Mathematics Stack Exchange
Mathematics Stack Exchange

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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A 2-variable function positive in exactly one quadrant

I've been trying to think of a function $f(x,y)$ that is only positive in the $+x, +y$ quadrant, but I'm stumped. To be more precise, I'm looking for a function that satisfies these conditions: $f$ is continuous and differentiable $f(x,y) > 0 \iff…
user3210986
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Partition the following graph into 4 parts

Partition the following graph into $4$ parts, each with the same shape-size, and each with one circle in it. $$\begin{array}{cc} 1& 1& 1& 1& 1& 1\\ 0 &0 &1 &1 &1 &1\\ 1 &1 &0 &1 &1 &1\\ 1 &1 &1 &1 &1 &1\\ 1 &1 &1 &1 &1 &0\\ 1 &1 &1 &1 &1 &1…
forlorn
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Problem about a process with bins of balls

A friend of mine give me this problem for fun: Given $\frac {n(n+1)}{2}$ balls, first we divide arbitrarily these balls in baskets, after that we make another basket with one ball of each basket e do this procedure infinitely. I want to prove that…
user85493
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Unusual definition of the sphere $S^n$

In a paper I’m reading, the author defines the sphere $S^{m(k-1)-1}$ ($k \geq 2$) as the set of $m \times k$ matrices $(a_{ij})$, with $a_{ij} \in \mathbb{R}$ and satisfying the following two properties: $$\forall i, \sum_{j=1}^k a_{ij} =…
MT_
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How to evaluate $\sum_{n=1}^{\infty} \frac{1}{n^2+4n+1}$

How would we show that $$\sum_{n=1}^{\infty} \frac{1}{n^2+4n+1} = \frac{1}{6}(-2 -\pi \sqrt3 \cot(\pi \sqrt3))$$ I'm not sure how I'd go about it, but got the answer off wolfram alpha. Could someone lead me in the right direction?-series
user817934
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Coincidence? $\left(\frac 1e\right)^{\frac 1e}\approx \ln 2$

Is it a coincidence that $$\color{lightgrey}{0.6922\cdots =}\left(\frac 1e\right)^{\frac 1e}\approx \ln 2\color{lightgrey}{=0.6931\cdots}$$ ?
Hypergeometricx
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Another puzzle with locks

There is a safe with three locks, like the ones in the hotel rooms that are opened with a "key" which is similar to a credit card. There are three keys, a correct one for one for each of the locks, but the correspondence is unknown. If only one or…
mau
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What length is needed to coil around a tube?

For a project I'm doing, I'm wrapping an led strip light around a tube. The tube is 19mm in diameter and 915mm tall. I'm going to coil the led strip around the tube from top to bottom and the strip is 8mm wide, so the coils will be 8mm apart. How…
Ryan
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What is the smallest number which begins with 7 and if you bring the 7 to the least significant position it becomes a third of the original number?

First I wrote the equation: $7\times 10^2+c_1\times10^1+c_0\times10^0 = 3(100c_1+10c_0+7)$ which becomes $679=290c_1+29c_0$ Then I try fix as many variables as possible. In this first iteration, for example, $c_0$ is obviously $1$ because otherwise…
gurghet
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speed word problem

I've got this question: ) A ladder 15ft long leans against a vertical wall. If the top slides down at 2ft per second, how fast along the ground is the base moving when it is 5ft from the wall? ..... I'm not entirely…
user436717
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Fermat's Last Theorem Alternate Solution

Have any other proofs beside Andrew Wiles proof been proposed and proved?
Brothersquid
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Too simple to prove?

Can a problem be too simple to prove completely one way or the other? Its a question I've been asking myself for a little while now. I've been playing around with some open math problems that (at first glance) appear to be simple, but alas,answers…
Lonnie Hibbs Jr
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Figure out what to multiply a number by to get it to double after x times.

I'm trying to figure out if there is a way to calculate what to multiply a number by to get it to double after $x$ times. For example, the number $100$, would be $200$ after multiplying it by $m$ $7$ times. I'm not sure of a way to do this aside…
Chris Sewell
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Formula on conference t-shirt: $\ell(\beta) = \sum_{i=1}^{N}y_i \sum_{k=0}^{K}x_{ik}\beta_{k}-\log\left(1+e^{\sum_{k=0}^{K}x_{ik}\beta_{k}}\right)$

I need some assistance figuring out what this formula signifies and what it does. It is from a shirt I got recently at a conference and am curious about it. Thanks! $$\ell(\beta) = \sum_{i=1}^{N}y_i…
vlad
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Division Without Division

Ok. I'm having a bit of a problem with a mathematical task my friend challenged me with, find the answer to two divided numbers without any division and the method used has to work for all whole numbers, so let's say I have the numbers $13 / 3$, by…
Bornui sndrs
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