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.

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To Mock A Mockingbird: Flower Garden (Math Puzzle)

Question: In a certain flower garden, each flower was either red, yellow, or blue, and all three colours were represented. A statistician once visited the garden and made the observation that whatever three flowers you picked, at least one of…
snmcdonald
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Jigsaw Puzzle Help

I have a puzzle I'm trying to solve and I have all the border pieces set out but I'm pretty sure some are missing. How do I figure out how many pieces are in the border? It's a 1000 piece puzzle and the dimensions are 20" by 27".
user92623
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A troublesome logic puzzle.

Here're two distinct integers $x,y$, both greater than $1$ but less than $100$. Student $A$ and $B$ know the values of $xy$ and $x+y$ respectively. Let's hear their conversation. $A$: I don't know what $x,y$ are. $B$: Me too, but I already know…
JSCB
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How can they guess my number just by knowing which rows it appears in?

I've saw this "trick" many times in math club, I'm just wondering if it's real that they know ESP, or is it just a scam? We're given 5 rows: $\newcommand{\tsf}[1]{\mathsf{\text{#1}}}$ $$\begin{array}{c|cccccccccccccccc} \tsf{Row 1} & \sf 1 & \sf 3 &…
user87624
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General form for math puzzle solution

A math puzzle from a friend who is on a math team: The irrational number: $0.12345678910111213141516171819\dots$ has the string $314$ first occurring starting at the $17$th decimal place. When does the first occurrence of $2012$ start? The answer to…
user14069
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Color a matrix such that each row and column has one color exceed $\frac{3}{4}$

Color a $m\times n$ matrix with black and white color. There is the same number of white squares and black squares. Is it possible to color in a way such that on each row and each column, the number of squares of one color exceeds $\frac{3}{4}$? I…
donguri
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Mathematical guessing

A total of 2,879 votes have been distributed among the seven candidates in a one-party primary election. It is known that none of the candidates has obtained the same number of votes as another and that if the number of votes obtained by any of the…
Carlos
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Riddle of the fox and the holes, with n holes

I was wondering if the problem of fox and holes (There are five holes in a line. One of them is occupied by a fox. Each night, the fox moves to a neighboring hole, either to the left or to the right. Each morning, you get to inspect a hole of…
Marine Galantin
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Arranging bricks safely

The goal is to arrange bricks safely so that there is no line that can be cut through. For example This arrangement is considered unsafe because you can cut through the red line. This is a safe arrangement because you cannot cut through any…
Pizzaroot
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A knights and knaves problem with one truth-saying knave; what is the minimum number of questions needed to find this atypical knave?

I found somewhere this 'knights and knaves' problem (I can't locate the source anymore): An Island is inhabited by exactly $n$ people, with $n>2$, of whom some (the exact number is not known) are knights, who alwais tell the truth, and some are…
L. Bresolin
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10 zeroes, 9 ones, and 8 twos are written on the board. Given the operations, can you set all numbers to become zero?

You are allowed to replace 0 and 1 with two 2s, 0 and 2 with two 1s, or one and two by two zeroes. My thinking was that you had to set all numbers to 1 and 2. However, this isn't possible since there are an odd number of numbers and each operation…
Gerard L.
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With 24 people, 4 tables, and 4 sessions, how to make sure that each person meets as many people as possible?

We have 24 people, and 4 tables. Over 4 sessions, each person will visit each table once. What system can I use to make sure each person gets to each table once, while making sure they meet as many other people as possible (so dont go from table to…
Mike Langlois
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How many possible combinations are there in Hua Rong Dao?

How many possible combinations are there in Hua Rong Dao? Hua Rong Dao is a Chinese sliding puzzle game, also called Daughter in a Box in Japan. You can see a picture here and an explanation here . The puzzle is a $4 \times 5$ grid with these…
Will Glass
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How many archers do I need to deploy to destroy an Archer Tower?

I was playing Clash of Clans and came across this interesting problem. Consider the case when I'm attacking an enemy war base with an Archer. My archer can cause a damage of 12 hitpoint per second. The enemy's Archer Tower has a total hitpoint of…
Joseph John
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A maths number puzzle

We have these digits : $1,2,3,4,5,6,7,8,9$. Using these digits, we have to make two numbers such that their product must be as large as possible. We have to use all digits only once. I did $97531\times 8642$ and got $842862902$
Amun - The god
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