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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2
votes
1answer
262 views

Geometry brain teaser (Candle in the room with mirrored walls)

King wants 2D room with smooth walls and columns (second derivative exists) that reflects light. King asks you to build it in such way that there exists a spot, where you can place a candle and there ...
5
votes
2answers
2k views

100-sided die probability

The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the ...
3
votes
2answers
457 views

What to bid for this treasure chest? (puzzle)

Suppose you are given the opportunity to bid for a treasure chest, which you know to be priced anywhere between 0-1000 dollars inclusive). Treasure price is uniformly distributed. If you bid equal to ...
1
vote
1answer
292 views

Polygon made up of 12 unit sticks with an area limit

A polygon is made up of 12 unit sticks and its area is 3 units^2. Find as many such polygons as possible. Note that a side of the polygon could be made up of more than 1 stick but a stick could not be ...
1
vote
2answers
92 views

Pigeon hole principle question

Their are a group of finite aliens on a spaceship. Show that their are at least two aliens who know the same number of aliens on the spaceship. I was given a hint, and that was to use the pigeon ...
54
votes
2answers
17k views

Predicting Real Numbers

Here is an astounding riddle that at first seems impossible to solve. I'm certain the axiom of choice is required in any solution, and I have an outline of one possible solution, but would like to ...
1
vote
1answer
100 views

A word problem concerning probability. Its pretty interesting

I found an interesting word problem. Check out this link: http://www.math.hmc.edu/~ajb/PCMI/pcmi12.pdf It is problem $A7$. I have been working on it and have reached the following conclusion: Say ...
4
votes
3answers
409 views

A puzzle about graph coloring.

Let $G$ be a graph with three disjoint triangles(i.e. the graph is not connectd and has three connected components each of which is a triangle). If each vertex of G is assigned a red or a green color, ...
0
votes
1answer
1k views

Faulty machine problem variation

I don't know if this problem is known by any other name. The classic problem is: We have 10 machines that produce balls, each weighing 10grams. One of the machines, however, produces balls weighing 9 ...
1
vote
2answers
167 views

Gold Coins and a Balance

Suppose we know that exactly $1$ of $n$ gold coins is counterfeit, and weighs slightly less than the rest. The maximum number of weighings on a balance needed to identify the counterfeit coin can be ...
5
votes
2answers
150 views

When is $\frac{2^n+1}{n^2}$ an integer? [duplicate]

Can anyone see how to solve this number puzzle? Find all integers $n>1$ such that $$\frac{2^n+1}{n^2}$$ is an integer.
4
votes
3answers
264 views

paper punch puzzle

I was told this lovely puzzle recently which I thought people here might enjoy. Consider a paper punch that can be centered at any point of the plane and that, when operated, removes from the plane ...
1
vote
2answers
54 views

Counting ordered triples of sets, with empty intersection.

I was recently asked this question which I couldn't solve. Give the number of ordered triples $(A_1, A_2, A_3)$ of sets which have the property that $A_1 \cup A_2 \cup A_3 = ...
4
votes
1answer
129 views

Classrooms and students puzzle

My school has many classes. Any two students share exactly one class. Any two classes share exactly one student. A class must have at minimum $3$ students, and there is at least one class with $17$ ...
3
votes
1answer
290 views

Safes and keys probability puzzle [duplicate]

I have $100$ keys and $100$ safes. Each key opens only one safe, and each safe is opened only by one key. Every safe contains a random key. 98 of these safes are locked. What's the probability that I ...
1
vote
1answer
247 views

Enigmatic optimization problem

My problem, which I proposed to myself months ago is based on the simple optimization problem in which you find the best path for a lifeguard to rescue a drowning victim. Obviously the shortest ...
4
votes
2answers
59 views

Find $x,y$ such that $x=4y$ and $1$-$9$ occur in $x$ or $y$ exactly once.

