HMMT 十一月 2008 · 冲刺赛 · 第 26 题
HMMT November 2008 — Guts Round — Problem 26
题目详情
英文原题
- [ 13 ] John M. is sitting at (0 , 0), looking across the aisle at his friends sitting at ( i, j ) for each 1 ≤ i ≤ 10
and 0 ≤ j ≤ 5. Unfortunately, John can only see a friend if the line connecting them doesn’t passthrough any other friend. How many friends can John see?
解析
英文解析
- [ 13 ] John M. is sitting at (0 , 0), looking across the aisle at his friends sitting at ( i, j ) for each 1 ≤ i ≤ 10
and 0 ≤ j ≤ 5. Unfortunately, John can only see a friend if the line connecting them doesn’t passthrough any other friend. How many friends can John see?
Answer: 36 The simplest method is to draw a picture and count which friends he can see. Johncan see the friend on point ( i, j ) if and only if i and j are relatively prime.