Sunday 27 December 2015

A Chess Puzzle

Once upon a time, in a former life, I used to do computer science.  This Christmas, my friend Ian sent me a reminder of some of the research we worked on together - a set of 3 mugs.  Our research involved a chess puzzle, "peaceably coexisting armies of queens":  given a chessboard, n squares by n squares, what is the maximum number of white queens that can be placed so that they don't attack any of the same number of black queens (and v.v.)?  (Two queens of different colours attack each other according to the rules of chess i.e. if they are on the same row, column or diagonal.)

The puzzle had only been solved for small-sized boards, but we were able to apply techniques we had developed to solve some larger instances.  The mugs that Ian sent show a solution for an 11 × 11 board, with 17 queens of each colour and none of the white queens attacking any of the black queens - we found this solution and showed that 17 is the maximum number for this size of board.  (If you want to stick to a proper 8 × 8 chess board, you can only have 9 queens of each colour.)

It makes a very striking picture, and I'm really proud of my mugs.

Nothing at all to do with knitting - sorry.

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