An old chestnut
goes like this:
The power's out in my house this morning, and I need to find a pair of matching socks and a pair of matching shoes. The only source of light is a window which does not shine on the dark drawer where I keep my shoes and socks.
I don't want to pull out the entire drawer and carry it into the light, but I need to find two socks that match and two shoes that match. I don't care if the socks match the shoes.
There are 10 pairs of socks and 10 pairs of shoes in the drawer. 5 pairs of each are white, the other 5 pairs of each are black. Socks are interchangeable -- I can wear any sock on either foot, and any two of the same color will match. Shoes are not quite so interchangeable -- a pair must be a left shoe and a right shoe -- but any such pair of the same color will work.
If I pull out socks at random, what is the minimum number I can pull out to guarantee that when I carry them over to the light, I will find a pair among them?
If I pull out shoes at random, what is the minimum number I need to ensure a pair? How does the answer change if I can feel the shoes to determine if they are left or right shoes before pulling them out?