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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1answer
35 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
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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. ...
0
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1answer
29 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 ...
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1answer
46 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
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1answer
385 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
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2answers
221 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
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3answers
365 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
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0answers
69 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
74 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
174 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

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
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1answer
247 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 ...
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2answers
58 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
33 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
210 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
75 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
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0answers
83 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
188 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
430 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
66 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
3k 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
486 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
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 ...
19
votes
6answers
2k views

Chicken Problem from Terry Tao's blog

This problem was posted by Terry Tao in his blog earlier. It's actually from his son's Math Circle. It took him $15$ minutes to solve it. I guess we all can take a crack at it. Three farmers were ...
0
votes
2answers
68 views

Combine four '4' and the basic operators to get 20 [closed]

4 4 4 4 ÷ × + - Using these operaters how to get answer 20.
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2answers
135 views

Algebraic solution to the Broken Weight Problem

Here is a problem I was sent, which it turns out was first posed by Claude Gaspard Bachet de Méziriac in a book of arithmetic problems. The problem is as follows: A few years ago, a King's ...
5
votes
1answer
123 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
191 views

Is this a correct solution to determine as to whom I should invite for the party?

I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen, when I came across the following question: When planning a party you want to know whom to invite. Among ...
2
votes
1answer
131 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 ...
1
vote
1answer
33 views

Finding the count of paths with K turns from corner to corner in a square box

I'm having trouble understanding the solution given for the problem here: http://www.codechef.com/DEC11/problems/MOVES/ Given a square table sized $N \times N$ ($3 ≤ N ≤ 5000$; rows and columns ...
1
vote
1answer
253 views

Is this a correct solution to determining which of two people is the liar using one question?

I am a newbie to Stack-Exchange and if there is any problem in my question -- I apologize beforehand . I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen , ...
1
vote
1answer
47 views

Pebble Problem Maximum$=\big\lceil \log_3(n)\big\rceil$?

In the pebbles problem, you are given $n$ number of pebbles that has one of the $n$ weigh less. If you are given a balence that you can you $k$ times, what is the minimum amount of $k$? ...
-7
votes
1answer
210 views

Why is it possible to find the birth year by subtracting one's age from 114?

I noticed that any person can find their birth year just by subtracting their age from the number $114$. For example, if I am $25$ years old then from $114-25=89$ I know the birth year is $1989 $. ...
4
votes
1answer
65 views

Puzzling Sequence

Today I was given a question that first I thought might be easy to solve but then no matter how hard I tried I couldn't solve it.(It's not really related to maths just some puzzle) if: $$ 9999=4\\ ...
1
vote
2answers
63 views

Scores of six soccer matches

In the first round of the city soccer tournament, the teams in group A finished as follows: ...
0
votes
1answer
77 views

How to find a recursive formula for some sequence

I know how to find a non-recursive formula for a recursively defined sequence. However, now I have this puzzle which gives me a sequence (but not the recursive definition) and challenges me to find ...
4
votes
1answer
105 views

The Island in the Miracle Sea. (Christmas edition)

To all of you who love math like me, I have this puzzling riddle that I hope you find interesting : On Christmas Eve just after midnight, Santa was riding his sleigh over the Miracle Sea when ...
3
votes
1answer
141 views

Knuth's algorithm for Mastermind question

I'm reading about Knuth's algorithm to solve the mastermind game, so I've looked in wikipedia and read the pseudo-code (http://en.wikipedia.org/wiki/Mastermind_(board_game)#Five-guess_algorithm). I ...
3
votes
2answers
55 views

Objects into two bags puzzle

I found a maths puzzle somewhere and a part of it as below: Kelly wants to place n objects $a_1,a_2,⋅⋅⋅,a_n$ into two bags. For each $i=1,2,⋅⋅⋅,n$, the weight of $a_i$ is $w_i$ kilograms. The ...
2
votes
1answer
50 views

Weights - Objects into bags puzzle

I found a maths puzzle somewhere and a part of it as below: Kelly wants to place n objects $a_1 , a_2 , ··· , a_n$ into $k > 1$ bags. For each $i = 1 , 2 , ··· , n $, the weight of $a_i$ is $w_i$ ...
10
votes
3answers
893 views

riddle that involves elementary geometry

$3$ frogs are positioned at the vertices of an equilateral triangle whos sides are of length $1$. We have $1$ frog on each vertex. The frogs are able to "leap" one over another. When they do, they ...
2
votes
0answers
76 views

How can this paradox be resolved?

I came up with a (probably unoriginal) paradox today, and was wondering how it might be resolved. Its approach to reasoning seems to resemble basic game theory techniques. Suppose a casino game has ...
15
votes
4answers
2k views

Solving 9 sons puzzle

The following math puzzle : ...
2
votes
3answers
168 views

Find the last non-zero digit of $30^{2345}$

Find the last non-zero digit of $30^{2345}$ Source: Athena Healthcare Interview Questions
8
votes
3answers
164 views

Dividing an obtuse triangle into acute triangles

Can an obtuse triangle be subdivided into only acute triangles (right triangles are not allowed)? Any number of subdivisions can be made as long as all of the angles in all resulting triangles are ...
4
votes
0answers
112 views

Is it a “paradox”, or a flaw in the question?

(Clearly not a pardox per-se but I would like to hear what you think) The basic riddle (not a very interesting one even) goes as follows: A first client comes into a barber shop, takes a hair cut ...
11
votes
8answers
471 views

Make the number $100$ out of $1,2,3,$ and $4$ digits, without repeats

How can we make the number $100$, using only the following digits: $1,2,3,4$. You cannot repeat any of them.
1
vote
1answer
96 views

Cutting chocolate diagonally

Given is chocolate with rectangular pieces of size $a \times b$. If cut diagonally, how many pieces will it be split into? If knife passes exactly by co-catenating we assume there is no damage to ...
1
vote
0answers
118 views

How to find solutions of coin weighing problems with multiple light coins and prove optimality

So the classical coin weighing problem with $3^n$ coins all equal weight except for one light coin, where we want to find the one light coin, can be solved optimally with $n$ uses of a balancing ...
0
votes
0answers
31 views

$n$th number of concatenating consecutive integers [duplicate]

How do I find the nth digit of concatenating consecutive integers as in: $123456789101112131415161718\cdots$ where the $10th$ digit = 1$ , $11$th$ = 0$, $12$th $= 1$, $13$th $= 1$ $\cdots$ How do I ...