Maths Olympiad Prep

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Combinatorics Difficulty 4.9 AIME Find the answer

6. Figure 1 is a chess endgame where the Red side (KaiTi font) is certain to win. If the Red side does not move the horse, but only moves the pawn, then, the number of shortest ways to checkmate the Black king is:

Pick one

Solution

6.C.

According to the rules, the red pawn can only checkmate the black general by moving to the position of the black advisor on the right. The numbers in Figure 4 represent the number of shortest moves for the red pawn to reach that intersection. Therefore, the number of shortest moves is 17.

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