# 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.

2,658 questions
Filter by
Sorted by
Tagged with
58 views

### Different ways to place the workers on Santorini board game

This combinatorics problem is based on the board game Santorini. Consider a $5 \times 5$ chess board (but all squares are equal, say they're all white). Player A places $2$ (equal) white workers in $2$...
38 views

### Theorem on embedding of Mazes

I was reading the Wikipedia article on mazes and at one point it makes with no citation the claim that 'Any maze can be mapped into a higher dimension without changing its topology.' I assume they ...
55 views

### Which theorems and definitions do I need to know to prove the impossible chessboard puzzle has a solution for every number of squares?

I saw this problem on the youtube channel called 3blue1brown. The problem is the following: There is a 8 x 8 chessboard, two prisoners (Prisoner 1 and prisoner 2), a key and a warden. Each of the ...
80 views

### Find the number of ways to move from top left corner of a grid to its bottom right corner

Consider a 36 by 36 grid and I'm currently standing on top left corner. I want to get to the bottom right corner while stepping on each of the square exactly once. I am only allowed to move up,down,...
96 views

### the slower grape crusher

Two Grape Crushers take 4 days to crush certain amount of grapes.If one of them crushed half the grapes and the other crushed other half , then they complete the job in 9 days. How many days will it ...
40 views

### Minimum stops to find all cats (Difficult Probability Question) [closed]

There are 8 houses, and 8 cats, with one cat in each house initially. Each house has capacity of 8. You can visit one house at a time and leave immediately after. Every time you leave the house, an ...
72 views

### Tricky probability problem (2 possible solutions ?!)

The problem is stated as follow: You are trying to complete the World Cup sticker album, for that you need distinct 600 normal stickers and 80 distinct holographic stickers. It is known that the ...
73 views

### Riddle on implication

There was this question I don't understand in quizz. Prosecutor says: If he is guilty, he must have had accomplice. The question was: which of the following proves that he was guilty. And the correct ...
33 views

### Matrix A,B,C 2/3 not invertible

Let A,B,C be matrices such that the algebraic operations are defined. Question: Disprove the following statement (by giving a counter example): If AB=C and 2 of the 3 matrices are not invertible, then ...
281 views

### Cutting a cuboid to fit in a hemisphere

Today while making dinner consisting of instant noodles, I thought of the most ridiculous question I've ever asked this site. The Instant Noodle Problem Suppose you are a college student preparing one ...
63 views

### A multiplication problem: $OUI \times OUI = OOUUI + OOUUI$

Here's a $6$th-grade exam problem: $$OUI \times OUI = OOUUI + OOUUI$$ $O, U$ and $I$ are digits. e.g $365 \times 365 = 33665 + 33665$ (not the case) Thus, because the digits are into account I ...
73 views

### How many squares in a three-dimensional $n \times n \times n$ cartesian grid?

This brings the classical question to three dimensions. Given a three-dimensional Cartesian grid of $n \times n \times n$ points (that is $(n-1) \times (n-1) \times (n-1)$ unit cubes), how many ...
62 views

### Filling numbers in 19 cells set in a big hexagon such that…

In social groups this question (see the photo below) of filling integers in 19 small cells set in a big hexagon is asked, such that their sum in each layer(row) in all three directions is 50. Next, it ...
31 views

### Solving method for fractions having Prime numbers as Denominator.

I have a question , like $30 = 1.18x$ , and $30 = 0.82 y$ , find $x+y$. when solving, $x=1500/59$, $y=1500/41$. Since the denominator is involving prime numbers I was wondering is there any method ...
1k views

### An illusionist and their assistant are about to perform the following magic trick

Let $k$ be a positive integer. A spectator is given $n=k!+k−1$ balls numbered $1,2,\dotsc,n$. Unseen by the illusionist, the spectator arranges the balls into a sequence as they see fit. The assistant ...
41 views

### Hypercube traversal algorithm

A recursive algorithm that I'm working on is based on traversing an $n$-dimensional hypercube. The quantity associated to each vertex can be computed by combining the values of all the adjacent ...
46 views

