Using the Pigeonhole Principle, we can prove that at least n people must have been born in the same month if:

n = ceiling(280/12) + 1

where “ceiling” is the ceiling function, which rounds up to the nearest integer.

To see why, consider the worst-case scenario: assume that exactly 23 people are born in each month (since 23 is the largest integer smaller than 280/12). Then we would have 23 people born in January, 23 in February, and so on, up to 23 in December. That accounts for 12 x 23 = 276 people. The remaining 4 people must be born in some month, and by the Pigeonhole Principle, at least two of them must be born in the same month as another pair.

Therefore, we have:

n = ceiling(280/12) + 1 = 24

So we can prove that at least 24 people must have been born in the same month