HMMT 二月 2006 · TEAM2 赛 · 第 9 题

英文解析

9. [25] Show a way to construct an equiangular hexagon with side lengths 1, 2, 3, 4, 5,
   and 6 (not necessarily in that order).
   Solution: The trick is to view an equiangular hexagon as an equilateral trianglewith its corners cut off. Consider an equilateral triangle with side length 9, and cutoff equilateral triangles of side length 1, 2, and 3 from its corners. This yields anequiangular hexagon with sides of length 1 , 6 , 2 , 4 , 3 , 5 in that order.