In a room there are 10 people, none of whom are older than 100 (ages are given in whole numbers only) but each of whom is at least 1 year old. Prove that one can always find two groups of people (possibly intersection, but different) the sums of whose ages are the same.
I know we have to use the pigeon hole principle. But I don't know how to find the pigeons and pigeonholes. Can someone help me out?