Question

Your sock drawer contains ten pairs of white socks and ten pairs of black socks. If you're only allowed to take one sock from the drawer at a time and you can't see what color sock you're taking until you've taken it, how many socks do you have to take before you're guaranteed to have at least one matching pair?

Answer 1

10 pairs of white socks and 10 pairs of black socks. One sock can be drawn at a time without looking at the color.

Let the white socks be 10L (left side) and 10R (right side)

Similarly, the black socks be 10L(left side) and 10R (right side)

So we have 40 socks in total.

Now it is possible that we choose 10 socks each of left side of the same color. Next, we choose 10 socks of another color but again of left side. Thus we have already taken 20 socks.

Next, if we choose one sock (of any color, it will be definitely of right side) it will match with one sock already chosen. So we need atleast 21 socks to guarantee that we have at least one matching pair.