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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 295,394 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."

Community 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

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• ↑ 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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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?

Problem Loading...

Note Loading...

Set Loading...

5 Logical Puzzles That Will Bend Your Brain

March 16, 2021 by Anthony Persico

5 Logical Puzzles That Will Bend Your Brain (Answers Included!)

A Post By: Anthony Persico

Are you looking to take on some fun and challenging logical puzzles and put your brain power to the test?

Attempting to solve logic puzzles is one of the best ways to improve your problem-solving and logical thinking skills while having lots of fun at the same time.

Today’s post shares a collection of 5 logical puzzles for kids and adults that gradually progress in difficulty—and there’s also a special bonus puzzle that has been stumping people for over 100 years!

Note that the solution to each logic puzzle is included at the bottom of the post (we recommend trying all of the problems on your own first and then checking to see if your answers are correct afterwards).

Are you ready to get started?

Some of these puzzles can be solved in under one minute, while others are tricky enough to stump you all day long, putting your brain to the test!

Today, you’ll have a chance to give your brain a workout by figuring out a few of these famous logic and number puzzles.

So, are you up for the challenge? And don’t forget to try the bonus puzzle—a simple yet tricky riddle that has been around for over 100 years.

And if you need more detailed explanations of how to solve each logic puzzle, check out our 5 Logical Puzzles That Will Bend Your Brain video below, and be sure to click the like button and leave a comment!

Watch the 5 Logic Puzzles Video:

Logical puzzle #1.

How many total blocks are in the diagram below?

Keep reading to the bottom of this page to see the answer key AND click here to see the video that explains the solution to this problem.

Click here to sign-up for our free weekly email newsletter!

Logical Puzzle #2

How far can a bear walk into the woods?

Logical Puzzle #3

How can you flip the gummy bear pyramid upside down by moving only 3 gummy bears?

Are you looking for more super fun Math Riddles, Puzzles, and Brain Teasers to share with your kids?

The best-selling workbook 101 Math Riddles, Puzzles, and Brain Teasers for Kids Ages 10+!  is now available as a PDF download. You can get yours today by clicking here .

Logical Puzzle #4

On Bert’s 14th Birthday, his younger brother Chip was half his age. If today is Bert’s 31st birthday, how old is Chip?

Logical Puzzle #5

If there are 7 bears in a room and they each hug each other once and only once, how many total bear hugs were there altogether?

Bonus Logical Puzzle!

An explorer who walks one mile south, one mile east, and one mile north and ends up right back where he started. While he is walking, he sees a bear. What color is the bear?

Ready for the answers?

Remember that there’s no rush to find the answers to today’s logic puzzles. It’s ok to wait to until you’ve found an answer to each problem before scrolling down to see the answers below.

ANSWER KEY:

1.) 11 Blocks

2.) Half-Way (after that, the bear is walking out of the woods)

3.) Diagram:

4.) Chip is 24 years old

5.) 21 Hugs

Bonus: The Bear is White (Polar Bear at the North Pole)

Are you looking for more super fun Math Puzzles to share with your kids?

My best-selling workbook 101 Daily Math Challenges for Engaging Students in Grades 3-8  is now available as a PDF download. You can get yours today by clicking here .

Did I miss your favorite math riddle for kids? Share your thoughts, questions, and suggestions in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's  MashUp Math  and an advisor to Amazon Education's ' With Math I Can ' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel  . Or spending way too much time at the gym or playing on my phone.

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 Logic Puzzles Questions

The Hardest Logic Puzzle Ever?

If a giraffe has two eyes, a monkey has two eyes, and an elephant has two eyes, how many eyes do we have?

Here in the question, it is asked how many Eyes We have so that means here the person who has asked the question is also including the person who is suppose to give the answer. In a clear understanding, the Conversation is happening between 2 people 1st who asked the question and 2nd to whom it has been asked, which means there are 4 eyes.

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Solve the Logical Puzzle ?

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90 D in a R A

90 D in a R A => 90 degrees in a Right Angle.  

This is similar to 

26 L of the A =  26 Letters of the Alphabet

12 S of the Z .

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One rabbit saw 6 elephants while going towards River. Every elephant saw 2 monkeys are going towards river. Every monkey holds one tortoice in their hands.

How many animals are going towards the river?

