Author Archives: Robin Houston

Superpermutations: lower bound

I wrote about superpermutations here: a superpermutation is a string that has as substrings all the permutations of some set of symbols. For example, there are six permutations of the symbols 1, 2, 3. They are: 123, 132, 213, 231, … Continue reading

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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

Posted in chatter, Mathematics | 1 Comment

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

Posted in chatter, Mathematics | 2 Comments

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

Posted in chatter, Mathematics | 2 Comments

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

The Government Statistical Service’s terrible spreadsheet advice

The UK Government Statistical Service recently released its good practice guidance for releasing statistics in spreadsheets. While this advice is clearly well-intentioned*, and parts of it are good, the overall effect is to encourage the release of data in formats … Continue reading

Posted in chatter, Kiln | 6 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

Posted in chatter, Mathematics, news | 6 Comments

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 | 3 Comments

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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The bicycle lock problem

Don’t lock your bicycle with a combination lock. Someone will steal it: I learnt this the hard way. It’s quite easy to open a combination lock by feel, without knowing the combination. Try it: with a bit of practice, you … Continue reading

Posted in algorithms, Mathematics | 4 Comments