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HMMT 二月 2010 · 冲刺赛 · 第 8 题

HMMT February 2010 — Guts Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Each square in the following hexomino has side length 1. Find the minimum area of any rectanglethat contains the entire hexomino.
解析

英文解析

  1. [ 6 ] Each square in the following hexomino has side length 1. Find the minimum area of any rectanglethat contains the entire hexomino.
    Answer: If a rectangle contains the entire hexomino, it must also contain its convex hull, which is 21
    an origin-symmetric hexagon. It is fairly clear that the smallest rectangle that contains such a hexagon 2
    must share one set of parallel sides with the hexagon. There are three such rectangles, and checkingthem all, we find that the one shown below is the smallest. It has area .21
    Guts Round 2