For you mathematical types, the solution goes as follows:

The probability that at least 2 people in the room have the same birthday is equal to (1-Probability that no 2 people in the room have the same birthday). So, let's say there are 8 people in the room. Then the probability that no 2 people have the same birthday is equal to

365/365 * 364/365 * 363/365 * 362/365 * 361/365 * 360/365 * 359/365 * 358/365 = .925664

So the probability that at least 2 of the 8 have the same birthday is 1 - .925664 = .074

Using this same logic, we need to find the number of people in the room so that the probability is .5. It's mostly a matter of trial and error at this point (or "plug and chug" as we called it in grad school), but after trying different numbers of people in the room we find that

1- (365/365 * 364/365 * 363/365 * ...* 344/365 * 343/365) = 1 - .492702 = .5072

There are 23 terms in the above formula, so we only need 23 people in the room!!!

Still not convinced? Check out my Java Example.

1