actually a third category, shirt color, which should help you get to your answer.
• Note : skip to Using a Grid if the puzzle already comes with a grid set up. Skip to Solving Other Logic Puzzles if your puzzle does not fit this description.

• Write each list separately. When the puzzle mentions a name, add it to a list of names. When the puzzle mentions a color, add it to a separate list of colors.
• Each list should have the same number of items once you've finished. If a list is too short, reread the puzzle carefully for more items.
• Some tricky puzzles will give you hints about what someone doesn't have, such as "Brad didn't make a dessert." In this case, you should add "none" to the list of desserts, which should make it the same length as the other lists.

• For instance, let's say you have three lists. Names : Anna, Brad, Caroline; Desserts : brownies, ice cream, none; and Color of Shirts : red; blue, yellow. Write a vertical list in this order: Anna; Brad; Caroline; (draw a thick line here); brownies; ice cream; none; (draw a thick line here); red; blue; yellow.

• Once you're more familiar with this system, you can get away with not writing every list in both places. We will be using this grid to match items in the vertical list (on the left) to items in the horizontal list (at the top), and sometimes you don't need to match every item. If you've never used this method before, stick with these instructions

• If the list to the left of a section and the list above a section are the same, cross it out. You'll never need to compare the list "Anna, Brad, Caroline" to the list "Anna, Brad, Caroline" – you already know that Anna is Anna.
• Cross out duplicate sections. For instance, the section that compares "Anna, Brad, Caroline" on the left and "red, blue yellow" on the top is the same as the section that compares "red, blue, yellow" on the left and "Anna, Brad, Caroline" on the top. Cross off one of these duplicate sections so you only have one to pay attention to. It doesn't matter which you cross off.

Using a Grid to Solve a Logic Puzzle

• Occasionally, a puzzle cannot be fully solved, meaning you won't be able to fill the entire grid. You should still be able to answer the question it asks.

• If you can't find that square, search the other way around. For instance, find the row labeled "blue" and the column labeled "Anna", instead of the other way around.
• Don't start with a clue that tells you something that doesn't apply, such as "Anna doesn't wear a red shirt." While that's a useful clue that should be marked with an "X", this method will assume you started with a clue that gives positive information.

• In our example, the section that has the clue you just circled compares the names of people to the colors of their shirts. The squares we're crossing off are the combinations we've ruled out, which include Brad or Caroline wearing a blue shirt, and Anna wearing a red or yellow shirt. (Typically, the introduction will tell you that each item can only be matched to one item in each other category.)

• If your puzzle gives you clues about what doesn't match, such as "Anna doesn't wear a red shirt", you should put an X in that column. However, since you haven't found a positive match, you should not cross out any other squares.

• Brad did not bring a dessert. Put a circle in the Brad-none square.
• The person wearing a yellow shirt is not Brad. Put an X in the Brad-yellow square.

• If you're solving a puzzle from another country, look up the names to find out whether they are male or female. Puzzle books that are printed more than 20 years ago will sometimes contain names that were once female, but have now become male (or vice versa).

• The green house comes before another house, so it can't be the last one.
• The black house comes after another house, so it can't be the first one.

• Marcus can't be the one who ran the mile in 6 minutes, no one was ahead of him. Cross out the Marcus-6 square.
• Marcus can't be the one who ran in 8 minutes, because that time is less than 5 minutes behind the one before it. Cross out the Marcus-8 square.
• Either the 15 or 25 minute times would work for this clue. You'll have to wait until more squares are crossed off before you can figure out which time was Marcus's.

• Let's say you've discovered that Caroline wears a yellow shirt. Check the yellow shirt column or row for information in other sections.
• Let's say you notice on your chart that the person with a yellow shirt did not bring ice cream. Because you know that person is Caroline, you can also cross out the square that connects Caroline and ice cream.
• Check Caroline's row or column too and transfer information the same way to the yellow shirt column or row.

• If a row or column within a section has every square crossed off, or more than one square with a circle in it, there was probably a mistake made along the way and you may need to start over.

• If an inconsistency occurs, your guess must have been wrong. Go back to what the chart looked like before you made your guess, and make the opposite one. Always keep track of when you made your guess with a new copy or a different color ink so it's easy to reverse if the guess was wrong.

• If you got the answer without filling out your entire chart, you may not be able to check every clue. As long as your chart doesn't contradict the clues you can check, you are probably correct.

Answering Logical Reasoning Problems

• For example: "A cell phone has fallen down a one foot (30cm) hole. How do you retrieve it? You have a wheel of cheese, three chicken feathers, and a flute." The question is designed to get you thinking about how to use bizarre objects in a creative way, but consider each word and you'll notice the hole is shallow enough to reach down and pick up the cell phone.

