Puzzle #65: Socks

You have quite a mess of socks in that drawer: five white, five yellow, six black, four brown, four blue, and one lime green. Except for colour, they are indistinguishable.

You need to select matching socks. There is no light. That summer job was really weird, and you have grown a third leg, so rather than selecting a matching pair, you need to select a matching triplet. “matching” means all the same colour.

What is the minimum number of socks you have to take to be sure of getting a matching triplet? What about if you want to be sure of getting two matching triplets?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, September 3, 2014 at noon Pacific Time. I will post the answer shortly after.