HMMT 二月 2011 · ALGCALC 赛 · 第 2 题
HMMT February 2011 — ALGCALC Round — Problem 2
题目详情
英文原题
- Josh takes a walk on a rectangular grid of n rows and 3 columns, starting from the bottom left corner.
At each step, he can either move one square to the right or simultaneously move one square to the leftand one square up. In how many ways can he reach the center square of the topmost row?
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解析
英文解析
- Josh takes a walk on a rectangular grid of n rows and 3 columns, starting from the bottom left corner.
At each step, he can either move one square to the right or simultaneously move one square to the leftand one square up. In how many ways can he reach the center square of the topmost row?
n − 1
Answer: 2 Note that Josh must pass through the center square of each row. There are 2 waysn − 1
to get from the center square of row k to the center square of row k + 1. So there are 2 ways to getto the center square of row n .
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