### The Optimal Toaster Problem

Suppose I have 3 slices of bread, say $b_1$, $b_2$, $b_3$, and I want each to be double toasted. My toaster has a capacity of 2 slices at a time. The 'perfect' way of doing this would be to toast in ...
49 views

### mathematical circles (Russian experience) hard problem [duplicate]

There are several cars on a circular track, and there is enough gas in all their tanks taken together to drive one car around the track. Prove that at least one of the cars can drive around the track ...
44 views

### Will you find a way to quickly find out if this number has a $0$ in the tens digit?

Here's how the puzzle works! Here is a list of numbers : $1,2,3,4,5,6,7,8,9$ I will give you some numbers in this list (numbers can be repeated). When receiving those numbers, you will multiply them ...
46 views

### Solution explanation: linear map with invariant subspaces

Problem 1. (20 points) Let $V$ be a 10-dimensional real vector space and $U_{1}, U_{2}$ two linear subspaces such that $U_{1} \subseteq U_{2}$, $\dim U_{1} = 3$ and $\dim U_{2} = 6$. Let $E$ be the ...
136 views

### Turning on a nuclear briefcase with the smallest possible number of keystrokes

On the front panel of the "nuclear briefcase" there are $12$ buttons. Each button controls its own switch: pressing it toggles it from ON to OFF and back. The initial position of the ...
31 views

### Solution verification: Picking stones consecutively puzzle

Puzzle:Two players pick consecutively 1,2,3 or 4 stones from a stack of 101 stones. The player who picks the last stone wins. Suppose that both players play perfect, does the first or second player ...
39 views

### Generalized solution to popular “Wires in elevator shaft brainteaser”

I recently came across this puzzle. The premise is there are N wires with ends at the top and bottom of an elevator shaft, but you don't know which ends are ...
61 views

### Solution verification: chess board all squares white except one

Problem: On a 8x8 chessboard all squares are the color white, except for one square (which is black). Show that you can't get to the situation that all squares are white by only recoloring whole rows ...
35 views

### Proof verification: circle pawn problem

Problem: A circle is divided in 6 sectors by 3 diameters. Each sector contains a pawn. We are allowed to chose two pawns and move each of them to a sector bordering the one it stands on at the moment. ...
24 views

### D&D Probability of 2 Attempts

I wanted to get the full probability of 2 attempts made at 60% chance of success. I was looking at a different chain of math and found my probability to hit an enemy is 60% per each attack but I was ...
118 views

### Throwing a dice and add the digit that appears to a sum and stopping when sum $\geq 100$.

You keep on throwing a dice and add the digit that appears to a sum. You stop when sum $\ge 100$. What’s the most frequently appearing digit in all such cases? $1$ or $6$? I believe the probability of ...
112 views

### Determine the number of ways to go from $(1,1)$ to $(n,1)$ on a chessboard

Problem: Let $S$ be a $n \times 3$ chessboard. Let a rook walk on the board, it is allowed to move $1$ step horizontally or vertically every step. Determine the number of ways the rook can go from the ...
25 views

