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- Jan 26, 2012
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A standard tic-tac-toe board (or noughts and crosses) is a 3x3 grid, with 9 total spaces.

There are many different ways that the X's and O's can be placed on the board. If we ignore for now the rule that 3 pieces of one type in a row wins, how many ways can we fill the board completely? Assume that the same piece, X or O, plays first each time so you will always have 1 more of that piece than the other.
Note: The problem isn't to count moves that lead to a certain position. 1 filled board can be reached many ways. Just count the number of total filled boards. Also, don't worry about rotations or reflections for you guys who are more advanced.
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Remember to read the POTW submission guidelines to find out how to submit your answers!

There are many different ways that the X's and O's can be placed on the board. If we ignore for now the rule that 3 pieces of one type in a row wins, how many ways can we fill the board completely? Assume that the same piece, X or O, plays first each time so you will always have 1 more of that piece than the other.
Note: The problem isn't to count moves that lead to a certain position. 1 filled board can be reached many ways. Just count the number of total filled boards. Also, don't worry about rotations or reflections for you guys who are more advanced.
--------------------
Remember to read the POTW submission guidelines to find out how to submit your answers!