HMMT 二月 2005 · TEAM2 赛 · 第 3 题

英文解析

3. [20] Prove that every ( a, b )-tileable rectangle contains a rectangle of these dimensions.
   Solution: An m × n rectangle, m ≤ n , does not contain a max { 1 , 2 a } × 2 b rectangle ifand only if m < 2 a or n < 2 b . But if either of these is the case, then the square closestto the center of the rectangle cannot be paired with any other square of the rectangleto form a domino of type ( a, b ), so the rectangle cannot be ( a, b )-tileable.