Any math which can be made into a game or puzzle (though some of these puzzles can be quite hard). Martin Gardner wrote a column on this subject called Mathematical Games in Scientific American, including such subjects as tiling, conway's game of life, fractals, prime numbers and lots of other number theory, eleusis, etc. These columns were reprinted in a series of books.

Douglas Hofstadter was Gardner's successor.

Most of the older recreational mathematics which was at all interesting has turned into old chestnuts.

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