$x$ is a $5$-digits number, while $y$ is $4$-digits number. $x=4y$, and they used up all numbers from 1 to 9. Find $x,y$. Can someone give me some ideas please? Thank you.
2
votes
1answer
206 views

puzzle: A spy and the keypad

A spy encounters a keypad that requires a 4 digit PIN. He uses a fine dust to find which keys are used in the combination. He does not know the sequence of keys, nor which ones repeat if any. ...
-8
votes
2answers
267 views

complex maths puzzle problems [closed]

What is the value of $X$ ? \begin{align} X= \frac{(76^2-67^2)}{(9^2-3^2)} \cdot \frac{(85^2-58^2)}{(9^2-8^2)} \cdot \frac{(93^2-39^2)}{(7^2-6^2)} \\ \cdot \frac{(98^2-89^2)}{(8^2-5^2)} \cdot ...
1
vote
1answer
114 views

Maximizing fire-breathing power of multi-headed dragons

Dragons are gathered up on a battlefield. Certain dragons are chosen in order to provide maximum fire breathing power. A dragon can have any number of heads. The only rule is that no more than $1000$ ...
6
votes
1answer
655 views

Unfaithful husbands [duplicate]

In a parallel universe when Neil Armstrong landed on the moon, he found it to be inhabited by a tribe of humanoids. He discovered that: they were all married the husbands of 10 of the wives were ...
3
votes
3answers
239 views

Find the poisoned pie

You are a pie maker and you are holding a fair to display your pies. You have 1000 pies. You have 10 workers to help you. The fair is in two hours. Unfortunately you discover that a rival pie maker ...
1
vote
2answers
303 views

How many cubes are left after removing the surface of a cube?

$n^{3}$ cubes are glued together to form one solid cube which is then hung in the air. As time proceeds, the most outer layer of this solid cube begins to dissolve and eventually those smaller cubes ...
11
votes
6answers
313 views

When two voters meet, they switch allegiance; might they all ally with the same candidate?

Let's assume that there are three candidates running in an election. Right before the elections (when there is no more propaganda), it is forbidden to gather in groups of more than two people ...
12
votes
1answer
243 views

How can one determine the chess configuration that maximizes the number of possible moves?

To clarify, what is the chess-board configuration that would maximize the number of valid moves one player could make on his or her turn? I thought of this question while playing chess, how apropos. I ...
3
votes
2answers
927 views

Probability Question relating prison break

I am stuck in a question regarding a prisoner trapped in a cell with 3 doors that actually has a probability associated with each door chosen(say $.5$ for door $A$, $.3$ for door $B$ and $.2$ for door ...
4
votes
2answers
257 views

Wolves and chicks puzzle

This problem is from the handheld video game, Professor Layton and the Curious Village. I think the solution is very cool, but more than that, I want to know how to show that the minimum number of ...
4
votes
4answers
1k views

Number system - sum of two digit numbers

The sum of four two digit numbers is $221$. None of the eight digits is 0 and none of them are same. Which of the following is not included among the eight digit ? $$(a) \;\;1 \\ (b)\;\; 2 \\ ...
0
votes
1answer
152 views

How to calculate Team Strength for future prediction?

You are given with $4$ players name, namely Player $A$, Player $B$, Player $C$ and Player $D$. These players are grouped into two teams with two players each. A Game is played between the two team.For ...
6
votes
3answers
957 views

Why does the infinite prisoners and hats puzzle require the axiom of choice?

Infinite prisoners puzzle. The link to Wikipedia describes the puzzle, and the solution. The axiom of choice is used to pick a sequence from each equivalence class, which the prisoners memorize ...
0
votes
1answer
321 views

LOVES+LIVE=THERE. How many “loves” are “there”?

This is a problem from Mathematical Circles ( Chapter 0, Problem#17 ). It goes like this:- The answer is that there are 95343 "loves" in "there". Now, this is something that I am unable to ...
3
votes
1answer
598 views

How to solve 5x5 grid with 16 diagonals?