• For instance, "A wind is blowing from the east, but you are facing the south side of a tree. Which way are the leaves blowing?" If you don't stop to think, you might have heard "east wind" and automatically answer "east". However, the wind is blowing from the east, so the leaves are actually blowing west.

• For timed tests, if you cannot narrow it down to exactly one answer (or however many the instructions request), you may need to take a guess and move on. Make a note on your notepaper to go back to that question at the end if you have time.

• There are many practice tests available online for free for any major standardized school exam. If you can't find your exact exam, search for practice logic tests that match your education level.

• If the question doesn't give you enough information, make an assumption or estimate and state it clearly. For instance, say "Let's say the skyscraper is 100 stories tall and has 20 windows on each story" or "First, I'll assume everyone is following the speed limit, and then I'll consider what changes if some people are traveling faster."

Expert Q&A

Things You'll Need

• Graph paper
• For difficult puzzles, keep track of which clue you used by putting the number of the clue in your grid instead of a circle. You may need to add numbers to each sentence of the puzzle description first if the clues do not come in a numbered list. Thanks Helpful 0 Not Helpful 0
• Some people prefer to keep the duplicate sections when setting up a graph, while others dislike having to keep the same information in two places. Thanks Helpful 0 Not Helpful 0
• If you have a spreadsheet program on your computer, you can set up your grid there using the border tool to outline the cells. Then, if you have to choose between two answers (see Step 13), you can simply copy and paste the entire 'solution so far' to another section of the spreadsheet to prove or disprove your guess. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ http://www.psychometricinstitute.com.au/Psychometric-Guide/Logical-Reasoning-test.html

About This Article

To solve logic puzzles, start by rewriting the question to eliminate any unnecessary or nonsensical information. Then, make a list of important clues, such as colors, names, and words that indicate a particular order, like “before” and “after.” If the puzzle is a multiple choice question, check each answer to see if it contradicts something in the question, or if the answer can’t be deduced from the given information. Afterwards, if you’re still stuck, reread the puzzle to see if you’ve missed any clues. To learn more, including how to solve logic puzzles using a grid, scroll down. Did this summary help you? Yes No

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How to Solve Logic Grid Puzzles

Logic grids are deduction puzzles that depend heavily on reading comprehension. You will be given a scenario that contains several groupings od names, traits, objects, places, times, etc. There will be a list of clues to help you figure out which unique part of each group goes with the single part of each other group until everything is matched up. Some advanced puzzles may bend the norms a bit on how things are matched up, but for most puzzles, this is how they work. Usually, a grid similar to the one here will already be drawn out for you, so you can work out the solution.

Playground Pals

Most afternoons, the same four children could be seen playing together on the same playground. Each has a different piece of equipment they like to use, and each brings a different toy with them. From the clues below, can you match each child up with their favorite toy and playground equipment?

• The child with a ball asked Kiera to hold it for them while they used the slide.
• The child on the see-saw wished they had a teddy bear to ride with.
• Lenora gets motion-sick, so she avoided certain equipment.
• Clovis was amazing at coming up with rhymes while playing with his toy.
• Most of the times he went down the slide, Peyton ran to get right back in line.
• The child with the car liked to roll it along the wall climb.

For most puzzles, it’s best to solve the straightforward clues first, then look at the ones with more complex sentence structure. So we’ll start with clue #2: “ The child with on the see-saw wished they had a teddy bear to ride with .”

This tells us that the child on the see-saw is NOT the child with the teddy bear. On the grid, that means we can mark out the cell where “teddy bear” and “see-saw” intersect.

Next, we’ll jump ahead to clue #5: “ Most of the times he went down the slide, Peyton ran to get right back in line. “

Now we know that Peyton was the child using the slide. We mark that cell with a circle.

Once we do that, it is important that we mark the other cells in that row and column with an X, so we know they aren’t possible for the other options. Note that we keep these X’s within the same section as the pairing we just solved.

One more easy clue is #6: “ The child with the car liked to roll it along the wall climb .”

So we can match up car and wall climb. Again, we add the circle and X’s into the grid.

A crucial part of solving logic grids is to check across sections as you find solutions. Here, I’ve highlighted the row for Peyton and the slide, and the column for the car and wall climb.

Because we know Peyton wasn’t on the wall climb, we can be sure Peyton didn’t have the toy car.