From the given data,

1 rabbit is going towards river not the six eephants. And these 6 elephants saw 2 monkeys are going towards river. Each monkey is holding 1 tortoice.

Hence, number of animals going towards river are 1 rabbit, 2 monkeys and 2 tortoice

= 1 + 2 + 2

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206 B in a B?

206 Bones in the Human Body.

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'Rhythm of eyes' city name in India?

'Rhythm of eyes' logically means  Nainital in India.

The other cities are:

No Zip - Chennai

Mr. City - Srinagar

Do Acting - Karnataka.

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A man was murdered in his office.

The suspects are Ericson , Maggi , Joel , Benny , Sona ,  Patick .

A calendar found near the man has blood written 6, 4, 9, 10, 11.

Who is the killer?

If we consider the given numbers  6, 4, 9, 10, 11 to be the month number then we can easily find the killer.

6 – June – J

4 – April – A

9 – September – S

10 – October – O

11 – November – N

Hence the answer is JOEL .

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They come out at night without being called and are lost in the day without being stolen. What are they?

Stars are what that come out at night without being called and are lost in the day without being stolen.

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Solving the Five-House Logic Problem by Hand

In this follow-up to my post on the classic Five-House Logic Problem, I provide the solution to the riddle plus a few tips for finding it.

SPOILER ALERT! This post contains the solution to a classic logic problem that I wrote about in my previous post :

Please stop reading now and visit the above link if you would like to solve this problem yourself before seeing the solution.

I promised in my previous post that I would share a solution to this brain teaser.

To avoid accidentally giving away the answer to readers who want to solve the puzzle on their own first, I'll use ChatGPT to provide some relevant filler material.

How To Solve a Logic Puzzle

[MIKE] : What are the basic steps to solving a logic puzzle?

[ChatGPT] : Solving a logic puzzle involves a systematic approach that requires careful analysis and deduction. While the specific steps may vary depending on the puzzle, here is a general outline of the basic steps to solve a logic puzzle:

• Read the instructions : Start by thoroughly reading the puzzle instructions to understand the rules, constraints, and objectives of the puzzle. Pay close attention to any given clues or hints.
• Identify the puzzle type : Logic puzzles come in various types, such as grid-based puzzles, deductive reasoning puzzles, or verbal puzzles. Determine the type of puzzle you are dealing with, as this will help you decide on the appropriate solving strategy.
• Analyze the given information : Carefully study all the information provided in the puzzle, including the clues, statements, and any accompanying diagrams or charts. Identify any direct or indirect relationships or constraints between the given elements.
• Create a visual representation : If the puzzle involves multiple elements or entities, it can be helpful to create a visual representation, such as a grid, chart, or diagram. This will allow you to track and organize the information more effectively.
• Deduce and make inferences : Based on the given information, start making deductions and inferences about the relationships between the elements. Look for clues that provide direct or indirect connections, eliminate possibilities, or provide conditional statements.
• Use logical reasoning : Apply logical reasoning skills, such as deduction, induction, and elimination, to narrow down the possibilities and eliminate incorrect or impossible scenarios. Use the information you have gathered to draw conclusions and make logical inferences.
• Test hypotheses and make educated guesses : As you gather more information and eliminate possibilities, test different hypotheses and make educated guesses to fill in the missing pieces of the puzzle. Use the process of elimination to discard incorrect options and focus on the most likely solutions.
• Iterate and refine : Continue iterating through the puzzle, revisiting the information and clues, refining your deductions, and updating your visual representation as needed. Cross-check your deductions to ensure they are consistent and coherent.
• Solve step-by-step : Break down the puzzle into smaller, more manageable parts or sub-problems. Solve one part at a time, using the information you have gathered and the deductions you have made. Gradually build on your solutions until you can solve the entire puzzle.
• Verify and check : Once you have completed the puzzle, go back and verify your solution. Double-check your deductions, ensure all the given constraints are satisfied, and confirm that your solution is logical and consistent.

Remember that practice and patience are essential for solving logic puzzles. With time and experience, you will become more adept at recognizing patterns, making deductions, and finding efficient strategies to tackle different types of puzzles.

Who drinks water? The Norwegian.

And who owns the zebra? The Japanese person.

