I need help with a question. I don't know how to start, but I do know that it focuses on the pigeonhole principle. I have no problem understanding the principle, but I want to know how to find the pigeons and the pigeonholes.
A set $M = \{1, 2, ..., 100\}$ is divided into seven subsets with no number in two or more subsets. Show that at least one subset either contains four numbers $a, b, c$ and $d$ such that $a + b = c + d$ or three numbers $p, q$ and $r$ such that $p + q = 2r$.