Questions tagged [puzzle]

This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an existing solution.

2,331 questions
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Hat guessing with 100 hats case

My question is regarding to the question which was asked here: A riddle about guessing hat colours (which is not among the commonly known ones) $100$ prisoners are put a hat on top of their head, ...
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Two squares of side 5 and 2 respectively. They are touching each other. Diagonals of the square are joined. find the area of the shaded part?
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$100$ prisoners problem - But here they write their guess on paper [duplicate]

A variant of the $100$ prisoners problem. $100$ prisoners are given each either a white hat or a black hat. They can see each other's hat but not their own and they cannot communicate. Each ...
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Four frogs are located at the corners of a square on the plane [duplicate]

Four frogs are located at the corners of a square on the plane. At each step a frog jumps over another frog and lands in the symmetrically opposite location. Question: Can the frogs find a way to ...
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how many guards are needed to protect a king from an assassin in n-torus ($\mathbb R^n/\mathbb Z^n$) [closed]

Question: how many guards are needed to protect a king from an assassin if all of them are located on the $n$-torus $\mathbb R^n/\mathbb Z^n$? The location of the king and the assassin are known, ...
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Solving the recurrence $g(n)=g(n-1)\left(1+\frac{1}{n}\right)+\left(1+\frac{1}{n}\right)$ with $g(0)=0$

I ran across the following math puzzle: a mouse is on a circle with circumference of 100 units and every turn he walks on the circle a unit of 1 after every turn the circle is increased by 100 units (...
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Proving all variables are equal

I came across a puzzle lately. Let $A$ be a matrix of size $(2n+1)$ by $(2n+1)$. The diagonal of $A$ is all zeros. Every other entry of $A$ is either $+1$ or $-1$. Each row of $A$ sum to zero. In ...
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Black and white shirts puzzle

I’m not familiar enough with probability to be able to even begin to approach this myself, but this puzzle has been plaguing me. Assume I have $m$ black shirts and $n$ white shirts, where $m > n$. ...
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Partition of a rectangle into squares problem

recently I encountered this problem: "Show that a rectangle can be partitioned into finitely many squares if and only if the ratio of its sides is rational." I have found the a solution which I need ...
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Solve Riddle With Algebra

There is a riddle and I believe it can be solved by algebra - please assist A boy has as many sisters as brothers, but each sister has only half as many sisters as brothers. How many brothers and ...
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Explanation of Freeman Dyson's solution of the counterfeit coin problem

Freeman Dyson's paper, The problem of the pennies Math. Gaz., 30 (1946) 231-234, offers a solution to a counterfeit coin detection problem. I quote his solution of one case as follows. I would ...
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5x5 Bingo Puzzle (odds)

I have a question that is very similar to this one 5x5 Bingo Puzzle [Logical thinking problem]. 5 people participate in a custom game. They are given blank cards, in which they have to fill numbers ...
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Searching for a special book in the Library of Babel

In The Library of Babel, there are all the possible 410-page books of a certain format and character set. There is a legendary book, called a total book, which is supposed to be the catalogue of the ...
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Is there a general effective method to solve Smullyan style Knights and Knaves problems? Is the truth table method the most appropriate one?

Below, an attempt at solving a knight/knave puzzle using the truth table method. Are there other methods? Source : https://en.wikipedia.org/wiki/Knights_and_Knaves
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Total number of ways to arrange objects subject to constraint [duplicate]

Suppose that you are ticket collector in Cinema office. It cost 50 dollars to watch a movie. There are 20 people in line. 10 people in that line have exactly 100 dollar bills and 10 people have ...
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Calculating the parity of number of heads on a 8x8 chessboard?