Clues can sometimes depend on the reader’s knowledge. Let’s examine clue #3: “ Lenora gets motion-sick, so she avoided certain equipment .”

In this case, we’re expected to know that motion sickness is most often caused by rapid or swaying movement. That most likely eliminates the slide, see-saw, and swings, leaving Lenore on the wall climb.

And because of the last clue we solved, we know she must also have the toy car.

Now we can jump back to clue #1: The child with a ball asked Kiera to hold it for them while they used the slide .”

If we had solved this clue at the beginning of the puzzle, it would have told us that the child with the ball was the one using the slide, and that Kiera was neither using the ball nor the slide.

But thanks to earlier solved clues, we already know that Peyton is the child with the using the slide, so we can just fill out that he also has the ball, and that the ball is matched to the slide..

Before we move on to the last clue, notice that because of eliminations from earlier solved clues, there is only one possibility left for the favored equipment of the child who owns the teddy bear.

Not all solved cells come from the clues directly, so check your puzzle occasionally for these last space solutions. Let’s fill out that the teddy bear matches with the swings, and it also tells us that the child with the jump rope used the see-saw.

Our final clue is #4: “ Clovis was amazing at coming up with rhymes while playing with his toy. “

This one again depends on reader knowledge. There aren’t common rhyming games for teddy bears or cars, but there are for jump rope and some ball games. Since ball is already eliminated, that tells us Clovis has the jump rope.

Then, by process of elimination and cross-referencing sections, we can fill in the rest of the puzzle.

To save space in the book, the grid will usually not be reprinted in the solution section. Typically, you will only see the correct matches, something like:

• Peyton had the ball and played on the slide.
• Lenora had the car and used the wall climb.
• Kiera and her teddy bear used the swing.
• Clovis played jump rope and went on the see-saw.

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Use relationship clues – solid lines are true, dashed lines are false – to determine the correct groupings of items from several lists.

How To Solve A Logic Grid Puzzle

This is a quick start guide on how to use a logic puzzle grid to complete logic puzzles using our free online interactive logic problems.

Getting Started

The first step is to read the scenario, or the story, introducing the puzzle. Then, it is your preference how you approach the clues – you might choose to work through them in order, or to quickly scan them for the easiest clues that you can knock out straight away.

Each value from each category of facts has one unique match to each of the other categories. The best way to demonstrate this is with an example of a completed grid:

Reading through the clues, you will need to find the position where the relevant information intersects in the grid, and cross out (X) the square for information you know to be false, or tick it for information you know to be true.

Using our interactive puzzle grids, you do this by clicking once for X , and a second click to tick the box .

When you tick a box, the other options in that row and column only within the group of intersecting facts you are working in will be crossed out automatically, as they can not be true. For example, once you have determined that Sally has the Chocolate cake, no other Flavors can relate to Sally , and no other Names can relate to the flavor Chocolate , so these options are automatically crossed out for you.

Correcting Mistakes

Clicking a ticked box one more time will clear it and the X’s around it that were added automatically. It will not clear any of those X’s if they were not added automatically – i.e. if you had previously crossed out a square in that row or column, it will remain as an X.

If you have crossed out (X) a box by mistake, you will need to click it twice to clear it . The first click will tick the box, the second click will clear.

Working With Clues

Some clues will be simple: giving you one or more facts that can be immediately marked in the grid, and nothing more. If you are satisfied that there is no further information you can gain from a clue, click it once to mark it as solved . It will be moved to a “Solved Clues” list beneath the Clues section.

Other clues will be more complex. They may give you some initial information that can be marked in the grid, but you will need to return to them later when you have more information.

In difficult puzzles, you may need to take notes. For example if you have a number of inconclusive facts, like “Mary won $100 less than Tom” and “Tom won less than Simon” and “Joseph won less than the person with the purple hat but more than the person with the orange hat”, taking notes is the easiest way to test out which arrangement of facts works, or at least to eliminate some further possibilities.

Working In The Grid

Logic puzzles require you to cross reference information in different parts of the grid in order to fill out more information in other parts, leading you to eliminate further possibilities. You can then revisit your more complex clues, and you may find that they are now more helpful.

While advanced puzzle solving techniques are beyond the scope of this article, remember to check for information in a column that has been ticked, and ensure that same information has been marked in the corresponding row. Also check that information in a row that has a tick has been applied in the relevant column below.

As a quick example, in the below puzzle, because Emma has the Carrot flavor ticked, we can cross out Farewell Party for Emma’s row, because if we look down the Carrot column we can see that Farewell Party is crossed out.

