An 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 tenth problem of the set Winning Strategies .
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1 solution
Every time Dan puts down a piece, Sam will put down a piece that is 180 ∘ away (rotating about the middle of the square). Since the board has even dimensions, by symmetry this will always be possible if Dan's move was possible. Therefore, Sam wins.