B-1) was a win by X?
B-2) was a win by O?
B-3) was a draw?
Game conventions:
The first move is X.
A game ends when one side wins or all 9 cells are occupied, which comes first. No further moves are made after end-of-game.
| A) Calculate the number of different possible games. Two games are different if the Nth move in each game is different, for at least one value of N. | |
| B) In how many of the total number of games: B-1) was a win by X? B-2) was a win by O? B-3) was a draw? |
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| C) Calculate the number of different possible board configurations in all possible games (not just final boards at ends of games, but all intermediate boards). Include the blank (beginning) board. In this calculation, these two boards are different. |
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| D) Most boards in C) above are reducible to other boards. Calculate the number of irreducible board families. All the boards to the right are reducible to each other via rotations of 90, 180 and 270 degrees, or a mirror flip plus a possible added rotation by 90, 180 or 270 degrees. Therefore the family of these 8 boards counts as a single irreducble board family. |
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