Below is an article where I facing a problem! Please refer this completely before answering my question! Impossible Escape : http://datagenetics.com/blog/december12014/index.html I got all the sub-...
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Puzzles and exercises to improve mathematical intelligence and spatial thinking

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking?...
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Game: Removing Matches from Stacks

Given two players $A$ and $B$ and two piles of matches with size $N$ and $M$ respectively. Player $A$ goes first and players alternate turns. On each turn, the player must remove a positive number of ...
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Finding the Shortest Path passing through all Routes [closed]

I'm wondering if there's actually an easy technique (other than trial & error) to find the shortest path (which covers all paths). I googled and discovered that all paths in this diagram cannot ...
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Hard puzzle about people walking in the street. [duplicate]

We have a 1 dimensional street (straight) where people can either walk left or right. They all walk with the same speed. If two people meet they instantly change their direction (without loss of speed)...
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n coin balancing problem

Rank weights of coins with a balance scale I want to generalized above problem into $n$ coins. i.e., using balance scale, sort $n$ coins in order. Slightly more generalizing the above post, [...
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Differential equation involving brachistochrone

I have that: $$f(x)=e^{\Psi'(x)}$$ So I took the natural log of both sides: $$\ln(f(x))=\Psi'(x)$$ Then I integrated both sides: $$\int \ln(f(x))dx =\Psi(x).$$ Here $f(x)$ is required to be ...
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A coin flipping game

I've been thinking about the following game for a while and am curious if anyone has any ideas of how to analyze it. Problem description Say I have two biased coins: coin 1 that shows heads with ...
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How to create the largest prime number using: $5,7,11$ eight times?

I can use these numbers nine times or less(repetitions are allowed), to create the largest prime number. My attempt: I know that the highest prime that could be made has to be less than $99$. The ...
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Cryptogram: $XYZ\div8 = ZX$, remainder $Y$

Say we have the division algorithm Where X,Y,Z represent a non-zero digit and the remainder is Y. What is the three-digit number XYZ? From what I gather, I re-arranged the division into an equation:...
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How to find the total number of auras possible for a tile of a given tier?

PLEASE NOTE! A different problem that uses the same ruleset (technically a subset of this one since i ask multiple questions here) that can be solved with brute force and pen-and-paper has been posted ...
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MU puzzle with an axiom it is solvable

Recently, I read about MU puzzle: https://en.wikipedia.org/wiki/MU_puzzle It is said about MU puzzle that: It can be interpreted as an analogy for a formal system — an encapsulation of ...
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Find out non-overlapping schedule to execute jobs

I have a set of 6 jobs to be run via a scheduler. Let's call them jobs A,B,C,D,E & F. 'A' & 'B' take 2 mins to complete, 'C' , 'D' , 'E' & 'F' take 3 min each to complete. No job is ...
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Expressing positive integers as $2a+4b+5c+6d$, for $a$, $b$, $c$, $d$ non-negative, with $a+c$ as small as possible

Let $n$ be a positive integer where $n > 1$ and $n \neq 3$ I need a way to return all solutions of $2a + 4b + 5c + 6d = n$ where $a, b, c$, and $d$ are non-negative integers and $a + c$ is as ...
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Prove there exists $2\times 2$ checkerboard-colored square in a $100\times 100$ table colored black and white.

"Each cell of a 100 × 100 table is painted either black or white and all the cells adjacent to the border of the table are black. It is known that in every 2 × 2 square there are cells of both colours....
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Question about a problem in Smullyan's Gödelian Puzzle Book

I'm reading the chapter "Fixed Point Puzzles" and there is a problem titled "An Open Problem" after problem #18. The chapter introduces a machine which operates on strings of upper case letters, which ...
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There are 314 coins in 21 open boxes. In each move you can take 1 coin from each of any two boxes and put them into a third box and…

There are 314 coins in 21 open boxes. In each move you can take 1 coin from each of any two boxes and put them into a third box and in the final move you take all the coins from one box. What is the ...
There is puzzle solution of which doesn't click for me. One person has $5$ bottles of wine, another one $3$ bottles. There is also third person. Together all three drank this $8$ bottles of wine ...