Here's the full neighborhood configuration from the MS Access-based solution that I'm still working on.  The houses are listed in numerical order from left to right:

• The Norwegian lives in the yellow house.  This person drinks water, has a fox, and grows roses.
• The Ukrainian lives in the blue house.  This person drinks tea, has a horse, and grows marigolds.
• The English person lives in the red house.  This person drinks milk, has snails, and grows geraniums.
• The Spaniard lives in the ivory house.  This person drinks orange juice, has a dog, and grows lilies.
• The Japanese person lives in the green house.  This person drinks coffee, has a zebra, and grows gardenias.

My By-Hand Approach

First, I started by creating a list of each category and the values that comprise it:

• Position of the house
• Nationality of the owner
• Color of house

Next, I drew five columns on my page with each column representing a house and its position.  I then filled in the items that directly related to the positions of the houses:

• Milk is drunk in the middle house
• The Norwegian lives in the first house on the left
• The Norwegian lives next to the blue house

After that, I reread the rules and put orange tally marks next to each value every time it was mentioned.  This helped me identify those items that were mentioned multiple times, as they tended to be the next lowest hanging fruit.  The following values each appeared twice in the rules:

• Green House

Next, I wrote the value pairs at the bottom of my sheet.  This gave me a quick reference with a higher signal-to-noise ratio than the original rules.  For example:

• roses - yellow (the yellow house had roses)
• geraniums - snails
• lilies - OJ
• ivory -> green (the green house is to the right of the ivory house)
• marigolds <--> fox (the house with the fox is next to the house with the marigolds)

After that, I used initials to show all the available values for each category and each house.  For example, "F/H/Z" in the Pet row would indicate that house might keep a fox, a horse, or a zebra as a pet, but not a dog or snails.

My next step was to draw lines between pairs of items that went together in the house columns.  This helped identify incompatible pairs of items.  For example, the Japanese person could not keep snails as a pet because they each went with a different flower.

For my final step, I had the three houses on the right side of the neighborhood that could be the following colors:

• House 3: Ivory or Red
• House 4: Ivory or Green
• House 5: Green or Red

Since several other items depended on these values, I simply wrote out all the remaining configurations and then compared them to see which three would be compatible.

* NOTE: In between each of the above steps, I set aside about 15 minutes for staring blankly at the page, scratching my head, and looking generally confused.  Total time to solution was about two hours.  If my actual approach was as systematic as my write-up made it appear, I might not have taken four times as long to solve the puzzle as fellow Access MVP Maria Barnes who finished in about 30 minutes (well done!).

No, I didn't Google the answer...

Here's what my scratch paper looked like when I was finished:

Acknowledgements

• Portions of this article's body generated with the help of ChatGPT
• Image by Aline Dassel from Pixabay

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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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BrainTwister #15: Domino strips

Can you solve this week’s logic puzzle? Plus our quick quiz and the answer to last week’s problem

By Peter Rowlett

10 April 2024

#15 Domino strips

Set by Peter Rowlett

There are three ways to cover a 3 × 2 grid with dominoes.

How many ways are there to cover a 4 × 2 grid? What about a 6 × 2 grid?

Can you find a pattern that would help you work out the number of different ways dominoes can be used to cover any n × 2 rectangle?

Solution next week

#14 Factor graphs

Here’s a factor graph of 1-10:

You can connect every number up to 14, but adding 15 requires drawing lines to 3 and 5, which leads to crossing. If we exclude…

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85 Tricky Riddles for Adults That Will Really Test Your Knowledge

These brain-teasers range from super easy to downright mind-boggling.

We've got plenty of clever, hard and downright mind-boggling brain-teasers for you to solve. But if you're looking for something a little easier, we also got a ton of kid-friendly riddles you can figure with your children. There are also plenty of math riddles , too, which will come in handy as icebreakers during work meetings, in the classroom or at a party.

And don't think we just left you hanging with these questions. All of the answers to the mysteries are included.

Be sure to let us know which was your favorite in the comments below!

Easy Riddles

Q: What 5-letter word typed in all capital letters can be read the same upside down?

Q: The more you take, the more you leave behind. What am I?

A: Footsteps.

Q:David's father has three sons: Snap, Crackle, and _____?

Q: What is more useful when it is broken?

Q: I am easy to lift, but hard to throw. What am I?

A: A feather.

Q: Where do you take a sick boat?

A: To the dock-tor.

Q: Which fish costs the most?

A: A goldfish.

Q: What goes up, but never comes down?

