HMMT 二月 2009 · GEN2 赛 · 第 2 题

HMMT February 2009 — GEN2 Round — Problem 2

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

解析

[ 2 ] How many ways can you tile the white squares of following 2 × 24 grid with dominoes? (A domino covers two adjacent squares, and a tiling is a non-overlapping arrangement of dominoes that covers every 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 3 ways of tiling each of these sub-rectangles independently, for a total of 3 = 27 possibilities. 2009