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 ...

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3answers
59 views

Swimming pool problem: Time required to empty the swimming pool

In a swimming pool, 6 swimmers have to swim such that 3 swimmers start from end A at intervals of 1 minute and the remaining 3 start from end B at intervals of 2 minutes where A and B are opposite ...
2
votes
0answers
42 views

The $8$-Puzzle and $2$-Cycles

I have been studying the $8$-puzzle and have thus far managed to wrap my head around the following information: The following illustrates the solved position of the $8$-puzzle, where $9$ is the empty ...
1
vote
0answers
52 views

Looking for an alternative solution for the mutilated chessboard problem

Given a mutilated chessboard where two diagonally opposite squares are missing (the unmutilated version of it has $64$ squares), and given $31$ domino pieces, is it possible to cover the entire ...
2
votes
5answers
97 views

A peasant and his cows

A peasant owns $2n+1$ cows. When he separates a cow from the rest of the herd, he can split the $2n$ remaining ones into two groups of $n$ cows such that the sum of weights of each group are equal. ...
4
votes
2answers
87 views

A tale of two palindromes (sum of squares of two palindromes is a perfect square).

I am just curious on wether there are infinitely many palindromes say $p_1$ and $p_2$ satisfying: $p_1^2+p_2^2$ is a perfect square with $\gcd(p_1,p_2)=1$. I believe that there are some but, are ...
0
votes
1answer
106 views

How many different ways can I add three numbers to get a certain sum?

I'm working on a little program and I stumbled across a small math problem I can't quite solve. This is what the program does. A sum is generated. Now, the user can subtract either 3, 4, or 5 from ...
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vote
1answer
56 views

Find appropriate number fill in the blanks [closed]

Find appropriate number fill in the blanks
3
votes
1answer
66 views

What gambling/board game or real life thing can (surprisingly) be modelled as a linear programming problem?

So I've taken Linear Programming 101. I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook ...
2
votes
0answers
202 views

How to solve instant insanity puzzle with graphs.

So I have a 10 cube insanity puzzle, I constructed the graph (I'll post pc later) based on the colors the problem is that there is just way to many lines and nodes to see the solution. Is there any ...
7
votes
1answer
1k views

Maths question from an IQ test [duplicate]

It is possible that 25 is the correct answer since I guessed (educated guess) that and got a predication of 170 IQ (obviously not accurate) I saw that 63 + 25 = 88 and 16 + 9 = 25 but then ...
3
votes
1answer
49 views

Numbers interpreted as sets and functions

In set theory numbers are defined as sets $$\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\},\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\},\dots$$ where $n+1=n\cup\{n\}$ and ...
2
votes
2answers
111 views

Prove a length of 6 in a triangle diagram.

A puzzle: Three equilateral triangles of size 3, 4, and 7 touch at a corner. The other corners of the size 4 triangle are 3 away from a 3 corner, and 7 away from a 7 corner. How far apart are the ...
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votes
2answers
328 views

logical problem (how long did you walk?)

My wife is very kind, she always picks me up at work by car and drives me home. Today, I finished at work 30 minutes earlier! So I decided to walk home... on the way I met my wife. She was on her way ...
0
votes
0answers
57 views

Systematic Gaussian elimination on a binary matrix?

I am trying to understand the mathematics behind the lights out puzzle (http://mathworld.wolfram.com/LightsOutPuzzle.html). There's a very helpful webpage at ...
19
votes
2answers
423 views

Shortest possible unreachable shape

This is a follow up to Is every shape possible with a snake? . Imagine a 2d snake formed by drawing a horizontal line of length $n$. At integer points along its body, this snake can rotate its body ...
1
vote
1answer
114 views

The sum of $1+1+1+1+…$

My teacher recently showed me a rather weird result and I would like to know if he was just tricking me or if he was serious. He showed me that $g=1-1+1-1+1-...=\frac{1}{2}$ Then he said that ...
3
votes
1answer
84 views

Are the odds one in a million? [closed]

This is a from a card game call Magic the Gathering And my question is regarding this video during a tournament match (best of 5). One in a million. You dont need watch the video I will explain the ...
57
votes
0answers
6k views

“The Bachelorette Problem” (slightly adapted from Tao's Google+ account) [duplicate]

