Prove that for every partition of $ \{ 1,2,3,4,5,6,7,8,9\} $ into two subsets, one of the subsets contains three numbers such that the sum of two of them is equal to the double of the third.
Source: Romanian TST 1978, Day 1, P1
Tags: counting
Prove that for every partition of $ \{ 1,2,3,4,5,6,7,8,9\} $ into two subsets, one of the subsets contains three numbers such that the sum of two of them is equal to the double of the third.