Q: A cowboy rode into town on Friday. He stayed for three nights and rode out on Friday. How is this possible?

A: His horse's name is Friday.

Q: What has a neck but no head?

A: A bottle

Q: What is full of holes but still holds water?

A: A sponge

Q: How do you spell COW in thirteen letters?

A: SEE O DOUBLE YOU.

Q: Why is Europe like a frying pan?

A: Because it has Greece at the bottom.

Math Riddles

Q: If 2 is company and 3 is a crowd, what are 4 and 5?

Q: I add 5 to 9 and get 2. The answer is correct, so what am I?

A: A clock. When it is 9 a.m., adding 5 hours would make it 2 p.m.

Q: Rachel goes to the supermarket and buys 10 tomatoes. Unfortunately, on the way back home, all but 9 get ruined. How many tomatoes are left in a good condition?

Q: What is 3/7 chicken, 2/3 cat, and 2/4 goat?

A: Chicago!

Q: If a zookeeper had 100 pairs of animals in her zoo, and two pairs of babies are born for each one of the original animals, then (sadly) 23 animals don’t survive, how many animals do you have left in total?

A: 977 animals (100 x 2 = 200; 200 + 800 = 1000; 1000 – 23 = 977)

Q: I saw my math teacher with a piece of graph paper yesterday.

A: I think he must be plotting something.

Q: If you multiply this number by any other number, the answer will always be the same. What number is this?

Q: I am an odd number. Take away a letter and I become even. What number am I?

Q: What 3 numbers give the same result when multiplied and added together?

A: 1, 2, and 3 (1 + 2 + 3 = 6 and 1 x 2 x 3 = 6).

Q: What's a single-digit number with no value?

Q: A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

A: Nine years.

Funny Riddles

Q: How can you drop a raw egg from a height onto a concrete floor without cracking it?

A: Concrete floors are very hard to crack.

Q: Pronounced as 1 letter, And written with 3, 2 letters there are, and 2 only in me. I’m double, I’m single, I’m black blue, and gray, I’m read from both ends, and the same either way. What am I?

Q: Who has married many women but was never married?

A: The priest

Q: Forward, I am heavy; backward, I am not. What am I?

Q: What can you hold in your right hand, but never in your left hand?

A: Your left hand.

Q: If two snakes marry, what will their towels say?

A: Hiss and hers

Q: What does a man do only once in his lifetime, but women do once a year after they are 29?

Hard Riddles

Q: Four cars come to a four-way stop, each coming from a different direction. They can’t decide who got there first, so they all go forward at the same time. All 4 cars go, but none crash into each other. How is this possible?

A: They all made right-hand turns.

Q: I have a head like a cat and feet like a cat, but I am not a cat. What am I?

A: A kitten.

Q: Who makes it, has no need of it. Who buys it, has no use for it. Who uses it can neither see nor feel it. What is it?

A: A coffin.

Q: What has hands but cannot clap?

A: A clock.

Q: Paul's height is six feet, he's an assistant at a butcher's shop, and wears size 9 shoes. What does he weigh?

Q: What gets broken without being held?

A: A promise.

Q: Poor people have it. Rich people need it. If you eat it you die. What is it?

A: Nothing.

Q: What is the longest word in the dictionary?

A: Smiles, because there is a mile between each ‘s’.

Q: Throw away the outside and cook the inside, then eat the outside and throw away the inside. What is it?

A: Corn on the cob.

Q: What is at the end of a rainbow?

A: The letter W!

Q: What kind of tree can you carry in your hand?

Q: They come out at night without being called, and are lost in the day without being stolen. What are they?

Q: What is always in front of you, but can’t be seen?

A: The future.

Q: You’ll find me in Mercury, Earth, Mars, Jupiter, Saturn, and Uranus. But never Neptune, or Venus. What am I?

A: The letter “R”.

Q: How many months have 28 days?

A: Every month has 28 days.

Q: I can be cracked, made, told, and played. What am I?

Q: I cannot talk, but I always reply when spoken to. What am I?

A: An echo.

Q: When is the top of a mountain similar to a savings account?

A: When it peaks one’s interest.

Q: A man goes out for a walk during a storm with nothing to protect him from the rain. He doesn’t have a hat, a hood, or an umbrella. But by the end of his walk, there isn’t a single wet hair on his head. Why doesn’t the man have wet hair?

