An exercise for the combinators and combinatrices out there:
How many different 2x2 Go games are there?
An unnamed source claims 386,356,909,593, but I don't find this
credible.
There are at most 3^4 = 81 POSITIONS on a 2x2 board, including the
illegal ones. If we require that at least one point on the board be
vacant (necessary for the position to be legal), then there are at
most 3^4 - 2^4 = 65. We can remove 8 more where one stone is captured
(but still on the board), leaving 57. A game therefore involves at
most 56 non-passing moves (as one more would violate superko).
Peter Drake
http://www.lclark.edu/~drake/
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