Logic puzzles additionally come with a table to enter your answers in a simplified easy to read form. However if you are using an app or a website like ours, this information will be filled in for you automatically.

Ready to have a go at solving a logic grid puzzle? Try our ‘Very Easy’ rated puzzle: Daycare Dropoffs .

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Logical Puzzles

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• Andrew Hayes

A logical puzzle is a problem that can be solved through deductive reasoning. This page gives a summary of the types of logical puzzles one might come across and the problem-solving techniques used to solve them.

Elimination Grids

Truth tellers and liars, cryptograms, arithmetic puzzles, river crossing puzzle, tour puzzles, battleship puzzles, chess puzzles, k-level thinking, other puzzles.

Main Article: Propositional Logic See Also: Predicate Logic

One of the simplest types of logical puzzles is a syllogism . In this type of puzzle, you are given a set of statements, and you are required to determine some truth from those statements. These types of puzzles can often be solved by applying principles from propositional logic and predicate logic . The following syllogism is from Charles Lutwidge Dodgson, better known under his pen name, Lewis Carroll.

I have a dish of potatoes. The following statements are true: No potatoes of mine, that are new, have been boiled. All my potatoes in this dish are fit to eat. No unboiled potatoes of mine are fit to eat. Are there any new potatoes in this dish? The first and third statements can be connected by a transitive argument. All of the new potatoes are unboiled, and unboiled potatoes aren't fit to eat, so no new potatoes are fit to eat. The second statement can be expressed as the equivalent contrapositive. All of the potatoes in the dish are fit to eat; if there is a potato that is not fit to eat, it isn't in the dish. Then, once again, a transitive argument is applied. New potatoes aren't fit to eat, and inedible potatoes aren't in the dish. Thus, there are no new potatoes in the dish. \(_\square\)

Given below are three statements followed by three conclusions. Take the three statements to be true even if they vary from commonly known facts. Read the statements and decide which conclusions follow logically from the statements.

Statements: 1. All actors are musicians. 2. No musician is a singer. 3. Some singers are dancers.

Conclusions: 1. Some actors are singers. 2. Some dancers are actors. 3. No actor is a singer.

Answer Choices: a) Only conclusion 1 follows. b) Only conclusion 2 follows. c) Only conclusion 3 follows. d) At least 2 of the conclusions follows.

Main Article: Elimination Grids

Some logical puzzles require you to determine the correct pairings for sets of objects. These puzzles can often be solved with the process of elimination, and an elimination grid is an effective tool to apply this process.

An example of an elimination grid

Elimination grids are aligned such that each row represents an object within a set, and each column represents an object to be paired with an object from that set. Check marks and X marks are used to show which objects pair, and which objects do not pair.

Mr. and Mrs. Tan have four children--three boys and a girl-- who each like one of the colors--blue, green, red, yellow-- and one of the letters--P, Q, R, S.

• The oldest child likes the letter Q.
• The youngest child likes green.
• Alfred likes the letter S.
• Brenda has an older brother who likes R.
• The one who likes blue isn't the oldest.
• The one who likes red likes the letter P.
• Charles likes yellow.

Based on the above facts, Darius is the \(\text{__________}.\)

Main Article: Truth-Tellers and Liars

A variation on elimination puzzles is a truth-teller and liar puzzle , also known as a knights and knaves puzzle . In this type of puzzle, you are given a set of people and their respective statements, and you are also told that some of the people always tell the truth and some always lie. The goal of the puzzle is to deduce the truth from the given statements.

20\(^\text{th}\) century mathematician Raymond Smullyan popularized these types of puzzles.

You are in a room with three chests. You know at least one has treasure, and if a chest has no treasure, it contains deadly poison.

Each chest has a message on it, but all the messages are lying .

• Left chest: "The middle chest has treasure."
• Middle chest: "All these chests have treasure."
• Right chest: "Only one of these chests has treasure."

Which chests have treasure?

There are two people, A and B , each of whom is either a knight or a knave.

A says, "At least one of us is a knave."

What are A and B ?

\(\) Details and Assumptions:

• A knight always tells the truth.
• A knave always lies.

Main Article: Cryptograms

A cryptogram is a puzzle in which numerical digits in a number sentence are replaced with characters, and the goal of the puzzle is to determine the values of these characters.

\[ \begin{array} { l l l l l } & &P & P & Q \\ & &P & Q & Q \\ + && Q & Q & Q \\ \hline & & 8 & 7 & 6 \\ \end{array} \]

In the sum shown above, \(P\) and \(Q\) each represent a digit. What is the value of \(P+Q\)?

\[ \overline{EVE} \div \overline{DID} = 0. \overline{TALKTALKTALKTALK\ldots} \]

Given that \(E,V,D,I,T,A,L\) and \(K \) are distinct single digits, let \(\overline{EVE} \) and \( \overline{DID} \) be two coprime 3-digit positive integers and \(\overline{TALK} \) be a 4-digit integer, such that the equation above holds true, where the right hand side is a repeating decimal number.

