Questions tagged [recreational-mathematics]

Mathematics done just for fun, often disjoint from typical school mathematics curriculum. Also see the [puzzle] and [contest-math] tags.

Recreational mathematics is a general term for mathematical problems studied for the sake of pure intellectual curiosity, or just for the enjoyment of thinking about mathematics, without necessarily having any practical application or expectation of deep theoretical results.

Recreational mathematics problems are often easy to understand even for people without an extensive mathematical education, even if the theory they lead to may turn out to be surprisingly deep. Thus, recreational mathematics can serve to attract the curiosity of non-mathematicians and to inspire them to develop their mathematical skills further.

Many typical recreational mathematics problems fall into the fields of discrete mathematics (combinatorics, elementary number theory, etc.), probability theory and geometry. Important contributors to recreational mathematics are Sam Loyd and Martin Gardner.

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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…
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Probability that a stick randomly broken in five places can form a tetrahedron

Edit (June. 2015) This question has been moved to MathOverflow, where a recent write-up finds a similar approximation as leonbloy's post below; see here. Randomly break a stick in five places. Question: What is the probability that the resulting…
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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 Laczkovich gave a solution with many hundreds of…
Ed Pegg
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Topology: The Board Game

Edit: I've drawn up some different rules, a map and some cards for playing an actual version of the game. They're available at my personal website with a Creative Commons Attribution 4.0 license. This is a math education question that I've been…
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Mondrian Art Problem Upper Bound for defect

Divide a square of side $n$ into any number of non-congruent rectangles. If all the sides are integers, what is the smallest possible difference in area between the largest and smallest rectangles? This is known as the Mondrian Art Problem. For…
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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…
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Can we remove any prime number with this strange process?

This is a little algorithm I made today, which may appear to be quite complex so I will start with an example. The process goes as follows: Start with the first prime number, $2$. From $2$, add the next prime number ($3$) to get $2+3=5$. There are…
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How do you find the center of a circle with a pencil and a book?

Given a circle on a paper, and a pencil and a book. Can you find the center of the circle with the pencil and the book?
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If $x$, $y$, $x+y$, and $x-y$ are prime numbers, what is their sum?

Suppose that $x$, $y$, $x−y$, and $x+y$ are all positive prime numbers. What is the sum of the four numbers? Well, I just guessed some values and I got the answer. $x=5$, $y=2$, $x-y=3$, $x+y=7$. All the numbers are prime and the answer is…
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What's the largest possible volume of a taco, and how do I make one that big?

Let $f$ be a continuous, even function over some interval $I=[-a,a]$ such that the total arc length of $f$ over $I$ is at least $2$, $f(0)=0$, and $f$ is increasing on $(0,a)$. [You might imagine something like $f(x)=x^2$.] View the graph of…
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$4494410$ and friends

The number $4494410$ has the property that when converted to base $16$ it is $44944A_{16}$, then if the $A$ is expanded to $10$ in the string we get back the original number. $3883544142410_{10}=3883544E24A_{16}$ is another. These numbers are in…
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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
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Can the golden ratio accurately be expressed in terms of $e$ and $\pi$

I was playing around with numbers when I noticed that $\sqrt e$ was very somewhat close to $\phi$ And so, I took it upon myself to try to find a way to express the golden ratio in terms of the infamous values, $\large\pi$ and $\large e$ The closest…
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100 blue-eyed islanders puzzle: 3 questions

I read the Blue Eyes puzzle here, and the solution which I find quite interesting. My questions: What is the quantified piece of information that the Guru provides that each person did not already have? Each person knows, from the beginning, no…
A Googler
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Reversing an integer's digits is multiplicative for small digits

So my 7 year old son pointed out to me something neat about the number 12: if you multiply it by itself, the result is the same as if you took 12 backwards multiplied by itself, then flipped the result backwards. In other words: $$12 × 12 =…