olymmath

HMMT November 2017 U15

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On a 3×33 \times 3 chessboard, each square contains a knight with 12\frac{1}{2} probability. What is the probability that there are two knights that can attack each other? (In chess, a knight can attack any piece which is two squares away from it in a particular direction and one square away in a perpendicular direction.)

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{209}{256}

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