How many people must be present to guarantee that at least t

How many people must be present to guarantee that at least two have the same birthday? at least two of their birthdays are in the same month? at least three of their birthdays are in one of the months January, February, March, April or at least four of their birthdays are in one of the remaining months?

Solution

Though I think, some statement is missing in the starting of the problem. Still i will try to answer with the provided information.

(a). Atleast 3 people must be present. So that any 2 of them may have same birthday. And all 3 can also have.

(b). Atleast 3 people must be present. So that any 2 of them may have birthday in the same month. And all 3 can also have.

(c). This can be possible in some of the cases with atleast 5 people. Other combinations will require higher number of people.

Again stating, i feel there was some line defining the relationships between the people and their birth months. So that some kind of boolean logic can be performed to get the answers.

Do comment if you can find the complete problem.

Thank You.