Now I understand it.
I just learnt this principle. I am doing a problem in which there's a box with many red socks, green socks and blue socks. First question was how many minimum socks should I pick out without looking to be absolutely sure to get a matching pair. This was an intuitive one. However, I am having trouble understanding an extension of this problem: how many socks should I pull out without looking to be absolutely sure that I have a three pairs of a color.
The book said 3 pairs. I presume it is 3 pairs of one color.
When I thought about it, I cannot understand why there should be a solution at all. How can I be absolutely certain, when I can pick out a red sock, a red sock, a red sock, infinite number of times. If I dont understand this, then I cannot proceed with learning this principle, as I do not see how it applies or relates.
Best Answer
In the first question, you presumably had an answer of 4, since after 3 socks you either already had a pair or had three odd socks, and so with 4 socks you must have a pair.
In your new version of the second question, you do the same. At some stage the worst case is that you have two pairs of each colour and three odd socks (all the pigeonholes are filled), so when you take the next sock you can be sure of having at least three pairs of a single colour.
If the three pairs can be any colours, then the worst case is two pairs and three odd socks and the next sock will ensure at least three pairs.