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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Finding parameter paths for beautiful fractal animations

So I just got renewed interest in fractals and especially animations with fractals. To make an image or a frame, we usually need to evaluate a fractal for a subset of it's parameters. However for many fractals a large portion of the possible subsets…
mathreadler
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Solve the maximal value point of B-spline basis function

Description Let $\vec{U}=\{u_0,u_1,\ldots,u_m\}$ denotes a non-decreasing sequence of real numbers, i.e, $u_i\leq u_{i+1} \quad i=0,1,2\ldots m-1$. and the $i$-th B-spline basis function of $p$-degree, denoted by $N_{i,p}(u)$, is defined as…
xyz
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A prime-finding constant

Consider $\lfloor 10^n \times 0.731926765612646213686753345587262244668218433356357832021 \rfloor$. For each $n$, reverse the digits. If the number isn't already prime, find the next prime. For the first 24 values of $n$, the result is prime. This…
Ed Pegg
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"Problems worthy of attack prove their worth by fighting back.”

That is quote has been attributed to Piet Hein, inventor of the Soma cube, which is how I know of him. Q. Is the attribution correct? I wonder because the quote has a nice ring in English that it might not have in Danish, his native language.
Joseph O'Rourke
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Is there a heuristic reason behind this numerical coincidence?

Write $N(m, n; c)$ for the number of $m\times n$ zero-one matrices where each zero is adjacent to precisely $c$ others, where by "adjacent" I mean up/down/left/right but not diagonally. (Notice that we need $0 \leq c \leq 2$ here, as $c = 3,4$ has…
Daniel McLaury
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In what system(s) of numeration is 11111 a perfect square?

From Charles Trigg's "Mathematical Quickies: 270 Stimulating Problems with Solutions": In what system(s) of numeration is 11111 a perfect square? I have found one base that works: 3. I am not sure whether this is the only solution or not. So far,…
Marconius
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Proof of a discovery involving the square of whole numbers

It was probably discovered by someone else but: When you take the square of a non-zero whole number the sum of the numbers digit is always equal to $1,4,7,9$ How can I write a mathematical proof of that?
DoubleOseven
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A fashion victim puzzle

Consider $n \in \mathbb{N}$ fashion-sensitive kids, each wearing a T-shirt; for simplicity, kid $i \in \{1, \ldots, n\}$ initially wears shirt $i$. Tastes over the shirts are summarized in an $n \times n$ matrix: entry $a_{ij} \in \mathbb{R}$ in row…
Felix
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Does other solutions exist for $29x+30y+31z = 366$?

I was asked this trick question: If $29x + 30y + 31z = 366$ then what is $x+y+z=?$ The answer is $12$ and it is said to be so because $29$ , $30$ and $31$ are respectively the number of days of months in a leap year. Therefore $x + y + z$ must be…
Aswin P J
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First 10 digits after decimal point in the number $(1+\sqrt{3})^{2015}$

The question is how to find first 10 digits after decimal point in the number $(1+\sqrt{3})^{2015}$. I keep running into this kind of problems in a context of symmetric polynomials.
Glinka
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any Math game for kids?

I need to plan a "game" for kids about 10-11 years old that involves mathematics and some physical activity or game. It must be short-time and not very difficult because it's a stage of a big game. Could anyone give me a good idea? Thanks!
josdios
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An interesting wire-tying problem to match wire ends in as few trips as possible

You have $N$ wires that all extend from one location to a second distant location. The wire ends at both locations are unlabeled, and the goal is to label them all (on both ends) with distinct labels $1,2,\ldots, N$ so that the two ends of the same…
user2566092
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If $n$ people are placed in a room, prove that at least $2$ of those people will have the same number of friends in the room.

If $n$ people are placed in a room, then at least $2$ of those people will have the same number of friends in the room. I want to prove this statement. Here are some of my thoughts: If all the people are strangers, then clearly everyone has zero…
idkmybffjill
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If $\frac{(b−c)}{a} + \frac{(a+c)}{b} + \frac{(a−b)}{c}=1$ and $a-b+c \neq 0 $, then prove that $\frac 1a = \frac 1b + \frac 1c$

The question given is If $\dfrac{(b−c)}{a} + \dfrac{(a+c)}{b} + \dfrac{(a−b)}{c}=1$ and $a-b+c \neq 0 $ then prove that $\dfrac 1a = \dfrac 1b + \dfrac 1c$ I tried to take $abc$ on the right hand side after taking the LCM, but ended up with…
user103816
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How to compute the derivative of $x^x$ using the definition

I want to prove that $\displaystyle\lim_{h\to 0}\frac{(x+h)^{x+h}-x^x}{h}=x^x(\ln(x)+1).$ If I write $x^x$ as $e^{x\ln(x)}$ I get: $\displaystyle\lim_{h\to0}\frac{e^{(x+h)\ln(x+h)}-e^{x\ln(x)}}{h}$ but then I'm stuck. What are the next steps? Thanks…
Cristopher
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