# Questions tagged [recreational-mathematics]

Applications of mathematics for the design and analysis of games and puzzles

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Motivation. The following has a real-life (!) inspiration from a discussion about how to connect lamps and switches in an efficient way. Question. Let $n\in\mathbb{N}$ be a positive integer and let $\{... 9 votes 0 answers 126 views ### Is there an open subset$A$of$[0,1]^2$with measure$>\frac{1}{100}$that satisfies this property? This is a crosspost from MSE. Can we find for any given$\varepsilon>0$an open subset$A\subseteq[0,1]^2$with measure$>\frac{1}{100}$such that, for any smooth curve$\gamma:[0,1]\to\mathbb{R}...
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Loosely inspired by the game Abalone, I've encountered the following simple problem I cannot solve. Suppose that we are given a finite set of marbles on an infinite chessboard. One move consists of ...
93 views

### Can you escape from two lions in a closed arena?

You're at the center of a circular arena. A pair of lions are at the border, planning to catch you. One of them moves as fast as you, but the other moves slower than you. The three of you are confined ...
231 views

### Math videos featuring interesting data animations

I am looking for interesting videos featuring pure data animations (not someone talking about math, but a video featuring some math phenomenon). I am interested in videos that tell a story, rather ...
1 vote
259 views

### Runtime for Terrible "Sorting Algorithm"?

Before I begin, I apologize for the bad wording. Consider the following "sorting algorithm": Suppose there are $n$ books on the bookshelf labeled $1$-$n$, and ordered from left to right in a ...
487 views

### How far away can we get by multiple rounding and unit change?

This question is inspired by xkcd #2585 (Rounding): Let $u_0,\ldots,u_n$ be positive real numbers (we can assume w.l.o.g. that $u_0=1$) or “units”. Consider the following directed graph: its vertices ...
445 views

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### Can Chang and Wang's proof of Thue’s Theorem on circular packing be extended into other dimentions?

The simplicity of Chang and Wang's proof of Thue’s Theorem (link on arxiv) on circular packing took me by surprise. Have similar ideas been found helpful in other dimensions? For example, partition ...
153 views

### Pathfinder Olympiad book's question [closed]

Let $$x_{n}=\sqrt{2+\sqrt{3+\sqrt{4+\cdots+\sqrt[n]{n}}}};$$ prove that $$x_{n+1}-x_{n}<\frac{1}{n !}, \quad n=2,3, \dotsc.$$