I wasn't sure how to title this post so excuse me on that part. The question which I'm trying to solve is the following:
Show that any collection of 8 positive integers whose sum is 20 has a subset summing to 4, Hint: Use PHP
I'm not too sure how to go about doing this question, if someone could get me pointed in the right direction I would appreciate it.
Edit: I should point out, I'm like 99.9% sure that PHP is pigeonhole principle
Hint: If such a subset does not exist, then $4$ cannot be a summand, there can be at most one $2$, and you cannot have both $1$ and $3$. What is the smallest sum you can obtain under these conditions?