ZA-SAMO 2005 Problem 3

A warehouse contains $175$ boots of size $8$ , $175$ boots of size $9$ and $200$ boots of size $10$ . Of these $550$ boots, $250$ are for the left foot and $300$ for the right foot. Let $n$ denote the total number of usable pairs of boots in the warehouse. (A usable pair consists of a left and a right boot of the same size.)

(a) Is $n=50$ possible?

(b) Is $n=51$ possible?