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
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
657 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
110 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
350 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
445 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
352 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
711 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
255 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
756 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
650 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
405 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
321 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
172 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
659 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
971 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
496 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 ...
22
votes
8answers
4k views

Which simple puzzles have fooled professional mathematicians?

Although I'm not a professional mathematician by training, I felt I should have easily been able to answer straight away the following puzzle: Three men go to a shop to buy a TV and the only one ...
11
votes
2answers
2k views

Enigma : of Wizards, Dwarves and Hats

I've got quite a hard enigma that require extensive knowledge in mathematics, and I thought some might appreciate it. An evil sorcerer holds in prison an infinite number of dwarves (countably ...
6
votes
1answer
663 views

Stone picking puzzle

Two players are playing a stone picking game. The players pick a stone from two pile of stone in turn. One can choose to pick any number of stones from either pile, or pick the same number of stone ...
1
vote
2answers
1k views

How to solve a cryptarithm?

Given multiplication is $$\begin{array}{cccccc} & & & P & E & N \\ & & & I & N & K \\\hline & & L & K & P & R \\ & ...
5
votes
1answer
405 views

A Nim game variant

We know how to win the classic regular Nim (two players) Classic rules: Any number of beans into any number of separate piles Each move, the player whose turn it is, must choose one pile of beans and ...
3
votes
2answers
246 views

Question about a puzzle on injecting a subset of $\mathbb{R}$ into $\mathbb{Q}$

I was just browsing through the Puzzle section on Noam Elkies website. The puzzle can be found here. The solution to the puzzle proves that any well-ordered subset of $\mathbb{R}$ is countable. In ...
1
vote
1answer
274 views

Word Problem Proof? (just for fun, help)

Players 1, 2, 3, …, n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, ...
16
votes
2answers
973 views

What is the complexity of succinct (binary) Nurikabe?

Nurikabe is a constraint-based grid-filling puzzle, loosely similar to Minesweeper/Nonograms; numbers are placed on a grid to be filled with on/off values for each cell, with each number indicating a ...
1
vote
3answers
218 views

Sum the infinite series $ \sum_{n=0}^\infty (2n^7 + n^6 + n^5 + 2n^2)/n! $

What is $$ \sum_{n=0}^\infty \frac{2n^7 + n^6 + n^5 + 2n^2}{n!} $$
10
votes
1answer
1k views

The Three Princesses

Is it possible to solve this problem: A prince wish to marry a princess. There are 3 princesses, one is young, one is a little older and one is old. The prince is able to tell the princesses apart. ...
28
votes
3answers
949 views

Tall fraction puzzle

I was given this problem 30 years ago by a coworker, posted it 15 years ago to rec.puzzles, and got a solution from Barry Wolk, but have never seen it again. Consider the series: $$1, ...
1
vote
4answers
3k views

Absolute values of 1-10 in a pyramid form

_ _ _ _ \/ \/ \/ _ _ _ \/ \/ _ _ \/ _ you have numbers 1-10. you can only use each number once and the number below is equal to the absolute ...
8
votes
2answers
357 views

Group-Interview Secretary Problem

The secretary problem is a well-studied optimal stopping problem with a simple solution. Suppose a set of $N$ candidates are interviewed for a secretarial problem, one at a time, in random order. ...
2
votes
2answers
434 views

Probability of an expected outcome

I'm in a class titled "Puzzle Based Learning" and we were given this problem: There is a new game show and you are the participant. There are two doors, each has a suitcase with gold coins ...
31
votes
3answers
466 views

Guessing a subset of $\{1,…,N\}$

I pick a random subset $S$ of $\{1,\ldots,N\}$, and you have to guess what it is. After each guess $G$, I tell you the number of elements in $G \cap S$. How many guesses do you need?
-1
votes
1answer
220 views

What is the name of that puzzle game? (slant)

What is that puzzle game? an example:: And where can I found some games like that? Thank you ..
10
votes
2answers
614 views

How many ways can we let people into a movie theater if they only have half-dollars and dollars?

My interest in combinatorics was recently sparked when I read about the many things that the Catalan numbers count, as found by Richard Stanley. I picked up a copy of Brualdi's Combinatorics, and ...