Question 23

In a single move a King $$K$$ is allowed to move to any of the squares touching the square it is on, including diagonals, as indicated in the figure. The number of different paths using exactly seven moves to go from $$A$$ to $$B$$ is

Correct Answer: 127

Solution

Because exactly seven moves are required, only the directed moves toward the target that can still reach $$B$$ in the remaining moves are relevant. Counting paths through the intermediate layers gives contributions $$1(1+3)+3(1+3+5)+5(3+5+4)+4(5+4)$$. This totals $$4+27+60+36=127$$ paths.

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In a single move a King $$K$$ is allowed to move to any of the squares touching the square it is on, including diagonals, as indicated in the figure. The number of different paths using exactly seven moves to go from $$A$$ to $$B$$ is

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