HMMT 二月 2004 · 冲刺赛 · 第 6 题
HMMT February 2004 — Guts Round — Problem 6
题目详情
- [6] Find the smallest integer n such that n + 99 − n < 1. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 28, 2004 — GUTS ROUND 2 2
解析
- Find the smallest integer n such that n + 99 − n < 1. Solution: 2402 This is equivalent to √ √ n + 99 < n + 1 √ n + 99 < n + 1 + 2 n √ 49 < n 2 So the smallest integer n with this property is 49 + 1 = 2402. 2 2