HMMT 二月 2012 · COMB 赛 · 第 4 题
HMMT February 2012 — COMB Round — Problem 4
题目详情
- A frog is at the point (0 , 0). Every second, he can jump one unit either up or right. He can only move to points ( x, y ) where x and y are not both odd. How many ways can he get to the point (8 , 14)?
解析
- A frog is at the point (0 , 0). Every second, he can jump one unit either up or right. He can only move to points ( x, y ) where x and y are not both odd. How many ways can he get to the point (8 , 14)? Combinatorics Test Answer: 330 When the frog is at a point ( x, y ) where x and y are both even, then if that frog chooses to move right, his next move will also have to be a step right; similarly, if he moves up, his next move will have to be up. If we “collapse” each double step into one step, the problem simply becomes how many ways are there to move to the point (4 , 7) using only right and up steps, with no other restrictions. That is 11 steps ( ) 11 total, so the answer is = 330. 4