MathDB

resiprocal sums differ by less than 0.01

Source: 2022 NZMO - New Zealand Maths Olympiad Round 2 p3

October 8, 2022

combinatoricsSubsets

Problem Statement

Let

S

be a set of

10

positive integers. Prove that one can find two disjoint subsets

A =\{a_1, ..., a_k\}

and

B = \{b_1, ... , b_k\}

S

with

|A| = |B|

such that the sums

x =\frac{1}{a_1}+ ... +\frac{1}{a_k}

and

y =\frac{1}{b_1}+ ... +\frac{1}{b_k}

differ by less than

0.01

, i.e.,

|x - y| < 1/100