Find the value of the sum \( \overline{EVE} + \overline{DID} + \overline{TALK} \).

Main Articles: Fill in the Blanks and Operator Search

Arithmetic puzzles contain a series of numbers, operations, and blanks in order, and the object of the puzzle is to fill in the blanks to obtain a desired result.

\[\huge{\Box \times \Box \Box = \Box \Box \Box}\]

Fill the boxes above with the digits \(1,2,3,4,5,6\), with no digit repeated, such that the equation is true.

Enter your answer by concatenating all digits in the order they appear. For example, if the answer is \(1 \times 23 = 456\), enter \(123456\) as your final answer.

Also try its sister problem.

\[ \LARGE{\begin{eqnarray} \boxed{\phantom0} \; + \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; - \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; \times \; \boxed{\phantom0}\; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; \div \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \end{eqnarray}} \]

Put one of the integers \(1, 2, \ldots , 13\) into each of the boxes, such that twelve of these numbers are used once for each (and one number is not used at all) and all four equations are true.

What is the sum of all possible values of the missing (not used) number?

Main Article: River Crossing Puzzles

In a river crossing puzzle , the goal is to find a way to move a group of people or objects across a river (or some other kind of obstacle), and to do it in the fewest amount of steps or least amount of time.

A famous river crossing problem is Richard Hovasse's bridge and torch problem , written below.

Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Person A can cross the bridge in one minute, B in two minutes, C in five minutes, and D in eight minutes. When two people cross the bridge together, they must move at the slower person's pace. The question is, can they all get across the bridge in 15 minutes or less? Assume that a solution minimizes the total number of crosses. This gives a total of five crosses--three pair crosses and two solo crosses. Also, assume we always choose the fastest for the solo cross. First, we show that if the two slowest persons (C and D) cross separately, they accumulate a total crossing time of 15. This is done by taking persons A, C, D: D+A+C+A = 8+1+5+1=15. (Here we use A because we know that using A to cross both C and D separately is the most efficient.) But, the time has elapsed and persons A and B are still on the starting side of the bridge and must cross. So it is not possible for the two slowest (C and D) to cross separately. Second, we show that in order for C and D to cross together that they need to cross on the second pair cross: i.e. not C or D, so A and B, must cross together first. Remember our assumption at the beginning states that we should minimize crosses, so we have five crosses--3 pair crossings and 2 single crossings. Assume that C and D cross first. But then C or D must cross back to bring the torch to the other side, so whoever solo-crossed must cross again. Hence, they will cross separately. Also, it is impossible for them to cross together last, since this implies that one of them must have crossed previously, otherwise there would be three persons total on the start side. So, since there are only three choices for the pair crossings and C and D cannot cross first or last, they must cross together on the second, or middle, pair crossing. Putting all this together, A and B must cross first, since we know C and D cannot and we are minimizing crossings. Then, A must cross next, since we assume we should choose the fastest to make the solo cross. Then we are at the second, or middle, pair crossing, so C and D must go. Then we choose to send the fastest back, which is B. A and B are now on the start side and must cross for the last pair crossing. This gives us, B+A+D+B+B = 2+1+8+2+2 = 15. It is possible for all four people to cross in 15 minutes. \(_\square\)

Main Article: Tour Puzzles See Also: Eulerian Path

In a tour puzzle , the goal is to determine the correct path for an object to traverse a graph. These kinds of puzzles can take several forms: chess tours, maze traversals, eulerian paths , and others.

Find the path that leads from the star in the center back to the star in the center. Paths can only go in the direction of an arrow. Image Credit: Eric Fisk Show Solution The solution path is outlined in red below.

Determine a path through the below graph such that each edge is traversed exactly once . Show Solution There are several possible solutions. One possible solution is shown below, with the edges marked in the order they are traversed.

A chess tour is an interesting type of puzzle in its own right, and is explained in detail further down the page.

Main Article: Nonograms

A nonogram is a grid-based puzzle in which a series of numerical clues are given beside a rectangular grid. When the puzzle is completed, a picture is formed in the grid.

