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HMMT 二月 2005 · TEAM2 赛 · 第 5 题

HMMT February 2005 — TEAM2 Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [35] Prove that an m × n rectangle is (0 , b )-tileable if and only if 2 b | m or 2 b | n .
解析

英文解析

  1. [35] Prove that an m × n rectangle is (0 , b )-tileable if and only if 2 b | m or 2 b | n .
    Solution: It is easy to exhibit a tiling of such a rectangle. The other direction followsfrom below. (It is also possible to prove this using a coloring argument as above:
    starting in one corner, divide the board into b × b blocks and color them checkerboardfashion. The details are left to the reader.)