parmenides51 wrote: In a group of $20$ people, each person sends a letter to $10$ of the others. Prove that there are two persons who send a letter to each other. There are $\binom{20}{2}=190$ pairs of two people and $200$ letters send in total. By the pigeon hole principle there are two letters such that the set of the sender and reciever are the same. These two persons send a letter to each other.