The puzzle begins with a series of numbers on the left and above the grid. Each of these numbers represents a consecutive run of shaded spaces in the corresponding row or column. Each consecutive run is separated from other runs by at least one empty space. The puzzle is complete when all of the numbers have been satisfied. The primary technique to solve these puzzles is the process of elimination. If the puzzle is designed correctly, there should be no guesswork required.

Complete the nonogram: Show Solution

One of the many logical puzzles is the Battleship puzzle (sometimes called Bimaru, Yubotu, Solitaire Battleships or Battleship Solitaire). The puzzle is based on the Battleship game.

Solitaire Battleships was invented by Jaime Poniachik in Argentina and was first featured in the magazine Humor & Juegos.

This is an example of a solved Battleship puzzle. The puzzle consists of a 10 × 10 small squares, which contain the following:

• 1 battleship 4 squares long
• 2 cruisers 3 squares long each
• 3 destroyers 2 squares long each
• 4 submarines 1 square long each.

They can be put horizontally or vertically, but never diagonally. The boats are placed so that no boats touch each other, not even vertically. The numbers beside the row/column indicate the numbers of squares occupied in the row/column, respectively. ⬤ indicates a submarine and ⬛ indicates the body of a ship, while the half circles indicate the beginning/end of a ship.

The goal of the game is to fill in the grid with water or ships.

Main Article: Sudoku

A sudoku is a puzzle on a \(9\times 9\) grid in which each row, column, and smaller square portion contains each of the digits 1 through 9, each no more than once. Each puzzle begins with some of the spaces on the grid filled in. The goal is to fill in the remaining spaces on the puzzle. The puzzle is solved primarily through the process of elimination. No guesswork should be required to solve, and there should be only one solution for any given puzzle.

Solve the sudoku puzzle: Puzzle generated by Open Sky Sudoku Generator Each row should contain the each of the digits 1 through 9 exactly once. The same is true for columns and the smaller \(3\times 3\) squares. Show Solution

Main Article: Chess Puzzles See Also: Reduced Games , Opening Strategies , and Rook Strategies

Chess puzzles take the rules of chess and challenge you to perform certain actions or deduce board states.

One kind of chess puzzle is a chess tour , related to the tour puzzles mentioned in the section above. This kind of puzzle challenges you to develop a tour of a chess piece around the board, applying the rules of how that piece moves.

Dan and Sam play a game on a \(5\times3\) board. Dan places a White Knight on a corner and Sam places a Black Knight on the nearest corner. Each one moves his Knight in his turn to squares that have not been already visited by any of the Knights at any moment of the match.

For example, Dan moves, then Sam, and Dan wants to go to Black Knight's initial square, but he can't, because this square has been occupied earlier.

When someone can't move, he loses. If Dan begins, who will win, assuming both players play optimally?

This is the seventeenth problem of the set Winning Strategies.

Due to its well-defined ruleset, the game of chess affords many different types of puzzles. The problem below shows that you can even deduce whose turn it is from a certain boardstate (or perhaps you cannot).

Whose move is it now?

Main Article: K-Level Thinking See Also: Induction - Introduction

K-level thinking is the name of a kind of assumption in certain logic puzzles. In these types of puzzles, there are a number of actors in a situation, and each of them is perfectly logical in their decision-making. Furthermore, each of these actors is aware that all other actors in the situation are perfectly logical in their decision-making.

Calvin, Zandra, and Eli are students in Mr. Silverman's math class. Mr. Silverman hands each of them a sealed envelope with a number written inside.

He tells them that they each have a positive integer and the sum of the three numbers is 14. They each open their envelope and inspect their own number without seeing the other numbers.

Calvin says,"I know that Zandra and Eli each have a different number." Zandra replies, "I already knew that all three of our numbers were different." After a brief pause Eli finally says, "Ah, now I know what number everyone has!"

What number did each student get?

Format your answer by writing Calvin's number first, then Zandra's number, and finally Eli's number. For example, if Calvin has 8, Zandra has 12, and Eli has 8, the answer would be 8128.

Two logicians must find two distinct integers \(A\) and \(B\) such that they are both between 2 and 100 inclusive, and \(A\) divides \(B\). The first logician knows the sum \( A + B \) and the second logician knows the difference \(B-A\).

Then the following discussion takes place:

Logician 1: I don't know them. Logician 2: I already knew that.

Logician 1: I already know that you are supposed to know that. Logician 2: I think that... I know... that you were about to say that!

Logician 1: I still can't figure out what the two numbers are. Logician 2: Oops! My bad... my previous conclusion was unwarranted. I didn't know that yet!

What are the two numbers?

