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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1
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1answer
259 views

Lexicographical rank of a string with duplicate characters

Given a string,you can find the lexicographic rank of a string using this algorithm: Let the given string be “STRING”. In the input string, ‘S’ is the first character. There are total 6 characters ...
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0answers
7 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 ...
6
votes
2answers
163 views
+100

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 ...
1
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0answers
41 views

explaining the pattern

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 present in ...
1
vote
1answer
27 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 ...
6
votes
5answers
2k views

Express logic puzzles with proposition calculus notation

I’m trying to solve a logic puzzle that goes like this: The police have three suspects for the murder of Mr. Cooper: Mr. Smith, Mr. Jones, and Mr. Williams. Smith, Jones, and Williams each declare ...
0
votes
2answers
666 views

How do I find the maximum number of knights on a chess board?

I came across this problem and after thinking a lot I could not get any idea how to calculate it. Please suggest to me the right way to calculate it. Given a position where a knight is placed on ...
0
votes
1answer
10 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
86 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 ...
15
votes
3answers
326 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
1answer
268 views

roulette wheel sequence

Is the sequence of numbers around a European roulette wheel (the integers from 0 to 36 inclusive) random or is there a pattern to it? It is said to have been devised by Pascal, which might be thought ...
6
votes
6answers
618 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. ...
4
votes
1answer
69 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
40 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 ...
2
votes
3answers
127 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
1answer
27 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, ...
0
votes
1answer
28 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
36 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.
14
votes
2answers
2k views

Is the game 2048 always solveable?

Games got me on math. I always want to play best. I don't know how to answer my question. My question is : How to show that the game 2048 is (always) solvable>? Is there any method other than ...
-1
votes
2answers
67 views

puzzle series (need help)

Can you give a hint on this puzzle please? \begin{align*}5+3+2&=151022\\ 9+2+4&=183652\\ 8+6+3&=482466\\ 5+4+5&=202541\\ 7+2+5&=?\end{align*}
-1
votes
0answers
26 views

Optimal size of n circles to fit an area given their relative sizes

Let us say that I have a rectangular area that has to always look "filled" with circles. (the void spaces with the given number of circles should be minimal)(Goal) Let us assume that, I am also told ...
4
votes
3answers
164 views

Variation on circular lake problem

An escaped prisoner finds himself in the middle of a SQUARE swimming pool. The guard that is chasing him is at one of the corners of the pool. The guard can run faster than the prisoner can swim. ...
10
votes
2answers
209 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 ...
2
votes
1answer
52 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 ...
7
votes
1answer
340 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 ...
2
votes
2answers
342 views

Seating Arrangement puzzle.

Not sure if its a correct place to post these kind of questions. Eight persons-P,S,Q,R,U,B,J and C are sitting in a field in a circle. Three are facing opposite side and other five are facing the ...
10
votes
1answer
217 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 ...
2
votes
3answers
1k views

Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
0
votes
1answer
316 views

Striking off a digit from each of the numbers written in seven rows, while preserving arithmetical operations

Problem Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another ...
3
votes
1answer
5k views

Probabalistic proof of green-eyed dragons logic puzzle

I came across the "green-eyed dragons" puzzle (alternatively known as the "blue eyed villagers" puzzle). The typical proof uses a straightforward inductive strategy. I came up with a probabalistic ...
0
votes
0answers
33 views

logic problem/puzzle solving [migrated]

I'm here to ask you if it is possible to find a way to solve this problem. I'm designing the puzzle-enigma section of a video game and try to find possible solutions and mechanic for it. Imagine each ...
2
votes
0answers
54 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
2answers
86 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
70 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
122 views

Problem about points on an equilateral triangle [duplicate]

Suppose that $A$, $B$, and $C$ are three points in a plane, such that $AB = AC = BC = 1$. At each point in time, $A$ is moving toward $B$, $B$ is moving toward $C$, and $C$ is moving towards $A$, all ...
17
votes
4answers
3k views

100 prisoners and a lightbulb

100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb ...
0
votes
1answer
482 views

Proof by induction in a game with water balloons

Consider the following description of a game. There are $n$ people playing, one of whom leads the game. They are playing on a playing field with no obstacles. Everyone carries one water balloon. ...
1
vote
2answers
52 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
12 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 ...
62
votes
13answers
17k views

Dividing 100% by 3 without any left

In mathematics, as far as I know, you can't divide 100% by 3 without having 0,1...% left. Imagine an apple which was cloned two times, so the other 2 are completely equal in 'quality'. The totality ...
21
votes
8answers
3k 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 ...
5
votes
1answer
82 views

Number of valid NxN Takuzu Boards a.k.a 0h h1 (details inside)?

Takuzu a logic puzzle which has a NxN grid filled with zero's and one's following these rules: 1) Every row/column has equal number of 0's and 1's 2) No two rows/columns are same 3) No three ...
2
votes
1answer
125 views

3 dimensional $6\times 6\times 6$ lit cube problem involving looking for a specific lit pattern and quantity of them.

Suppose we have a $6\times 6\times 6$ cube such that it has $216$ subcubes, each with a visible, discernible light in it. A random number generator is connected to the cube and it will choose ...
0
votes
2answers
73 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 ...
2
votes
1answer
180 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 ...
77
votes
10answers
9k views

Mathematician vs. Computer: A Game

A mathematician and a computer are playing a game: First, the mathematician chooses an integer from the range $2,...,1000$. Then, the computer chooses an integer uniformly at random from the same ...
0
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0answers
63 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?
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2answers
317 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
54 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
4answers
1k 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 ...