I have a grid 5x5 and I have to fill 16 little squares with a diagonal Rules You cannot place more than 1 diagonal in each square The diagonals cannot touch each other (example bellow) Click ...
6
votes
2answers
974 views

Fun Math Topics, Activities, and Riddles

I'll be teaching college algebra this summer. Last summer when I taught the same course, I finished lectures early (thanks mainly to LaTeX's Beamer package). I want to fill these gaps this time ...
3
votes
1answer
415 views

line of mathematicians guess their own hat color out of c colors

There is a common problem in which a long line of N mathematicians are each given a hat that is either red or blue. They cannot see their own hat but can see all in front of time and can hear any ...
4
votes
4answers
1k views

How to calculate the number of pieces in the border of a puzzle?

Is there any way to calculate how many border-pieces a puzzle has, without knowing it's width-height ratio? I guess it's not even possible, but I am trying to be sure about it. Thanks for your help! ...
6
votes
3answers
668 views

Using the digits $7,7,7,7,1$ and the operators $+,-,*,/$ to make a formula which equals $100$

I know the answer is $(7+7)*(7+(1/7))$ or a more ghetto answer is $177-77$. I'm not interested in the answer, more in the problem itself. What is the name of this class of problem? Is there a ...
1
vote
2answers
156 views

Interesting and irritating problem.

How to deal this problem. I found this problem in math competation in 2012. But, I could not solve. Could you help me... Uncle John has taken blood pressure drops for a long time according to the ...
8
votes
1answer
386 views

Bodyguards and Laser Beams

Suppose you are a point in a square room. The walls of the room are mirrors, and there is a man with a laser gun standing somewhere else in the room. The man is also a point, and both of your ...
5
votes
3answers
1k views

programming brain teaser

Given a programming language where you could make as many variables up as possible and you could only perform these three operators find b-1. ...
1
vote
2answers
175 views

Easy Probability Problem

I was told the following probability problem: While doing a math problem today at the contest the probability of Annie, Tom and Karen getting the problem correct first is 1/7, 1/2, and 5/14 ...
3
votes
3answers
3k views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
2
votes
1answer
95 views

How many unique rotating sequences?

This is a small puzzle I've been playing with for the past couple of days: For some length N, how many unique sequences of digits can be created when any 'rotation' of the digits is considered as the ...
6
votes
4answers
140 views

Shortest string possible

I was at an interview, and I was asked to give the shortest string generated given this context free grammar. I did not review in years, so I think I got it wrong. What is the answer so I know it for ...
1
vote
1answer
188 views

Would I be able to use mathematics to prove properties that would help me solve this series of puzzles?

I realise that this may be a little different from most of the questions you get on math.stackexchange, so for that I apologize. I also apologize if there's no "one right answer" given the way I've ...
10
votes
3answers
548 views

What is the least amount of questions to find out the number that a person is thinking between 1 to 1000 when they are allowed to lie at most once

A person is thinking of a number between 1 and 1000. What is the least number of yes/no questions that we can ask and know what that person's number is given that the person is allowed to lie on at ...
3
votes
2answers
206 views

Checking Sudoku - sufficient sums

Are the following condition sufficient for checking if solution of Sudoku with (extended output) is valide : sum of values in each row, column and subsquare is equal to 45 and sum of squares of ...
4
votes
1answer
110 views

creating a more complex sudoku (69x6)

I would like to know if its possible to create a "sodoku" with this rule: in a table $69\times 6$ i want to put in the numbers from $1$ to $46$ repeated $9$ times, each numbers HAS to stay in the same ...
3
votes
2answers
502 views

Permutation of 1…9 with no ascending or descending subsequence of length 4

Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise) in ascending or descending order. Show that there is no arrangement of the numbers $1,2,...,10$ ...
2
votes
1answer
673 views

The minimum number of mice required to find a poisoned bottle.

Here's an interesting question. There are $1000$ mice and $1000$ bottles (numbered $1,2,3....1000$). One of the bottles is poisoned. You can mix the solution with the other bottles any number of ...
0
votes
1answer
198 views

Where is the logical error in this Math question? when it say where is the remaining 1? [duplicate]

Three person buying something by 30, each pay 10, after a while, the owner making a discount of -5, but he realize that 5/2 is not good, so, he will return 1 for each, and gives the remaining (2) to ...