Let $ab$ be a two-digit number($a \ne b$) with its reverse as $ba$, it is simple to check that $|ab-ba|=9|a-b|$. Interestingly, if we continue as $$|ab-ba|=cd \to |cd-dc|=ef \to |ef-fe|=gh \to |gh-hg|... 1answer 89 views ### Alibaba is the leader of Forty Thieves. One day, the thieves found 100 golden coins. The Forty Thieves wanted 80 golden coins, but.. Alibaba is the leader of Forty Thieves. One day, the thieves found 100 golden coins. The Forty Thieves wanted 80 golden coins, but the greedy Alibaba just want to own all the treasure. So he said to ... 2answers 130 views ### Handshaking puzzle Problem: At a party there are n people, some people give each other a hand. After the party everyone writes down on a piece of paper how many people he/she shook hands with. It turns out there are ... 1answer 53 views ### Does anyone know what branch of mathematics this biconditional is from or recognize the notation? While looking into a picture-based puzzle, I came across the following expression: \Xi \leftrightarrow( T ( \ulcorner \Xi \urcorner ) \rightarrow S ) T ( \ulcorner \Xi \urcorner ) \leftrightarrow \... 2answers 73 views ### Puzzle about a spinning table with a coin on each corner. [The first part of this puzzle was inspired by a puzzle I found on fivethirtyeight.com, but the rest is novel] Part 1 There is a square table with a coin on each corner. You cannot see the table. The ... 1answer 93 views ### Probability of the Sex of a Child In this Probability Theory course, the question A girl I met told me she has one sibling. What is the probability that her sibling is a boy? is asked, with the answer stated as \frac{2}{3}. I'm ... 2answers 63 views ### Coloring the numbers 1 and to including 10 with constraint The question: Consider the colors red, green, blue. In how many ways can we color the numbers 1 up to including 10 such that: 2 consecutive numbers dont have the same color odd numbers cant be red. ... 0answers 36 views ### Determine the number of ordered triples The question: Determine the amount of ordered triples of sets (A_1,A_2,A_3) such that: A_1 \cup A_2 \cup A_3 =\{1,2,3....,10\}, A_i \cap A_j=\emptyset for i\neq j. My approach: Consider ... 2answers 58 views ### Puzzle on Reasoning The following puzzle was introduced by the psychologist Peter Wason in 1966, and is one of the most famous subject tests in the psychology of reasoning. Four cards are placed on the table in front of ... 2answers 101 views ### What are some puzzles that are solved by using invariants? This is certainly not a question with one "correct answer", but I think it's interesting and mathematical in nature. Essentially, my question is: do people know any not-well-known puzzles ... 1answer 30 views ### What number should be placed in that last slot? I came across a very difficult puzzle. What number should be placed in that last slot? I only know 16 is not the correct answer, because 11 is before 10. 1answer 55 views ### I don't get why the answer is 5-diamond? It could also be Queen-heart and 4-heart. The aim is for A and B to guess the right card from the below deck of cards. A is told the number only of the card. B is told the shape only of the card. Based on the following conversation between A ... 2answers 100 views ### How many triangles in a chess board, allowing diagonals? So I saw a question about how many rectangles in a grid of squares that looked like an "L", and it got me thinking: If we have an 8\times 8 grid, how many triangles are there? This has its ... 6answers 471 views ### In a row of 40 kids, 22 are sitting next to girls and 30 are sitting next to boys. How many girls are there? There are 40 kids sitting in a row. Number of kids sitting next to girls is 22, Number of kids sitting next to boys is 30. How many girls are sitting in a row? This is a problem from my brother's ... 1answer 34 views ### Given K * N grid such that L spots on the grid are filled, what is the expected number of columns with at least one spot filled? This seems to be a simple question but I can't seem to wrap my head around it. let's say we throw L marbles onto a K*N grid, such that each spot in the grid can hold at most one marble. how many ... 1answer 134 views ### A square is cut into three equal area regions by two parallel lines find area of square. [closed] A square is cut into three equal area regions by two parallel lines that are 1 cm apart, each one passing through exactly one of two diagonally opposed vertices. What is the area of the square ? 1answer 35 views ### Smallest subset of integers that you can use to produce 1,2,…,40 Find the smallest subset of integers that you can use to produce 1,2,...,40 by only using "+" or "-", and each number in the subset can be used at most one time. There is a hint that 0 must be ... 0answers 72 views ### What is the minimum number of doors to a laboratory that would satisfy these conditions? S scientists are working in a lab that they want to keep secure. They want to install D doors to the lab, such that each door has L locks that each require a different key to open. The ... 4answers 289 views ### Ratio of area covered by four equilateral triangles in a rectangle The following puzzle is taken from social media (NuBay Science communication group). It asks to calculate the fraction (ratio) of colored area in the schematic figure below where the four colored ... 1answer 216 views ### If 11+11=4 and 22+22=16, then 33+33=\text{???} (Facebook math quiz) [closed] From a Facebook math quiz:$$\begin{align} 11 + 11 &= 4 \\ 22 + 22 &= 16 \\ 33 + 33 &= \text{???} \end{align} Maybe I'm just stupid but the answer to this is $36$, however I think it ...
Suppose $A>B>C>D$ be four unit digit natural number and $P_1=ABCD$(descending digits) and $Q_1=DCBA$ (ascending digits) and $R_1=P_1-Q_1$, according to Kaprekar $R_1$ could be 6174. If not ...