A: He’s bald.

Q: I love to dance, and twist. I shake my tail as I sail away. When I fly wingless into the sky. What am I?

Q: When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

A: The horizon

Q: You see a boat filled with people. It has not sunk. But when you look back, you don’t see a single person on the boat. Why?

A: All the people on board are married.

Q: What is it that no one wants to have, but no one wants to lose either?

A: A lawsuit.

Q: I welcome the day with a show of light, I stealthily came here in the night.I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

A: The morning dew.

Q: What goes through cities and fields, but never moves?

Q: What can be touched but can't be seen?

A: Someone’s heart.

Q: In a bus, there is a 26-year-old pregnant lady, a 30-year-old policeman, a 52-year-old random woman, and the driver who is 65 years old. Who is the youngest?

A: The baby of the pregnant lady.

Q: When it is alive we sing, when it is dead we clap our hands. What is it?

A: A birthday candle.

Q: What can go through glass without breaking it?

Q: What gets bigger the more you take away?

Q: I have no life, but I can die. What am I?

A: A battery.

Q: What kind of room has no walls, door or windows?

A: A mushroom.

Q: It belongs to you, but your friends use it more. What is it?

A: Your name.

Q: What 2 things can you never eat for breakfast?

A: Lunch and dinner.

Q: I make a loud sound when I’m changing. When I do change, I get bigger but weigh less. What am I?

A: Popcorn.

Q: It has keys, but no locks. It has space, but no room. You can enter, but can’t go inside. What is it?

A: A keyboard.

Q: I’m orange, I wear a green hat and I sound like a parrot. What am I?

A: A carrot.

Q: What runs all around a backyard, yet never moves?

A: A fence.

Q: Take off my skin - I won't cry, but you will! What am I?

A: An onion.

Q: What invention lets you look right through a wall?

A: A window.

Q: What is always on its way but never arrives?

A: Tomorrow.

Q: Two girls were born to the same mother, on the same day, at the same time, in the same month and year, and yet they're not twins. How can this be?

A: The two babies are two of a set of triplets.

Q: What has a bottom at the top?

A: Your legs.

Q: What can you catch but never throw?

Q: What has many teeth but cannot bite?

Q: What has branches, but no fruit, trunk, or leaves?

Q: What thrives when you feed it but dies when you water it?

Q: What do you buy to eat but never consume?

A: Cutlery.

Q: Two fathers and two sons are in a car, yet there are only three people in the car. How?

A: They are grandfather, father, and son.

Q: A bus driver goes the wrong way down a one-way street. He passes the cops, but they don’t stop him. Why?

A: He was walking.

Q: If an electric train is traveling south, then which way is the smoke going?

A: There is no smoke—it's an electric train.

Q: Where is the only place where today comes before yesterday?

A: The dictionary.

Q: What can you put in a bucket to make it weigh less?

Q: How can kids drink beer and not get drunk?

A: By sticking to root beer.

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NYT Connections Answers And Hints - April 11, 2024 Solution #305

Need some help sorting your mermaids from your pixies?

It's a new day and that means a new puzzle wall to solve in the New York Times's Connections game. If you're looking to save your streak and only want to nail down that last pesky category, don't worry - we have all the hints you could need.

10 Best Indie Puzzle Games

You'll find everything you need below, from vague hints as to what you should be looking for to the outright answers. Whether you're looking for a nudge in the right direction or a sneaky way to preserve your blemish-free record, you've come to the right place.

If you're here by mistake and instead need the answers for April 10 , click here .

Category Hints

Today's puzzle is pretty nasty, but has some fun categories to work out.

We'll present these hints from the easiest category to the hardest , as prescribed by the puzzle itself - Yellow, Green, Blue, then Purple.

If you want today's category hints, click below ! These will not spoil the actual names of the categories but will nudge you in the right direction.

Today's yellow category has things you might ask a hairdresser for.

Today's green category has items you'd use if being very precise was important.

Today's blue category has things connected to buildings that supply them with crucial necessities.

Today's purple category may put you in mind of burgers, chips (fries, if you insist on being wrong), and advertising.

Herring Watch : There are some clues that may put you in mind of people in charge of other people (King, Ruler, Colonel) - ignore this false connection. Popular costumes for Halloween is also a false connection... but not far off the true connection.

