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HMMT 二月 2004 · 冲刺赛 · 第 6 题

HMMT February 2004 — Guts Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. [6] Find the smallest integer n such that n + 99 − n < 1.
    HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 28, 2004 — GUTS ROUND
    2 2

英文原题

[6] Find the smallest integer n such that √ n + 99 − √ n < 1.
1
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HARVARD-MIT MATHEMATICS TOURNAMENT, FEBRUARY 28, 2004 — GUTS ROUND

解析

英文解析

  1. 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
    So the smallest integer n with this property is 49 + 1 = 2402.2
    2 2