## Tagged Questions

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### Covering a Cube with a Square

Suppose you are given a single unit square, and you would like to completely cover the surface of a cube by cutting up the square and pasting it onto the cube's surface. Q1. Wh …
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### Looking for a “scientific” application of a recreational puzzle.

First of all the puzzle. A barman's got 15 glasses which are initially somehow divided into several stacks. The barman repeats the following process a thousand times. He takes th …
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### Does the set of happy numbers have a limiting density?

A positive integer $n$ is said to be happy if the sequence $$n, s(n), s(s(n)), s(s(s(n))), \ldots$$ eventually reaches 1, where $s(n)$ denotes the sum of the squared digits of $n$. …
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### Surface equivalent of catenary curve

A catenary curve is the shape taken by an idealized hanging chain or rope under the influence of gravity. It has the equation $y= a \cosh (x/a)$. My question is: What is the s …
Rain falls steadily on an island, a 2-manifold $M$, which you may assume, as you prefer, is: (a) smooth, or (b) a PL-manifold, or perhaps even (c) a triangulated irregular network …