Students in a hostel are asked which month they were born in. What is the least number of students needed to be CERTAIN that at least three of them share a birth month?

Picture the worst case, in which the twelve months fill as evenly as possible. Two students in every month accounts for 24 students with no month holding three, so 24 is not enough. The next student, the 25th, has to join a month that already holds two, and 25 therefore makes it certain. The answer 24 is the largest number for which it can still fail; 13 answers the easier question about TWO students sharing a month; and $36=3\times 12$ is far more than is needed.