HMMT 二月 2010 · 冲刺赛 · 第 8 题

HMMT February 2010 — Guts Round — Problem 8

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

解析

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