Is there an easy way to list all different configurations of a tictactoe game? For the first turn it is still quite simple, e.g. all these
x - - - - x - - - - - - x = 1st player
- - - - - - - - - - - - o = 2nd player
- - - - - - - - x x - - - = empty
are the same configuration, because of the rotational symmetry and there are only 3 "different" ones for the first turn:
x - - - x - - - -
- - - - - - - x -
- - - - - - - - -
However, already for the second turn I can't think of anything more clever than brute force trying all moves and check them against all symmetries. Is there any efficient way to get a list of all configurations that can occur in a normal tictactoe game (ie once one player has 3 in a row, the game is over)?