A Grid of Pieces
Dan and Sam play a game on a grid, on which each one chooses and puts, in his turn, a single piece like these:
The pieces must not overlap and can't be partially outside of the grid.
The game finishes when someone can't put a piece on the board in his turn following the rules (who is the loser). If Dan begins, who will win? This means, who has a winning strategy?
This is the eleventh problem of the set Winning Strategies .
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1 solution
Not a solution, but a comment. This game is known as Cram , and as far as I know, the general odd-by-odd case is unsolved (but the even-by-even and even-by-odd cases are easy to analyze). If someone has a proof for the 9 × 9 case, I would like to see it.