Problem

Source: Indonesian Stage 1 TST for IMO 2022, Test 1 (Combinatorics)

Tags: combinatorics, Sum, equal, choose



Five numbers are chosen from $\{1, 2, \ldots, n\}$. Determine the largest $n$ such that we can always pick some of the 5 chosen numbers so that they can be made into two groups whose numbers have the same sum (a group may contain only one number).