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.