Enter your answer as a decimal number \(A.B\). \((\)For example, if \(A=23\) and \(B=92\), write \(23.92.)\)

Note: In this problem, the participants are not in a contest on who finds numbers first. If one of them has sufficient information to determine the numbers, he may keep this quiet. Therefore nothing may be inferred from silence. The only information to be used are the explicit declarations in the dialogue.

Of course, the puzzles outlined above aren't the only types of puzzles one might encounter. Below are a few more logical puzzles that are unrelated to the types outlined above.

You are asked to guess an integer between \(1\) and \(N\) inclusive.

Each time you make a guess, you are told either

(a) you are too high, (b) you are too low, or (c) you got it!

You are allowed to guess too high twice and too low twice, but if you have a \(3^\text{rd}\) guess that is too high or a \(3^\text{rd}\) guess that is too low, you are out.

What is the maximum \(N\) for which you are guaranteed to accomplish this?

\(\) Clarification : For example, if you were allowed to guess too high once and too low once, you could guarantee to guess the right answer if \(N=5\), but not for \(N>5\). So, in this case, the answer would be \(5\).

You play a game with a pile of \(N\) gold coins.

You and a friend take turns removing 1, 3, or 6 coins from the pile. The winner is the one who takes the last coin.

For the person that goes first, how many winning strategies are there for \(N < 1000?\)

\(\) Clarification: For \(1 \leq N \leq 999\), for how many values of \(N\) can the first player develop a winning strategy?

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Math and Logic Puzzles

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Whosoever shall solve these puzzles shall Rule The Universe!

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The Ultimate Sudoku Challenge: Master Every Grid: A Sudoku Journey Through Easy, Medium, and Expert Puzzles, Enhance Your Logic and Problem-Solving ... Sudoku, Sharpen Your Mind and Test Yourself Paperback – June 2, 2024

The Ultimate Sudoku Challenge: Master Every Grid

The Ultimate Sudoku Challenge: Master Every Grid, a comprehensive collection designed to engage your mind and enhance your problem-solving skills. With 100 pages of Sudoku puzzles of varying difficulty, this book is perfect for both beginners and seasoned solvers.

**Inside this book, you'll find:**

- **A Diverse Range of Puzzles:** Whether you're just starting out or a seasoned Sudoku expert, our puzzles range from easy to medium to expert level, ensuring there's something for everyone.

- **100 Pages of Fun and Challenge:** Enjoy hours of entertainment and mental stimulation with puzzles that are crafted to challenge and delight.

- **Skill Development:** Sharpen your logic, boost your concentration, and enhance your problem-solving abilities with each puzzle you tackle.

**Special Features:**

- **Progress Tracking:** Keep track of your progress and see how you improve over time as you work through puzzles of increasing difficulty.

- **Perfect for, teens, adults, and seniors, making it an excellent gift for any Sudoku enthusiast.

- **Great for Relaxation:** Enjoy the calming and satisfying process of solving Sudoku puzzles, perfect for unwinding after a long day.

- **Enhances Cognitive Skills:** Regularly solving Sudoku puzzles can help improve memory, focus, and overall cognitive function.

**Join the Sudoku Community:**

Join countless Sudoku enthusiasts who have discovered the joy and benefits of solving puzzles. Whether you're looking to relax, challenge yourself, or keep your mind sharp, **The Ultimate Sudoku Challenge: Master Every Grid** is your perfect companion.

**Order your copy today and start your journey to becoming a Sudoku grandmaster!**

• Reading age 5 - 18 years
• Print length 100 pages
• Language English
• Dimensions 8.5 x 0.23 x 11 inches
• Publication date June 2, 2024
• ISBN-13 979-8327359772
• See all details

Product details

• ASIN ‏ : ‎ B0D71LVYBP
• Publisher ‏ : ‎ Independently published (June 2, 2024)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 100 pages
• ISBN-13 ‏ : ‎ 979-8327359772
• Reading age ‏ : ‎ 5 - 18 years
• Item Weight ‏ : ‎ 11.2 ounces
• Dimensions ‏ : ‎ 8.5 x 0.23 x 11 inches

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BrainFlex+: Tricky Puzzles 4+

Play, learn, improve, brainflex, co., designed for iphone.

