Problem
COM-B1-M05-P023 Subset Sum Divisible by \(n\)
#23
★★★★☆ Level 4 of 5
Prove that among any \(n\) integers, there is a nonempty subset whose sum is divisible by \(n\).
It is enough to find a consecutive block after listing the numbers in any order.
List the numbers in any order and apply the partial-sum lemma to this sequence of length \(n\). We get a nonempty consecutive block whose sum is divisible by \(n\). This block is a subset of the chosen numbers.
Strong form, but proof relies on the known template.