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Dear GAP Forum,

Ed Pegg informed the forum of the Alien Tiles puzzle, which is indeed very

pretty, and does have connections to quite a lot of interesting topics

relevant to GAP, including group theory, linear algebra and algebraic

combinatorics.

Without giving away secrets, some algebra and a few dozen lines of GAP code

enable one to find the shortest move sequence to any position very quickly,

and to answer questions such as the one Ed asks (if I understand his question

correctly). Some interesting questions still remain however, about both the

game as given (7x7, 4 colours) and generalizations to other board sizes,

numbers of colours and different but related sets of rules.

Steve Linton

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