The following puzzle being very much recreational for me, I couldn't resist myself from sharing it with my fellow MSE user friends. Let's have a look at it. You are the most eligible bachelorette ...
7
votes
5answers
1k views

Hank and his old car

I'm sort of struggling with this riddle told to me by a friend: Hank owns a car. He has been taking good care of his car; In fact, he has been taking such good care of it that the age of Hank, ...
0
votes
1answer
28 views

Counting length of pyramid's sides puzzle

I have four blocks, the first block of length two, the second of length three, the third of length four and the fourth of length five, and I can arrange them in the following way: I am allowed to ...
1
vote
1answer
50 views

Puzzle - Finding which balls are heavy

Puzzle my sister told me about, I've yet to solve it and im open to ideas. You have 6 balls, 2 red ones, 2 blue ones, and 2 green ones. Out of each pair, 1 is heavy and 1 is light (so overall you ...
0
votes
1answer
23 views

A limited composition of two unlimited functions on natural numbers?

Can someone give an example of two functions $f,g:\Bbb N\to \Bbb N$ such that $|\operatorname{Im}f|,|\operatorname{Im}\,g|\notin\Bbb N$, but such that $|\operatorname{Im}\,g\circ f|\in\Bbb N$?
4
votes
2answers
143 views

A puzzle about a sum and product of two numbers

The Gray Man wants to test The Hardy Boys. He says to them, "I've selected 2 positive integers, both bigger than one." He then proceeds to reveal their total and product to Frank and Joe ...
2
votes
2answers
92 views

Explaining a Pattern in a Matrix Generated by Minimum Excluded Number in Rows & Columns

I have been given the following math puzzle: You are given a matrix that is filled by the following rule: Every cell i,j is evaluated by taking the lowest non-negative number that is not ...
9
votes
2answers
164 views

Is every shape possible with a snake?

Imagine a 2d snake formed by drawing a horizontal line of length $n$. At integer points along its body, this snake can rotate its body by $90$ degrees either clockwise or counter clockwise. If we ...
1
vote
1answer
60 views

How do you calculate 45 min without any clock and sense of time? [duplicate]

There is two non uniform,unequal ropes. Every thing like weight,length etc are not same. But one thing is same. Each one is burned down within 1 hour. I'm giving you these two ropes and a candle just ...
17
votes
2answers
492 views

Is it true that we can get zero for all $(x,y,z)\in\mathbb{N}^3$?

There are three distinct positive integers $x$, $y$, and $z$. We can choose two numbers $a,b\in\{x,y,z\}$, where $b\leq a$, then replace $b$ by $2b$ and replace $a$ by $a-b$. Is it true that there ...
0
votes
1answer
79 views

Progressive Matrices Puzzle

I have this mind puzzle which has bothered me the latest days. QUESTION: CHOOSE ANSWER: . I realize that there are relations (rotation and translation) between three pairs of the matrices (1-4, ...
6
votes
6answers
3k views

A number when divided by 2, 3, 4, 5, 6 leaves a remainder of 1 but it is divided by 7 completely.

I came across a question which is as follows: Find out the smallest number which leaves remainder of 1 when divided by 2, 3, 4, 5, 6 but divided by 7 completely. What I did is given below step wise. ...
1
vote
1answer
32 views

Rigorous proof for a maximization problem

Problem: Eight players entered a round-robin tennis tournament. At the end of the tournament, a player who wins $N$ sets will take home $N^2$ dollars. The entry fee is $17.50 per player. Why is this ...
1
vote
1answer
47 views

Can this be proven for any maze?

http://9gag.com/gag/aKgrQDj Is there a maze that can't be solved simply by following that strategy. Assumption Solution must exist Sticking your hand to the right or left don't solve that.
7
votes
1answer
416 views

A gameshow logic puzzle

A friend posed this puzzle to me a few months ago, and it has tortured me ever since. The puzzle goes something like this: Suppose you're on a gameshow, and there are three doors: two doors have a ...
10
votes
2answers
223 views

Gardner riddle on mathemagicians

A cute riddle (but maybe not so easy!) from Gardner: At a gathering of mathemagicians, the Grand Master and his 8 disciples are seated at a round table. The Grand Master will judge each of his ...
15
votes
3answers
375 views

Is it possible to uniquely number faces of a hexagonal grid with consecutive numbers?

