Socks in a drawer

pfly said:

Hi
I have a tricky problem my teacher gave our class.

A draw contains an unsorted collection of black, navy, white, and brown coloured socks. If socks are taken at random, one at a time, what is the minimum number which must be taken to be certain of finding five matching pairs?

He gave us the answer of 13, but I can't see how?
Couldn't you just keep drawing one color forever?

thanks

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DrPhil said:

If you draw one color "forever," then you will have five matched pairs on ten draws.

There are four colors. If you have an odd number of a color, you have an unpaired sock. The most unpaired you can have is 3 of the 4 colors. That makes the minimum to be certain to have 5 pairs is 10+3 = 13.

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pfly said:

Ahh...ok. I read it as five different color pairs. Ok your solution makes sense.

Is there a way to solve it if the problem is the way I imagined it?

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