Category Archives: Mathematics

Squares of squares, and the group of rational points on the circle

The purpose of this post is to describe a slightly different way of thinking about the existence – or otherwise – of a 3×3 magic square of squares. Of course it may not lead to any real progress, but it … Continue reading

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Almost-magic squares of squares

In the last post we saw that every 3×3 almost-magic square is a rearrangement of three three-term arithmetic progressions that have the same common difference. In other words, if we pick any three numbers x, y and z, and any … Continue reading

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Magic squares of squares: Part I

A recent Numberphile video discussed an intriguing unsolved problem in number theory: is there a 3×3 magic square whose entries are all square numbers? (Matt Parker proposed a solution which doesn’t quite work: see the video for more. The “Parker … Continue reading

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Counting coins

This afternoon, Matt Locke tweeted the following problem from his nine-year-old daughter’s maths homework:

Posted in algorithms, Mathematics | 14 Comments

Tackling the Minimal Superpermutation Problem

What’s the shortest string that contains every possible permutation of ABCD somewhere inside it? As it happens, it’s 33 letters long: ABCDABCADBCABDCABACDBACBDACBADCBA. A string like this is called a minimal superpermutation. So what’s the shortest string that contains every possible … Continue reading

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Revisiting “On editing text”

This document is an incomplete draft. About two years ago I wrote about a category-theoretic treatment of collaborative text editing. That post is unique in the history of Bosker Blog in having been cited – twice so far that I know … Continue reading

Posted in algorithms, category theory, Mathematics | 1 Comment

Decoding the mysterious symmetry of the bicycle lock numbers

Suppose you have a lock of this sort that has n dials and k numbers on each dial. Let m(n, k) be the minimum number of turns that always suffice to open the lock from any starting position, where a turn … Continue reading

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