What is the minimum number of people in a single room so that it can be sure to say"There are two people in this room whose birthday is in February "?

Question

This problem is from BdMO. I am confused with the problem. Shouldn't it be infinity as there can be many people who have same birthday?

Answer 1

There is no number of people big enough for us to be completely certain that there are 2 people with birthdays in February.

Answer 2

Assume there are 28 days in February. Now, according to pigeonhole-principle, If there are 365 people in a room, we can't be sure that their birthday date are same. But if there are 366 people , then we can say that at least two of them have same birthday date. Thus, if there are 12 people, we can't be sure that their birthdays are in same month. But if there are 13 people in that room, we can say that at least 2 people have birthdays which are in same month. But in this question, the birthdays will have to be in February, which can't be figured out according to me. So, if we don't talk about matching February month, we can say that if there's 13 people ,at least two of them will have birthdays in same month