HMMT 二月 2005 · TEAM1 赛 · 第 3 题
HMMT February 2005 — TEAM1 Round — Problem 3
题目详情
- [10] Show that no rectangle of the form 1 × k or 2 × n , where 4 - n , is (1 , 2)-tileable.
解析
- [10] Show that no rectangle of the form 1 × k or 2 × n , where 4 - n , is (1 , 2)-tileable. Solution: The claim is obvious for 1 × k rectangles. For the others, color the first two columns black, the next two white, the next two black, etc. Each (1 , 2) domino will contain one square of each color, so in order to be tileable, the rectangle must contain the same number of black and white squares. This is the case only when 4 | n .