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HMMT 二月 2009 · GEN2 赛 · 第 2 题

HMMT February 2009 — GEN2 Round — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 2 ] How many ways can you tile the white squares of following 2 × 24 grid with dominoes? (A dominocovers two adjacent squares, and a tiling is a non-overlapping arrangement of dominoes that coversevery white square and does not intersect any black square.)
    2009
解析

英文解析

  1. [ 2 ] How many ways can you tile the white squares of following 2 × 24 grid with dominoes? (A dominocovers two adjacent squares, and a tiling is a non-overlapping arrangement of dominoes that coversevery white square and does not intersect any black square.)
    Answer: 27
    Solution: Divide the rectangle into three 3 × 8 sub-rectangles. It is easy to count that there are 3
    ways of tiling each of these sub-rectangles independently, for a total of 3 = 27 possibilities.3
    2009