HMMT 二月 2005 · TEAM2 赛 · 第 2 题

英文解析

2. [10] What are the dimensions of the rectangle of smallest area that is ( a, b )-tileable?
   Solution: If a = 0, then a 1 × 2 b rectangle is tileable in an obvious way. If a > 0, thena 2 a × 2 b rectangle is tileable by dividing the rectangle into quarters and pairing eachsquare with a square from the diagonally opposite quarter. The answer is thereforemax { 1 , 2 a } × 2 b . Minimality of area follows from the next question.
   b ba
   1 a