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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0
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1answer
16 views

Conditions for magic square.

So I've messing around with magic squares and something occured to me: Assume we have a nxn grid of numbers which respects the sum conditions of a magic square as in it has the appropriate column, ...
-3
votes
1answer
117 views

SEVEN - NINE= EIGHT [on hold]

Things are not always what they seem. What is true from one point of view may be false from another and vice-versa, and here is a puzzle to prove it. Despite the fact that every arithmetic teacher in ...
2
votes
2answers
733 views

Puzzle, Permutation and Combination problem?

I have a puzzle here: There are five colored balls: 2 green, 2 blue and 1 yellow Rule 1: All balls of the same color must be adjacent to each other. I wrote a program to find all the ...
0
votes
1answer
63 views

Probability Paradoxes that Puzzle Professors.

There is a class of probability puzzles that includes Monty Hall/Three Prisoners, Three Cards/Pancakes, Two Children/Boy or Girl, their common antecedent Bertrand's Box Paradox, and (a more ...
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0answers
64 views
41
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16answers
13k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
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 ...
10
votes
11answers
164 views

Get the numbers from (0-30) by using the number $2$ four times

How can I get the numbers from (0-30) by using the number $2$ four times.Use any common mathematical function and the (+,-,*,/,^) I tried to solve this puzzle, but I couldn't solve it completely. Some ...
5
votes
2answers
109 views

Prisoners Problem

We have an infinite number of prisoners enumerated $\{1, 2, \dots\}$, and on each prisoner there is a hat of either blue or red color. The $n$th prisoner sees the hats of prisoners $\{n+1, n+2, ...
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votes
2answers
55 views

Lights Out with custom rules set

I'm trying to understand how to use linear algebra to solve a custom Lights Out puzzle with the following rules: There are 8 lights, all the lights are off at the starting point, I need to turn on ...
1
vote
1answer
35 views

Probability puzzle : Expected no. of coins in the smaller pot

There are two pots of coins having size m & n. A new coin is thrown and goes to 1st pot with probability m/(m+n) and to 2nd pot with probability n/(m+n). We start with both pots of size 1 & 1 ...
1
vote
1answer
32 views

Probability : Maximize the expected payoff

Given $2$ random variables $X, Y$ that take integer values with uniform distribution from $0$ to $100$. You play a game in which a random value of $x$ comes first & you have to decide if the ...
0
votes
1answer
31 views

How to count jigsaw puzzle height and width in pieces.

How can I calculate jigsaw puzzle dimensions (height & width) in puzzle pieces? I have a puzzle which consist of $3,000$ pieces (the paper inside the box says that because of technical reasons ...
5
votes
4answers
665 views

A maths number puzzle

We have these digits : $1,2,3,4,5,6,7,8,9$. Using these digits, we have to make two numbers such that their product must be as large as possible. We have to use all digits only once. I did ...
7
votes
6answers
2k views

Rainbow Hats Puzzle

Seven prisoners are given the chance to be set free tomorrow. An executioner will put a hat on each prisoner's head. Each hat can be one of the seven colors of the rainbow and the hat colors ...
1
vote
1answer
37 views

What is the relation between these numbers? [closed]

This in an IQ question. I need to find relation between these: I appreciate if anyone can help to find relation between these numbers. By the way the answer is A (number 3) from this link and then ...
3
votes
1answer
34 views

Four Isosceles Trapezoids

Suppose we have four isosceles triangles with the same area, which must some whole number less than $29$. Denote the the lower base and upper base of the $i$-th triangle with $y_i$ and $x_i$, ...
3
votes
1answer
39 views

Find a seven digit number which describes itself

Find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, ...
0
votes
2answers
42 views

how many days at work?

There are scheduled buses traveling between Somewhere and Nowhere. There is only one road between the two villages, so the buses take this road. From both villages the buses leave for the other ...
2
votes
2answers
46 views

What is the probability for a wood stick of real number length breaking in three piece that can forming precisely a triangle?

What is the probability for a wood stick of any real number length breaking in three piece that can forming precisely a triangle without any extra segment extend from the side of the triangle? My ...
18
votes
4answers
355 views

How many $\mathbb R$s must a Mathematician walk down?

A mathematician is lost on the complex plane. He knows neither his position nor the direction he is facing. He wants to return to the main road, a strip of width $1$ around the real axis (that is, ...
0
votes
3answers
111 views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
2
votes
0answers
28 views

determine the number thought of

Ten people are seated around a circular table. Each of the ten people thinks of a number and whispers it to his/her two neighbours. Then these ten people announce the average of the two numbers they ...
15
votes
5answers
1k views

Puzzle of gold coins in the bag

At the end of Probability class, our professor gave us the following puzzle: There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of ...
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 : ...
4
votes
3answers
95 views

Using up letters on a refrigerator is NP-complete

You spend some time with your preschool-age daughter trying to use up all of the magnet letters on the refrigerator to spell words that she knows. Formally, you have a set of letters and you are ...
60
votes
12answers
15k 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 ...
0
votes
1answer
51 views

Cops and robbers in a square

A problem from Moscow Mathematical Olympiad in 1973. goes like this: At the center of a square stands a cop and at one of the square’s vertices stands a robber. The Rule allows the cop to run ...
4
votes
1answer
795 views

Can you make an equilateral triangle from 3identical trapezoids?

