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Applications of mathematics for the design and analysis of games and puzzles

12 votes
3 answers
1k views

How to sample a uniform random polyomino?

A polyomino is formed by joining finitely many unit squares edge to edge. It may be regarded as a finite subset of the regular square tiling with a connected interior. In particular, for us, polyomino …
Matthew Kahle's user avatar
6 votes
1 answer
631 views

How many convex shapes can be made with the pieces of the Stomachion?

Tangrams are a well-known dissection of the square into seven convex polygons. One fun mathematical question is: how many convex rearrangements of the seven pieces are there? Answer: there are 12 mor …
Matthew Kahle's user avatar