On the wikipedia page regarding the birthday problem there are several variations to it:
https://en.wikipedia.org/wiki/Birthday_problem
One of the variations is this one:
as people enter a room one at a time, which one is most likely to be the first to have the same birthday as someone already in the room? That is, for what n is p(n) − p(n − 1) maximum?
How should I do this in the most efficient way, by hand, i.e. no laptop and no calculator?