PUMaC 2018 · 团队赛 · 第 15 题

PUMaC 2018 — Team Round — Problem 15

Aaron the Ant is somewhere on the exterior of a hollow cube of side length 2 inches, and Fred the Flea is on the inside, at one of the vertices. At some instant, Fred flies in a straight line towards the opposite vertex, and simultaneously Aaron begins crawling on the exterior of the √ √ cube towards that same vertex. Fred moves at 3 inches per second and Aaron moves at 2 inches per second. If Aaron arrives before Fred, the area of the surface on the cube from which √ Aaron could have started can be written as aπ + b + c where a, b , and c are integers. Find a + b + c .

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