HMMT 二月 2012 · COMB 赛 · 第 4 题
HMMT February 2012 — COMB Round — Problem 4
题目详情
英文原题
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 xand yare not both odd. How many ways can he get to the point (8 ,14)?
解析
英文解析
- A frog is at the point (0 , 0). Every second, he can jump one unit either up or right. He can only moveto 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 frogchooses to move right, his next move will also have to be a step right; similarly, if he moves up, hisnext move will have to be up.
If we “collapse” each double step into one step, the problem simply becomes how many ways are thereto move to the point (4 , 7) using only right and up steps, with no other restrictions. That is 11 steps
( )
total, so the answer is = 330.11 4