Well, this time, the question is:
Assuming that birthdays are evenly distributed around 365 days of the year...
what is the minimum number of people I must have in a room, such that the odds are that at least n people share the same birthday?

Let's limit this question to n values from 1 to 12.

We know that for n=1, 1 person is sufficient.

For n=2, as is described in Happy Birthday, 23 people are sufficient.

What are the minimum numbers for n=3 to 12?