Quote:
Originally Posted by petrw1
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, backtracking and early termination detection. A lot fewer than
^{80}C
_{40} positions to examine.