MathDB

1/a_1+1/a_2+...+1/a_k -(1/b_1+1/b_2+...+1/b_k)<0.001

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1998 p2

February 20, 2020

SumalgebraSubsets

Problem Statement

Given any set of

14

(different) natural numbers, prove that for some

k

(

1 \le k \le 7

) there exist two disjoint

k

-element subsets

\{a_1,...,a_k\}

and

\{b_1,...,b_k\}

such that

A =\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_k}

and

B =\frac{1}{b_1}+\frac{1}{b_2}+...+\frac{1}{b_k}

differ by less than

0.001

, i.e.

|A-B| < 0.001