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
325 views

One drunk receptionist and four brilliant mathematicians

Suppose that there is one hotel with nine floors (first floor = ground floor + 1) where the math seminar takes place, four brilliant mathematicians who are guests of the hotel, one drunk receptionist ...
-1
votes
3answers
720 views

Triangle whose height and sides are consecutive integers

This is probably a old puzzle,and maybe you have seen it somewhere else before.Imagine a special triangle. The height and the three sides of this triangle are 4 consecutive integers.Can you figure out ...
4
votes
1answer
223 views

Expressing any given number in the form of $x^y + y^x$

I was told by one of my friends that any given positive integer can be expressed in the form of $x^y + y^x$ where x & y are integers. For example: 17 = $2^3+3^2$ Surprisingly,this could be done ...
10
votes
4answers
1k views

Ten soldiers puzzle

This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way that each ...
2
votes
4answers
635 views

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ show that $x=-c/b$ when $a=0$

OK, this one has me stumped. Given that the solution for $ax^2+bx+c =0$ $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\qquad(*)$$ How would you show using $(*)$ that $x=-c/b$ when $a=0$ (Please dont use $a=0$ ...
5
votes
2answers
4k views

Finding the n-th lexicographic permutation of a string

I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a ...
1
vote
1answer
191 views

In how many ways can $10$ letters be placed in $10$ addressed envelope such that exactly $9$ letters are in correct envelope?

I have one problem which goes like this: "In how many ways can $10$ letters be placed in $10$ addressed envelope such that exactly $9$ letters are in correct envelope?" If I understand the problem ...
2
votes
2answers
122 views

Simplifying a Double Random procedure

Thought this would be a nice puzzle for some. :) First, I take a random number from 1 to 10, then take that number and multiply it by 5, we'll call this result 'threshold'. Then I take another new ...
3
votes
2answers
1k views

To Mock A Mockingbird: Flower Garden (Math Puzzle)

Question: In a certain flower garden, each flower was either red, yellow, or blue, and all three colours were represented. A statistician once visited the garden and made the observation that ...
10
votes
1answer
1k views

After swapping the positions of the hour and the minute hand, when will a clock still give a valid time?

At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and ...
2
votes
1answer
247 views

fill the board with dominos

Imagine a 8x8 cell board, but missing two cell at the opposite corners, a domino take up exactly two cell, how to fill the board with dominoes so that none overlap or hang off the edge?
4
votes
2answers
411 views

Puzzle - gloves in a closet, three colors

This is probably a old puzzle which i encountered today: A lady has fine gloves and hats in her closet- $18$ blue, $32$ red, and $25$ yellow. The lights are out and it is totally dark. In spite ...
14
votes
2answers
782 views

Minimally inconsistent Sudoku puzzle

A sudoku puzzle is a partially filled $9\times 9$ grid with numbers $1,\ldots,9$ such that each column, each row, and each of the nine 3×3 sub-grids that compose the grid does not contain two of the ...
-1
votes
2answers
176 views

Logic question:hiding a treasure

A sailor gets some treasure and wants to hide it. He finds an island where there are two poles $P_1$ and $P_2$ and a tree $T$. He goes from $P_1$ to $T$ and turns right angle anti-clockwise and ...
5
votes
4answers
2k views

Better than random

I have been trying to solve this question, but in vain. Please help. You are given two boxes with a number inside each box. The two numbers are different but you have no idea what they are. You ...
0
votes
1answer
318 views

A puzzle from Perfectly Reasonable Deviations from the Beaten Track by Richard Feynman

The following is a puzzle I found while reading Perfectly Reasonable Deviations from the Beaten Track by Richard P Feynman. There are 2 shops which sell oranges.At Shop A you get 2 oranges for 5 ...
1
vote
1answer
1k views

Number Of races needed?

25 horses, 5 race tracks; we need to choose the top 3 horses. What is the minimum number of races you need? I have thinking deeply and figure out this: First race all 25 horses in groups of 5 to ...
0
votes
1answer
178 views

Is the average of many “random” numbers useful information?

Ok, so I found this site: http://tweetcracker.com/. Essentially, people just tweet 10 digit numbers in hopes it is the correct number (like lottery, except free). I heard that if you took all the ...
6
votes
2answers
3k views

How can four employees calculate the average of their salaries without knowing other's salary using RSA?

I know of a solution. But this has a limitation that information is partially passed around and there needs some trust level. I'm wondering if any variant of public-private key (e.g. RSA) algorithm ...
1
vote
0answers
130 views

Can someone please explain the catch behind this question? [duplicate]

Possible Duplicate: Riddle (simple arithmetic problem/illusion) I don't know if this is off-topic, but I recently saw this riddle, which I believe many of you have seen before: There ...
27
votes
1answer
661 views

A fun Pascal-like triangle

Inspired by Pascal, I put on some shackles and a thorny belt. Inspiration came pouring in, and I thought of the following triangle: $$ \begin{array}{rcccccccccc} & & & & ...
2
votes
2answers
180 views

An experiment was performed n times. The exact success rate rounds to 85.8%. What is the minimum value of n?

An experiment was performed n times. The success rate was given as 85.8% Clearly, if there were 858 successes out of 1000 trials it would give that percentage. However, the percentages are rounded to ...
5
votes
5answers
6k views

How many bananas can a camel deliver without eating them all?