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Get Smarter with Brain-Boosting Puzzle Games! Train your cognitive skills like memory, logic, and problem-solving through our fun and challenging brain games. Based on cognitive research, these tricky puzzles will give your mind a workout while keeping you entertained. Unique Puzzles: • Block Escape - control small blocks to find a best route from chaotic obstacles, improving your thinking ability; • Pointer Rotation - aim the pointer at the disc quickly and accurately, which is an excellent and interesting reaction training; • Logic Connection - use your imagination and logical ability to connect 1000+ different but closely related pictures; • Double Ring Rotation - control two rings to make timely and correct reactions, exercising your left and right brains concurrently. Super Assistance: • 30+ unique brain teasers for all ages and levels • Personalized daily training and progress tracking • Increasing difficulty to continually challenge you Excited? Try This App to Start Brain Training! Elevate your brainpower and unlock your full potential. User Agreement: https://plusbrainflex.com/userEn.html Privacy Policy: https://plusbrainflex.com/Privacy.html If you have any questions or suggestions, contact us([email protected]).

Version 1.2

Our update contents: 1. New game for brain training added: Logic Fill, a game use your logical thinking to solve puzzles and fill in the grids according to the clues. 2. New game for reacion training released: Miner Master. Seize the opportunity and grab the brightest treasure!

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Crossword puzzles helping solve the problem of Aphasia

CLEARWATER, Fla. — What might look like a room full of people filling out crossword puzzles iss really so much more.

The group that gathered recently in Clearwater truly appreciate words. And they know how hard words are to come by some times.

What You Need To Know

 the annual voices of hope for aphasia fundraiser shined a spotlight on the disease that affects so many families.  the word play event featured a crossword puzzle competition.  member of the tampa bay rays leant their support and showed off their crossword puzzle skills..

Some of the people in the room suffer from aphasia, a disorder where finding the right words is a daily struggle. People like Mark Severini, whose wife Mikhele brought him to the word play event to help raise funds to combat the disease that robs those afflicted with it of the simple art of conversation.

“It’s so encouraging to see to that this disease is out there and it’s becoming more knowledgeable,” Mikhele said. “People are understanding what it is.”

Mark’s struggled with Aphasia for years. He has trouble forming words, but not doing puzzles. They actually help keep his brain sharp, one of the many things that help him cope with his disorder. Many had never heard of aphasia until Hollywood superstar Bruce Willis announced in 2022 that he had the disease, an affliction that affects a part of the brain controlling language. According to the National Aphasia Organization, more than 180,000 people in the United States are diagnosed each year. Part of the goal of this fundraiser is to inform and enlighten.

“Know that everything is still in here, they’re just having difficulty getting it out or understanding what you’re saying,” said Debbie Yones, Voice of Hope for Aphasia Program Director. “So have patience. Have a little bit of compassion.”

In its second year, the Voices of Hope for Aphasia fundraiser drew a packed room. Two of the competitors were Tampa Bay Rays pitchers Pete Fairbanks and Jason Adam. The two leant their support to the cause and showed off their crossword puzzle skills. Rays pitchers routinely do puzzles as part of their pre-game rituals. But this was a different game. This time, the words they were writing down were literally raising money for a great cause. Last year’s event raised more than $120,000, a number they hope to surpass this year.

“I really hope people will come out of this event appreciating and having a little bit more understanding of aphasia because I think part of our mission is to raise awareness,” Debbie said.

That’s what Mikhele Severini wants for her husband. She wants people to understand that even though he might have trouble communicating, he knows what he wants to say, he just can’t get it out sometimes.

“It’s something that nobody would ever dream up but it just hits you and it’s mind numbing for a lot of people,” she said.

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wordplay, the crossword column

Potential Goal for a Unicorn

Paolo Pasco and Sarah Sinclair deliver.

By Deb Amlen

Jump to: Today’s Theme | Tricky Clues

Note to readers: In the past, Wordplay indicated crossword clues with quotation marks. In crossword construction and editing, though, clues are typically indicated by brackets, a practice Wordplay is now following .

THURSDAY PUZZLE — I’m hungry. Are you hungry?

Let’s sink our teeth into this crossword by Paolo Pasco and Sarah Sinclair. That should assuage our cravings for a fun puzzle. If you’re solving online, try not to get any pixels caught in your teeth; I’m all out of grid floss.

And if you are tempted to give up on this one for some reason, don’t — there’s a nice surprise when you’ve had your fill.

Today’s Theme

At first, I thought that Mr. Pasco and Ms. Sinclair’s rounded grid represented a cell, with all its parts swirling around inside, and that the revealer was going to be something like “The mitochondria is the powerhouse of the cell.”

I was disabused of that notion when I got to the actual revealer, at 26A, which reads [Pepperoni, mushroom or green pepper … or what each cluster of black squares represents in this puzzle]. The answer is PIZZA TOPPING, but I had a problem: The answer, like many of this puzzle’s entries, didn’t fit in its slot.

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