Prove that if four numbers are chosen from the set $\{1,2,3,4,5,6\}$, at least one pair must add up to $7$ using the Pigeonhole principle.
I am supposed to identify the pigeons and the pigeonholes.
We know that $\{1,6\},\{2,5\},$ and $\{3,4\}$ all add up to $7$, so I am guessing these are perhaps the pigeonholes?
We also know that any set of four numbers has six unique pairs in it. I am not really sure how to tie this to one of the pairs adding up to $7$, though.