As the first 4 socks could be r,g,bl,bk he must draw at least 5 socks to

ensure 1 pair (suppose this pair is bk). Now as the next sock may be bk

he must draw another 2 socks to ensure another pair (total 6 socks drawn)

and so on for each additional pair.

In general he will have to draw 5+2*(n-1) socks to guaranty getting n pairs

So to get 10 pairs he will need to draw 23 socks.

RonL