Is it possible to make an equilateral triangle from 3 identical trapezoids? If so, what angles would be needed in the trapezoids?
2
votes
1answer
34 views

counting hands shake

Mr. and Mrs. Brown gave a party for their friends they have not seen for a long time. Three couples came. During the party, some of the people were so happy to see each other again, that they even ...
3
votes
1answer
4k 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
1answer
14 views

Show that an integer in an odd base system is odd in the base 10 system…

Show that an integer in an odd base system is odd in the base 10 system if and only if it has an odd number of odd digits. I have an idea of how the proof should go in my head, but how do I express ...
4
votes
4answers
71 views

Find a positive integer with prime factors of at most 2, 3, 5, 7 and ends in the digits 11

Does there exist a positive integer whose prime factors include at most 2, 3, 5, and 7, and ends in the digits 11? If so find the smallest positive integer. If not, show why none exists. My professor ...
3
votes
7answers
186 views

How can I formulate the two guards puzzle to disallow references to the other guard?

An old logic puzzle goes as follows: There is a gate with two doors, each leading to a different city – Tannenbaum or Belvedere. You wish to get to Tannenbaum, but you do not know which of ...
7
votes
6answers
2k views

10 little dwarves

A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a ...
6
votes
4answers
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 ...
3
votes
2answers
93 views

how to solve triangles count puzzle

Below is a puzzle of counting triangles.How to solve such puzzle ? source: http://gpuzzles.com/mind-teasers/how-many-triangles-challenge/?source=stackmath
0
votes
3answers
59 views

Recovering the original values from given information.

We have some N numbers[1..N] and N students. Originally we assign each number to single student. Call this assignment as the initial state of the assignments. Instance of assignment is described as ...
3
votes
3answers
814 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 ...
1
vote
2answers
55 views

Counting problem about pirates and gold coins [duplicate]

Five pirates find a cache of 500 gold coins. They decide that the shortest pirate will serve as the bursar and determine a distribution of the coins however he sees fit, and then they all will vote. ...
0
votes
2answers
39 views

Formula to have have a nonnegative integer go > 0 and < 127 [closed]

I'm working on a digital music composition where I have nonnegative integer x. I need a formula to translate x into a nonnegative integer between 0 and 127. Any ...
3
votes
3answers
82 views

Proof of 3-chain subsequence problem from assignment 2 of MIT OCW 6.042

I was trying to solve this question but stuck with how do I prove it so. I do have the intuition but how to prove it? Here is the link to the page and this one is the problem 1!! ...
2
votes
1answer
27 views

Calculate percentage between two sensorvalues

I've got two distance sensors on the sides of a car, and I'm trying to come up with a formula that will attempt to put the car so that it has an equal distance on both sides. There is an IR sensor on ...
1
vote
4answers
54 views

How many faces does the resulting polyhedron have?

Take a regular tetrahedron of edge one. Also take a square-based pyramid, whose edges are all one (therefore the side faces are equilateral triangles of same size as the faces of the tetrahedron). ...
20
votes
3answers
489 views

Math puzzle: 10 digit strings generations

There was a question in a math competition that I attended last year. At the end of competition, I realized that my answer was wrong for the question below and I have never been able to figure out how ...
1
vote
0answers
29 views

3D Extension of a Fun Geometric Series Puzzle

After being inspired by this question, and in particular Semiclassical's excellent response and generalisation, I thought of another generalisation to a 3-dimensional plane.: Suppose you start at ...
2
votes
3answers
407 views

balance scale problem for 13 (not 12) items

The 12-item balance scale puzzle is very familiar. The object is to find the lone non-standard item (if one exists) out of a group of 12 seemingly identical items, using a balance scale and a maximum ...
1
vote
1answer
37 views

The Special Table

Consider a $n\times n$ table which is filled with numbers $1,2,3,...,n^2$ (in no particular order).We'd call such table "Special" if the sum of each column and each row and each diameter is a constant ...
2
votes
1answer
34 views

Forming peaceful teams

Let us have set of $n=mk$ people that have to be divided into $m$ teams, each with $k$ members. Let us denote the set of the people $S=\{1,2,\dots,n\}$ and the teams $S_i\subset S$. We consider a ...
6
votes
4answers
173 views

A puzzle that came when I am half awake

When I am about to wake up in the morning, a puzzle crept into my mind.It is when $\sqrt{a}$ and $\sqrt{b}$ are both non-integers where $a,b$ are positive integers is it possible for $\sqrt{ab}$ to ...