返回题库

HMMT 二月 2008 · 冲刺赛 · 第 10 题

HMMT February 2008 — Guts Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 7 ] Find the number of subsets S of { 1 , 2 , . . . 63 } the sum of whose elements is 2008.
    ∑ ∑
    2008 ∞
    1 1 1 1
解析

英文解析

  1. [ 7 ] Find the number of subsets S of { 1 , 2 , . . . 63 } the sum of whose elements is 2008.
    Answer: 6 Note that 1 + 2 + · · · + 63 = 2016. So the problem is equivalent to finding the numberof subsets of { 1 , 2 , · · · 63 } whose sum of elements is 8. We can count this by hand: { 8 } , { 1 , 7 } , { 2 , 6 } ,
    { 3 , 5 } , { 1 , 2 , 5 } , { 1 , 3 , 4 } .
    ∑ ∑2
    2008 ∞
    1 1 1 1