Today's Answers

Today's puzzle is on the trickier side; we only had one life remaining when we solved it.

If you want today's answers, click below !

Today's answers are listed below:

Yellow Category : Haircuts, With "Cut"

Bowl, Buzz, Crew, Pixie

Green Category : Measuring Instruments

Compass, Ruler, Scale, Watch

Blue Category : Water And Gas Conduits

Channel, Line, Main, Pipe

Purple Category : Fast Food Mascots

Clown, Colonel, King, Mermaid

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wordplay, the crossword column

Carding at a Bar

Peter Gordon rises to the occasion.

By Sam Corbin

Jump to: Today’s Theme | Tricky Clues

MONDAY PUZZLE — Solve crosswords for long enough, and you may start to perceive entries not as words, but as mere strings of letters whose meaning rests entirely on their clues. At 29-Across, for example, we have a “Witty reply to ‘You’re the kind of person who asks too many questions’” — AM I? But if the clue were “French friend,” we would interpret this same string as AMI. The same ambiguity could be true of “Door.” As one word, it represents a “Way out.” As two words, the entry fills in the blank for “____ die.”

Peter Gordon also relies on multiple meanings for his theme in today’s crossword. In this case, however, seeing through the ruse isn’t so much about peering downward into the puzzle as it is about looking up.

Today’s Theme

The good news about Mr. Gordon’s theme, in contrast to the subject of its theme, is that you won’t need any special glasses to take it in. This TOTAL ECLIPSE, revealed to the naked eye at 46-Across, is clued as both an “Event across the U.S.” and part of a “1983 Bonnie Tyler hit” perfect for such an occasion. With 57-Across, we complete the hit’s title: “TOTAL ECLIPSE OF THE HEART.”

The rest of the theme set makes up what one might call the ideal eclipse playlist, filled with songs deemed “apt to play” during the moon’s passage between the Earth and the sun. There’s “MOONSHADOW” (17A) by Cat Stevens, Santana’s “INTO THE NIGHT” (23A) and U2’s “STARING AT THE SUN” (36A).

Do you have any songs to add to Mr. Gordon’s list? I would love to hear your recommendations for eclipse-viewing music. (New York City, while not in the path of totality , will still have an impressive partial eclipse if clear skies prevail.)

Tricky Clues

6A. Government agents are generally known as G-men. A more specific “Government agent targeting counterfeiters, in dated lingo” is a T-MAN, in which the T indicates the U.S. Treasury. In a puzzle from 1994 by Chet Currier, this figure was clued as a “U.S. narc.”

40A. The “Radioactive element discovered by the Curies” in 1898 is POLONIUM — named after Marie Curie’s native Poland.

43A. “Shown to the door” is an oddly lengthy past participle, and requires some grammatical untangling to arrive at its entry — SEEN OUT.

5D. We get the adjective for “Bearlike” via Latin: URSINE comes from the noun form for bear, ursus. Incidentally, the name Ursula is a diminutive form of “she-bear,” which gives me a newfound respect for the villain of “The Little Mermaid.”

22D. I ate a beef-filled variety of this “Potato turnover” — most often found “in a Jewish deli,” per the clue — roughly once a week while growing up. It’s called a KNISH, and because of its import from Yiddish, it is one of those rare words in which both the K and the N are voiced.

45D. In lofty language, to “Deliberately avoid” something is to ESCHEW it. ( Gesundheit .)

Constructor Notes

The original version of this puzzle had the Rolling Stones’ “Paint It, Black” at 23-Across. The puzzle was rejected because that entry didn’t feel “as persuasive thematically as the other songs in the theme set.” With the lyrics “I wanna see the sun blotted out from the sky/I wanna see it painted, painted, painted/Painted black,” it seemed pretty good to me, given that the moon blots out the sun during an eclipse. But I was allowed to offer replacements, and INTO THE NIGHT was accepted. (The Goo Goo Dolls’ “Black Balloon” and Garry Miles’s “Look for a Star” were some of my other suggested replacements.) I will be leaving the American Crossword Puzzle Tournament immediately after Puzzle 7 to head north for Plattsburgh, N.Y., where there will be more than three minutes of totality. May all of you eclipse chasers have cloudless skies!

