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MathNet 2019-part-02 — 184 problems (EN–VI) Question 128

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 128

Kings and rooks are placed on an $8 \times 8$ board, so that none of the pieces is under attack. A king attacks neighbouring squares (there are eight of them, except when the king is placed on the edge of the board), and a rook attacks all squares in the same row or column as the square where the rook is placed. At most how many pieces are on the board, if there is an equal number of rooks and kings?
(Borna Vukorepa)