HMMT 二月 2004 · 冲刺赛 · 第 22 题
HMMT February 2004 — Guts Round — Problem 22
题目详情
- [9] I have written a strictly increasing sequence of six positive integers, such that each number (besides the first) is a multiple of the one before it, and the sum of all six numbers is 79. What is the largest number in my sequence? 512 n
解析
- I have written a strictly increasing sequence of six positive integers, such that each number (besides the first) is a multiple of the one before it, and the sum of all six numbers is 79. What is the largest number in my sequence? Solution: 48 If the fourth number is ≥ 12, then the last three numbers must sum to at least 12 + 2 2 · 12 + 2 · 12 = 84 > 79. This is impossible, so the fourth number must be less than