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JProgrammer

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3. A man has 10 black socks, 11 brown socks and 12 blue socks in a drawer. He isn’t a morning person, so every morning he just reaches in and pulls out socks until he gets two that match.

a. Use the generalized pigeonhole principle to determine how many socks he has to pull out before he gets two of the same color.

b. How many must he pull out to be certain of getting a blue pair?

a. I am thinking that the pigeons are the colors and the pigeon holes are the number of socks that are pulled out. If that were the case, I believe the answer would be 5. But the number of each color of socks is not the same. So am I right about this or do I need to take into consideration the different amount of socks?

b. The most I could go with this problem is that since there are 33 socks total and 12 of those socks are blue, the pigeon hold theory would yield 3. My question is: where would I go from here?