- #1

Jameson

Gold Member

MHB

- 4,541

- 13

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

View attachment 1796

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,

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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View attachment 1796

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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