Question

let there be 800 people at school. prove that 3 of them do share a birthday. how can we prove it according to the pigeonhole principle?

Answer 1

According to the Pigeonhole Principle, if you have more objects than available spaces, then at least two of the objects must occupy the same space. In this case, we have 800 people at school, and only 365 days in a year. This means that at least three of the people must share the same birthday, since there are not enough days in the year for each person to have a unique birthday.