Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [puzzle]

For questions about the mathematical principles behind puzzle, games, riddles, or their possible solutions. Questions that are not strictly mathematical in nature should be asked on Puzzling Stack Exchange.

Many puzzles, games, and riddles are based on mathematical concepts. This tag is for questions that ask about the mathematics behind a puzzle, game, or riddle, or about the solutions to mathematical puzzles.

If you already know the answer to the puzzle you are posting, you might consider posting your question on Puzzling Stack Exchange, instead. If you do end up posting your question on Mathematics Stack Exchange (MSE), please read the following meta posts on these kinds of questions before asking your question:

If you do end up posting on MSE, please make it clear in your question that you are "puzzling" the community and that you will be answer the question yourself if no one in the community posts your desired solution.

3301 questions
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Math for sequential movement puzzles?

It feels like there should be some area of math that can be used to make sequential movement puzzles like the 15-puzzle or Sokoban puzzles easier to solve. I guess for symmetrical examples like the 15-puzzle group theory can be helpful, but what…
Jeff Bass
  • 221
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A Combinations Logic Puzzle.

So there's a puzzle I heard, and I think I know the answer to, but I wanted to share my logic to see if I am correct. I am also interested in a more mathematical way to solve it which escapes me. Here's the setup: There are 4 boxes labelled A,B,C…
Josh Knight
  • 99
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Given a square pattern as shown. What is the missing number?

$$\begin{array}{|c|c|c|}\hline 2&11&2243\\\hline4&19&3739\\\hline 5&23&4487\\\hline 3&186&?\\\hline\end{array}$$ What is the missing number ? I have searched for days but still no results, the only thing I noticed is…
jdsjhcbjhde
  • 153
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A simple yet confusing puzzle - Fake money involved!

A very simple but confusing puzzle.A lady buys goods worth rs.200 from a shop.(Shopkeeper selling the goods with zero profit).The lady gives him 1000 rs note. The shopkeeper gets the change from the next shop and keeps 200 for himself and returns…
selvin
  • 161
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Mice and poisonous wine brainteaser

The question is: You have 1000 bottles of wine for a birthday party. 20 hours before the party, the winery indicate 1 bottle of wine is filled with poison, without telling you which bottle. You have 10 lab mice to test this on. The poison is so…
24n8
  • 1,455
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Arranging 10 counters in 5×5 grid

Draw a 5×5 grid. Place 10 counters in it. You can place only one counter in each space. Get an even number of them in each row and column and two main diagonals. Unfortunately, I have not been able to solve this one :(
Manu Chadha
  • 135
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A book is $90\%$ likely to be illustrated; an illustration is $90\%$ likely to be in color. How many of $10000$ books must have a color illustration?

This problem is in Art and Craft of Problem Solving by Paul Zeitz. It's an easy looking puzzle which is not "so obvious" according to the problem itself. It says - Of all the books at a certain library, if you select one at random, then there is a…
user732848
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3 answers

How to calculate the time it will take to solve a jigsaw puzzle

Is there a way to know how much time it would take to solve a jigsaw puzzle if I already solve this same puzzle with a different number of pieces while timing myself? Example of a landscape puzzle: (number of pieces) time to solve mm:ss (24)…
pikarie
  • 23
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Making $61$ by inserting arithmetical operations between $5\;5\;7\;3$. (The Australian Carriage Game (Number Puzzle))

I know this isn't really the theme of what is going on here, but this problem is killing me, so I thought you guys could help. The Australian Carriage Game comes from the fact that Australian trains have 2 letters and 4 numbers making up a carriage…
Pedro Hablespanyos
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How many numbers from $1$ to $1000$ can be written as the sum of $4$s and $5$s?

I like the numbers $4$ and $5$. I also like any number that can be added together using $4$s and $5$s. Eg, $$9 = 4+5 \qquad 40 = 5 + 5 + 5 + 5 + 5 + 5 + 5 +5$$ How many number have this property from 1 to 1000? Multiples of $4$s and $5$s are…
OvermanZarathustra
  • 85
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Filling in the blanks on a magic triangle

I am struggling with this problem. I have tried out a few numbers with no luck, and I have a feeling there is a slick method to this that I am missing, rather than just guesswork. Any hints, would be appreciated.
Jamminermit
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Is it possible to send a suitcase with an illegal measurements inside legal one

The airport allows sending a suitcase if the sum of its length, width and height does not exceed a certain constant. Question: Is it possible to send a suitcase with an illegal measurements by placing it inside one with legal ones?
Ilan Aizelman WS
  • 4,128
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Four Bug Problem - why is the solution referencing from the vertex of the square to the middle of the square

Imagine four bugs situated at each vertex of a unit square. Suddenly, each bug begins to chase its counterclockwise neighbour. If the bugs travel at 1 unit per minute, how long will it take for the four bugs to crash into one another? First, the…
ilovetolearn
  • 1,341
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Prove that two sums must be equal among the possible sums of the rows, columns, and diagonals of a $3\times 3$ arrangement of boxes.

A $3 \times 3$ arrangement of boxes is filled with one of the numbers one, seven, or nine. Prove that of the eight possible sums along the rows, the columns, and the diagonals, two sums must be equal. I tried to use the pigeonhole principle, but…
joem
  • 43
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How to separate kinder surprise eggs?

Andrew and Bob got $37$ kinder surprise eggs. In $20$ of them there are cars and in $17$ there are hippo. Unfortunately, it is not known which surprise in the each eggs. They want to divide all the eggs among themselves, not opening them so that the…
aid78
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