This is a fun puzzle I was assigned on the first day of highschool (over a decade ago). I just dug it up randomly from under my bed and thought I'd share it with the SE community. At the time, I ...
2
votes
1answer
111 views

Preferences Paradox [duplicate]

Possible Duplicate: Card doubling paradox I came across the following preferences paradox: Suppose you have two identical boxes $A$ and $B$. One of them contains an unspecified number ...
1
vote
1answer
354 views

The Game of Nim

A position in Nim consists of some piles of coins. Two players alternate, with each move removing a portion of one pile. The winner is the player who takes the last coin. Suppose that the starting ...
1
vote
2answers
99 views

Exchange without changes

There are three type of amount currencies that is less than 10 namely: 1, 2, and 5. You are going to drug store, supermarket, restaurant today where you will have ...
4
votes
1answer
458 views

Is this mechanical puzzle (Loony loop) solvable?

"The aim of this puzzle is to free the tied cord from the figure-eight metal loop, without breaking or untying the cord."
9
votes
1answer
356 views

Honest and Deceitful Professors Problem

I found this in An Introduction to Bioinformatics Algorithms. I've paraphrased for clarity. There are 100 professors. Some are honest, while others are dishonest. There are more honest professors ...
4
votes
3answers
713 views

What is the highest number that can be got from 4383 by moving exactly 2 matches?

What is the highest number that can be got from 4383 by moving exactly 2 matches? Number 1 has got 2 matches, so I thought it will be 47831 as I remove two matches from second number (3), but it ...
8
votes
3answers
723 views

A polyomino puzzle

Is there a polyomino such that it can be glued to an I-shaped pentomino and to a X-shaped pentomino to obtain the same polyomino? Or is there simple proof for non-existence of such polyomino? ...
2
votes
3answers
256 views

Squares on a checkerboard

How many squares of all sizes arise using an $n$-by-$n$ checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length $n$ ?
15
votes
2answers
767 views

Puzzle: $(\Box @)+(\Box @) = (\Box\bigstar\Box$)

Some ETs follow a positional number system, with the same base as the number of fingers on their hand. The following inscription is all the evidence we have: $$(\Box @)+(\Box @) = \Box\bigstar\Box ...
14
votes
5answers
1k views

Four men, hats and probability

I encountered the four men in hats puzzle for the first time today. My question is about a realisation I (think I) had while arriving at the solution, but I have no idea whether I've made a mistake ...
0
votes
3answers
663 views

I was wondering what is the simplest yet difficult mathematical question? [closed]

I am not a math's guy, however I like maths that have to do with puzzle, not just solving an exercise. I was wondering which is the simplest yet difficult math question ever been in the form of an ...
3
votes
3answers
407 views

grid puzzle about combinatorics

Here is a puzzle about combinatorics. Suppose you have a square grid with $n^2$ points. You want to go from the origin $(0, 0)$ to $(n-1, n-1)$. Assuming you can only go right or up, in how many ways ...
75
votes
4answers
4k views

What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?

What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into? The image below is a flawed example, from http://www.mathpuzzle.com/flawed456075.gif ...
4
votes
1answer
327 views

Transforming puzzle to graph theory?

I am trying to solve the puzzle below and am thinking that there ought to be some way of formulating it as a problem about counting matchings, but I can not make it work. I would appreciate a hint or ...
27
votes
9answers
2k views

how to find the balls?

You have 15 balls, 2 of them are radioactive. You have to run 7 tests (no more) on the balls which will sort out the 2 radioactive ones guarenteed every time. You can test them in groups, or even one ...
12
votes
3answers
1k views

evaluate the last digit of $7^{7^{7^{7^{7}}}}$

I found this puzzle online. Since I'm not good at number theoretic kind of problems I'm going to propose it in this form. If you have a number $x$, in this case $x=7$, how do you evaluate the last ...
8
votes
2answers
3k views

Understanding a famous riddle

This is quite a popular riddle in interviews and in general: In a bouquet of flowers, all but two are roses, all but two are tulips, and all but two are daisies. How many flowers are in the ...
2
votes
2answers
1k views

Variation on the Monty Hall Problem

Many of us know the Monty Hall Problem But the other day I was asked a variation of this riddle. The answer of the original question is, of course, $ 66\% $ in favor of changing doors, but this is ...
3
votes
1answer
3k views

Logic Puzzle of the age of three sons

There is a puzzle, it goes something like this: Someone talks to a guy, and asks, Give me the age of my three sons, The other guy asks for some clues: The product of the age of the three sons (of ...
4
votes
1answer
154 views

Specific ten digit number

I'm trying to solve this little problem. So far no luck. Could anyone help? Thanks in advance :) What is the ten digit number such that the i-th digit is the number of i's in the number ( 0<= i ...
5
votes
3answers
174 views

What are good ways of understandng a permutation group from a set of generators?

I'm trying to understand the structure of a Rubik's Cube-style puzzle I'm playing with; I have an expression of the solutions as the permutation group generated by four elements of $S_{16}$, each a ...
1
vote
2answers
207 views

Zeno-like riddle with additional complication: Runner with dog running back and forth at different speeds

I came across this little riddle: An amateur runner trains on a 1 250 m long track at a speed of $v_L = 2 m/s$. His dog runs ahead to the target, turns around and then runs back to him, then he ...
0
votes
1answer
88 views

Getting 5 or 7 and returning the opposite? [closed]

I get 5 or 7 and if i get 5 i need to return 7 if i get 7 i need to return 5. i need to do this in 1 mathematical formula. I have those: 12 - x 35 / x There ...
2
votes
2answers
671 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 ...
4
votes
1answer
987 views

Knights & Knaves Logic Problem Help

Can anyone please help me with this knights & knaves logic problem? It is from Raymond Smullyan's Forever Undecided. P= Proposition, and Q = Different Proposition. Properties: 1) R(P) -> B(P) ...
2
votes
1answer
501 views

Four Fours puzzle

The theory is here. It is pretty simple: form any integer bigger or equal that 0 using four fours and symbols. Is there any demonstration which explains why with four fours is possible to form ...