Mathematics
Strategies in Games
Non-Attacking Rooks Placement Game

Non-Attacking Rooks Placement Game

Two people take turns placing rooks on the chessboard (one rook at a time) so that they do not beat each other. (Who placed which rook is not taken into account. You cannot place a rook even under the battle of your own rook.) Whoever cannot place a rook loses. Who will win if played correctly – first or second?

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Non-Attacking Rooks — Take-Turns Puzzle

Your turn. Place a rook so it doesn’t share a row or column with any other rook.
How to play: Tap/click a square to place a rook. Rooks cannot share a row or column. If it’s your turn and there’s no legal square, you lose.
legal squares blocked squares

Fun fact: With perfect play, the second player wins by mirroring each non-diagonal move \((i,j)\) with \((j,i)\). If you play on the diagonal, they play another free diagonal. Max 8 rooks fit—so the second player places the 8th and you get stuck.

Answer
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