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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
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
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
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
“Venn diagram” partitioning
Paddy3118 wrote about partitioning elements in the same way a Venn diagram does. So, if we have sets A, B and C, the partitions are
Posted in algorithms, chatter
1 Comment
Linear Logic without Units
My PhD thesis (2007) was available for several years from my web site at the University of Manchester, but since that site was taken down it’s been unavailable. Today’s announcement is that I’ve finally got round to uploading it to GitHub.
Posted in chatter
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Puzzles like Adrift
Quite a few people were surprised by my description of Adrift as a “new game” – even though it was very new at the time – because they had seen similar games or puzzles before. You can read some of … Continue reading
Posted in chatter
3 Comments
