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MathNet 2017-part-07 — 172 problems (EN–VI) Question 133

Math Olympiad Vault · MathNet 2017-part-07 — 172 problems (EN–VI)

Question 133

On a $3 \times 3$ chessboard, each square contains a Chinese knight with $\frac{1}{2}$ probability. What is the probability that there are two Chinese knights that can attack each other? (In Chinese chess, a Chinese knight can attack any piece which is two squares away from it in a particular direction and one square away in a perpendicular direction, under the condition that there is no other piece immediately adjacent to it in the first direction.)