Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [puzzle]

For questions about the mathematical principles behind puzzle, games, riddles, or their possible solutions. Questions that are not strictly mathematical in nature should be asked on Puzzling Stack Exchange.

Many puzzles, games, and riddles are based on mathematical concepts. This tag is for questions that ask about the mathematics behind a puzzle, game, or riddle, or about the solutions to mathematical puzzles.

If you already know the answer to the puzzle you are posting, you might consider posting your question on Puzzling Stack Exchange, instead. If you do end up posting your question on Mathematics Stack Exchange (MSE), please read the following meta posts on these kinds of questions before asking your question:

If you do end up posting on MSE, please make it clear in your question that you are "puzzling" the community and that you will be answer the question yourself if no one in the community posts your desired solution.

3426 questions
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10 answers

V.I. Arnold says Russian students can't solve this problem, but American students can -- why?

In a book of word problems by V.I Arnold, the following appears: The hypotenuse of a right-angled triangle (in a standard American examination) is $10$ inches, the altitude dropped onto it is 6 inches. Find the area of the triangle. American…
Eli Rose
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306
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40 answers

One question to know if the number is 1, 2 or 3

I've recently heard a riddle, which looks quite simple, but I can't solve it. A girl thinks of a number which is 1, 2, or 3, and a boy then gets to ask just one question about the number. The girl can only answer "Yes", "No", or "I don't know," and…
Gintas K
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267
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15 answers

"Which answer in this list is the correct answer to this question?"

I received this question from my mathematics professor as a leisure-time logic quiz, and although I thought I answered it right, he denied. Can someone explain the reasoning behind the correct solution? Which answer in this list is the correct…
Bora M. Alper
  • 2,233
228
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4 answers

How many fours are needed to represent numbers up to $N$?

The goal of the four fours puzzle is to represent each natural number using four copies of the digit $4$ and common mathematical symbols. For example, $165=\left(\sqrt{4} + \sqrt{\sqrt{{\sqrt{4^{4!}}}}}\right) \div .4$. If we remove the restriction…
David Bevan
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209
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24 answers

Taking Seats on a Plane

This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless Imagine there are a 100 people in line to board a plane that seats 100. The first person in…
crasic
  • 5,139
162
votes
20 answers

Are there any open mathematical puzzles?

Are there any (mathematical) puzzles that are still unresolved? I only mean questions that are accessible to and understandable by the complete layman and which have not been solved, despite serious efforts, by mathematicians (or laymen for that…
Řídící
  • 3,268
161
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2 answers

Slice of pizza with no crust

The following question came up at a conference and a solution took a while to find. Puzzle. Find a way of cutting a pizza into finitely many congruent pieces such that at least one piece of pizza has no crust on it. We can make this more…
Dan Rust
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137
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5 answers

Help find hard integrals that evaluate to $59$?

My father and I, on birthday cards, give mathematical equations for each others new age. This year, my father will be turning $59$. I want to try and make a definite integral that equals $59$. So far I can only think of ones that are easy to…
Argon
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120
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18 answers

Fastest way to meet, without communication, on a sphere?

I was puzzled by a question my colleague asked me, and now seeking your help. Suppose you and your friend* end up on a big sphere. There are no visual cues on where on the sphere you both are, and the sphere is way bigger than you two. There are no…
Rob Audenaerde
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113
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5 answers

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 Laczkovich gave a solution with many hundreds of…
Ed Pegg
  • 21,868
109
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12 answers

Logic puzzle: Which octopus is telling the truth?

King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always tell the truth. One day, four servants met. The blue one says, “Altogether, we have 28…
a1bcdef
  • 2,315
107
votes
11 answers

Riddles that can be solved by meta-assumptions

The website of my university posted a riddle that goes something like this: Riddle There are three men named 1,2 and 3 and each one has two colored dots on his forehead. Possible colors are black and red. No color is used more than four times. The…
M. Winter
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104
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22 answers

What are Your Favourite Maths Puzzles?

We all love a good puzzle To a certain extent, any piece of mathematics is a puzzle in some sense: whether we are classifying the homological intersection forms of four manifolds or calculating the optimum dimensions of a cylinder, it is an element…
Tom Boardman
  • 3,675
103
votes
11 answers

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 range. If the numbers chosen share a prime factor,…
user139000
103
votes
2 answers

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 see how others might think about it. $100$ rooms…
Jared
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