MHB Solve Pigeon Hole Theory Problems

[JProgrammer]

So I need to use pigeon hole theory to solve these problems:

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?

 

[I like Serena]

So I need to use pigeon hole theory to solve these problems:

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?

Hey JProgrammer! ;)

a. We're talking about a bad day here.
Worst case scenario is that he pulls out a black sock, a brown sock, and a blue sock.
After that there is no choice anymore - he will pull out one of the colors he already has.
So that means that with 4 socks he will get a pair.
That is, the pidgeon hole theory says that if you pull 4 items when there are only 3 choices, you'll get at least 2 identical choices.

b. Same thing - a bad day.
He can pick 10 black socks and 11 brown socks before getting to blue socks.
And then he still has to pull 2 blue socks.