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Category Archives: chatter
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
Posted in chatter
4 Comments
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
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 wellintentioned*, 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
I hate the Pumping Lemma
I hate the Pumping Lemma for regular languages. It’s a complicated way to express an idea that is fundamentally very simple, and it isn’t even a very good way to prove that a language is not regular. Here it is, … Continue reading
Posted in chatter
45 Comments