PUMaC 2019 · 团队赛 · 第 1 题

PUMaC 2019 — Team Round — Problem 1

Two unit squares are stacked on top of one another to form a 1 × 2 rectangle. Each of the seven edges is colored either red or blue. How many ways are there to color the edges in this way such that there is exactly one path along all-blue edges from the bottom-left corner to the top-right corner?

解析

Two unit squares are stacked on top of one another to form a 1 × 2 rectangle. Each of the seven edges is colored either red or blue. How many ways are there to color the edges in this way such that there is exactly one path along all-blue edges from the bottom-left corner to the top-right corner? Proposed by: Nathan Bergman Answer: 30 There are four cases. First, the path that goes right then up; there are 10 ways to color this. Then the path that goes up then right; there are also 10 for this by symmetry. The path that goes up, right, up has 9 ways to be colored. Lastly, the path that goes right, up, left, up, right has 1 way. Then the answer is 30.