Question

Can someone help me?

Your sock drawer has 10 blue socks, 16 red socks, and 12 white socks. If you reach into the drawer in the dark, how many socks do you need to pull out to be sure you have a matching pair?

I can't figure out.

Answer 1

If you pull out one blue sock, then you could pull out another blue sock on the next draw. That may not happen, since you may pull out a red or white sock.

Let's say on the second draw, you pull out a red sock. On the third draw, you may pull a white sock out.

So far, we have pulled out a blue, red and white sock. So no matches so far.

However, by the fourth draw, the next sock is guaranteed to match since there are only 3 colors. If the fourth sock is red, then it matches with the second sock drawn. If the fourth sock is blue, then it matches with the first. If it's white, then it matches with the third sock.

So you need to pull out 4 socks to make sure you have a matching pair