Join Our Other Game Discussions

Want to be part of the conversation about New York Times Games, or maybe get some help with a particularly thorny puzzle? Here are the:

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Connections Companion

Improve Your Crossword Solving

Work your way through our guide, “ How to Solve the New York Times Crossword .” It contains an explanation of most of the types of clues you will see in the puzzles and a practice Mini at the end of each section.

Want to Submit Crosswords to The New York Times?

The New York Times Crossword has an open submission system, and you can submit your puzzles online . For tips on how to get started, read our series “ How to Make a Crossword Puzzle .”

Totally in the Dark?

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Trying to get back to the main Gameplay page? You can find it here .

Sam Corbin writes about language, wordplay and the daily crossword for The Times. More about Sam Corbin

It’s Game Time!

Take your puzzling skills in new directions..

WordleBot , our daily Wordle companion that tells you how skillful or lucky you are, is getting an upgrade. Here’s what to know .

The editor of Connections , our new game about finding common threads between words, talks about how she makes this daily puzzle feel fun .

We asked some of the best Sudoku  solvers in the world for their tips and tricks. Try them to  tackle even the most challenging puzzles.

Read today’s Wordle Review , and get insights on the game from our columnists.

We asked Times readers how they play Spelling Bee. The hive mind weighed in with their favorite tips and tricks .

Ready to play? Try Wordle , Spelling Bee  or The Crossword .

How to Solve a Logic Puzzle

If you're new to grid-based logic puzzles, this tutorial will teach you the basics. Start with the "Introduction" first, then move on to the tutorials discussing specific clues or solving methods. Each tutorial contains a number of different slides - you can advance to the next slide by clicking "Next slide" at the bottom of each page, or by using the circled numerical links below each slide. Choose your specific tutorial from the list below to get started.

True and False Clues

The easiest types of clues in logic puzzles are generally the true and false clues, as they lay out a simple one-to-one proposition, i.e. A is equal to B, or A is not equal to B. In this first example, we have a false clue: "Laura's tattoo didn't cost $55." How do we represent this relationship on the grid?

Next slide »

It's simple. You find the column for "Laura" and the row for "$55" and you mark an X (representing a false relationship) where the two intersect.

« Prev slide » Next slide »

Easy enough, right? Now we have an example of a true clue. "The green tattoo cost $40." So how would you represent this true relationship on the grid?

Just like with the false relationship, we find the column for "green" and the row for "$40" and we mark a green circle (representing a true relationship) where the two intersect. But there's more to be done when it comes to true relationships...

Remember: in a logic puzzle, every item in every group can be used once and only once. So if you know the green tattoo is $40, as in this example, you immediately know that the green tattoo isn't any of the other price options ($35, $45, $50 or $55). Similarly, the $40 tattoo can't be any color other than green. So whenever you mark a true relationship on the grid, you must always mark all other options within that subgrid false for those two items. (Our website will always mark these false relationships for you automatically.)

« Prev slide »

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How many letters are in cow?

Puzzle solutions for Wednesday, April 10, 2024

Note: Most subscribers have some, but not all, of the puzzles that correspond to the following set of solutions for their local newspaper.

USA TODAY crossword

Play the USA TODAY Crossword Puzzle .

Los Angeles Times crossword

Today’s crossword (mcmeel), daily commuter crossword.

Play the USA TODAY Sudoku Game .

Jumbles: GEESE      AROMA      PLIGHT      HYMNAL      

Answer: When the lunar colony opened a new domed restaurant, diners enjoyed its − ATMOSPHERE

(Distributed by Tribune Content Agency)

CRYPTOGRAPHY PUZZLES 

Celebrity cipher.

"Hope makes people good, a lot of the time. You hope for a brighter future, and resentment is outweighed." − Daisy Ridley

(Distributed by Andrews McMeel)

Cryptoquote

WE'RE FOOLS WHETHER WE DANCE OR NOT, SO WE MIGHT AS WELL DANCE. − JAPANESE PROVERB

(Distributed by King Features)

WHEN THE HONEYBEE HAD OTHERS AT ITS RESIDENCE, IT WOULD SAY, "WELCOME TO MY BUMBLE ABODE."

OTHER PUZZLES

DRUM      LUTE      FLUTE      BUGLE      CLARINET      

TESTS, SELECTED, DESTITUTE, ELECTION, NAUSEA

Scrabblegrams

7 little words, find the words.

Into the rough again

(Distributed by Creators Syndicate)