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Old 2020-06-22, 02:43   #1
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petrw1's Avatar
Nov 2006
Saskatchewan, Canada

43·107 Posts
Default 9x9 board game odds

There's a game that is played on a 9x9 grid with a free space in the middle. Each player has 40 pieces to be played in any of the 80 remaining tiles, one at a time, in alternation. I'm interested in the proportion (or equivalently the number) of arrangements in which the 80 tiles can be placed on the board such that no player gets 5 in a row, orthogonally or diagonally. And, as a more complicated version, how many ways such that neither player gets more than one row of 5 on the board.
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