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Old 2020-06-22, 04:06   #2
retina
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"The unspeakable one"
Jun 2006
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Quote:
Originally Posted by petrw1 View Post
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.
I don't have an answer.

But I suspect that would be doable by brute force if one incorporated mirroring, back-tracking and early termination detection. A lot fewer than 80C40 positions to examine.
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