PUMaC 2025 · 团队赛 · 第 9 题

PUMaC 2025 — Team Round — Problem 9

For all ( a, b ) ∈ Z (excluding the origin), Biao draws the perpendicular bisector of the line 2 segment from (0 , 0) to ( a, b ). An ant starts at (0, 0) and walks around on R . Let S be n the set of points that the ant can reach by crossing up to n of Biao’s perpendicular bisectors. 1 1 Thus S is the square whose vertices are ( ± , ± ) and S is the square whose vertices are 0 1 2 2 (0 , 1) , (1 , 0) , (0 , − 1) , ( − 1 , 0). Find the perimeter of S . 3

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