An old chestnut goes like this:

How many people do you need to have together for the probability that two of them have the same birthday to be at least 50%?

Usually these simplifying assumptions are used:

• Ignore leap years
• Assume that births on each of the remaining 365 days of the year are equally likely, and that there is no correlation between birthdays of different people.

This is also written up in Birthday paradox (Warning: partial spoiler in link) but it's not really a paradox and the calculation is not described over there, only the answer, so I'm not using that node for this puzzle.

Answer