PUMaC 2024 · 团队赛 · 第 4 题

PUMaC 2024 — Team Round — Problem 4

Consider the 100 × 100 grid of points with integer coordinates S = { ( x, y ) ∈ Z | 1 ≤ x ≤ 1 100 , 1 ≤ y ≤ 100 } . A set C is formed by selecting each point p ∈ S with probability 2 uniformly at random. The expansion of C is defined as the set of points q ∈ S such that min d ( q, p ) ≤ 1, where d ( q, p ) denotes the Euclidean distance between q, p . If the expected p ∈ C A size of the expansion of C can be written as for relatively prime positive integers A, B , find B A + B .

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