You have a grid of regular hexagons. The aim of the game is to have each hex contain the numbers 1-6 on its edges. Each edge must also be connected to another edge that has a value one higher and ...
2
votes
0answers
71 views

A river crossing puzzle with relatively prime problem

I want to share a problem on a facebook group : https://www.facebook.com/groups/419858384791916/permalink/640398286071257/ 99 people, numbered 2 to 100, are all on one side of a river and wish to ...
2
votes
1answer
75 views

Three people want to personally meet each other as fast as possible: optimization problem.

Problem: Three people want to be all gathered at the same place, and they want it to happen as soon as possible. Where should they head to? P.S. Assume they all travel with the same speed. Think of ...
2
votes
2answers
202 views

Solving Rubik's cube and other permutation puzzles

I've seen two questions on solving the Rubik's cube but none of the answers have given a complete solution using mainly mathematical techniques. Furthermore, I've not seen a good explanation of ...
2
votes
1answer
77 views

math in horseshoe puzzle

We know that Rubik's Cube is a good demonstration of group theory. Correspondingly, for the horseshoe puzzle as in the picture below, is there a math language for it? Does it demonstrate any math ...
10
votes
1answer
261 views

Bidding Tic Tac Toe

In regular tic tac toe, both the players get alternate chances. This is a variant of that. Player $A$ has $\$x$ amount and player $B$ has $\$y$ amount as initial balance. Assume that $y>x$. Both ...
1
vote
2answers
61 views

Minimum number of moves in Chocolate Puzzle

I've seen this problem on an algorithms competition and although there is an explanation on the website, I couldn't understand it. The abridged problem statement is as follows: Suppose you have two ...
1
vote
1answer
40 views

Figuring out the amount of 'straight edge' pieces in a puzzle?

I was wondering if there was any set way to determine the number of 'straight edge' pieces in a puzzle, assuming the pieces are all in neat rows and columns? Does the ratio of edge pieces to middle ...
2
votes
3answers
244 views

Simple puzzle from The Moscow Puzzles with wrong solution?

I have a book of mathematical puzzles -- The Moscow Puzzles, edited by Martin Gardner -- and I'm struggling to make sense of the following puzzle. It seems utterly simple, yet the solution given seems ...
0
votes
2answers
82 views

Points on a sphere puzzler [closed]

For a perfect sphere that has $n$ random points on it's surface: is it possible to connect all the points on the surface with geodetic segments around the surface of the sphere such that each point ...
0
votes
0answers
95 views

Algorithm to calculate powers

Is it possible to write an algorithm that uses only multiplication and addition to calculate $a^b$ where both a and b are real numbers?
2
votes
1answer
189 views

Game between 2014 card players where everyone with at least 2 cards passes a card to each of his neighbors

2014 card players sit around a big table. One of the players begins with 2014 cards on his hand, and the other have none. The rules for the game are: Every minute shall every player, who ...
1
vote
2answers
432 views

Could one be a friend of all?

The social network "ILM" has a lot of members. It is well known: If you choose any 4 members of the network, then one of these 4 members is a friend of the other 3. Proof: Is then among any 4 ...
2
votes
2answers
68 views

Cracking license plate checksum

Suppose a city has license plates assigned to cars with 7 digits $a_1$ to $a_7$ and a checksum calculated by the following algorithm: ($m_k$ are integers) $$m_1a_1+m_2a_2+\cdots+m_7a_7\mod 28$$ (which ...
0
votes
5answers
6k views

Math Riddle in Combinatorics.

A blind man is on a strange island and he has 2 red pills and 2 white pills, completely identical and has kept in his pockets, he needs to take 1 red pill and 1 white pill order doesn't matter. If he ...
8
votes
1answer
516 views

Puzzle: Give an algorithm for finding a frog that jumps along the number line

You are playing a game, your goal in this game is to catch a frog that's leaping between natural numbers. At first, the frog is found at the number $a \in \mathbb N$ which is not known to you. Each ...
22
votes
8answers
2k views

There is a subset of positive integers which no computer program can print

It's said that a computer program "prints" a set A ($A \subset \mathbb N$, positive integers.) if it prints every element in A in ascending order (Even if A is infinite.). For example, the program can ...