PUMaC 2024 · 个人决赛（B 组） · 第 3 题

PUMaC 2024 — Individual Finals (Division B) — Problem 3

Moby has an infinite piece of paper, an infinite straightedge, and a magic triangle. The paper starts with two points a distance 1 away. With the straightedge, he can connect any two points to form a line. With the magic triangle, he can take two points A and B and draw the two points C and D such that △ ABC and △ ABD are equilateral triangles. He can also draw a point at the intersection of any two lines or line segments. With finitely many operations, can Moby draw a square on the paper? A proof in the affirmative should consist of a clear depiction or description of steps taken. 1

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