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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
Posted in chatter, Mathematics
1 Comment
Almostmagic squares of squares
In the last post we saw that every 3×3 almostmagic square is a rearrangement of three threeterm 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 nineyearold 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
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 categorytheoretic 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
Posted in Mathematics
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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
Beyond Bézier curves
There is a new feature of Pages and Keynote, not mentioned in any of Apple’s publicity nor in any press coverage I’ve seen, that is really very interesting. Perhaps it will even one day prove to have been revolutionary, in … Continue reading
The algebra of Unix command substitution
Shadab Ahmed raised an interesting question. Open a Unix command shell, type : ‘!!’ and press return. Then type : “!!” ‘!!’ and press return. Now repeat the following a few times: press the up arrow, and press return.
Posted in Mathematics
6 Comments