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HMMT 二月 2006 · TEAM2 赛 · 第 9 题

HMMT February 2006 — TEAM2 Round — Problem 9

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

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