Hello, The Birthday problem is usually cast in terms of finding the number of people at which the probability that at least two have the same birthday is equal to (or just more than) 1/2. It's fairly straightforward, using Stirling's approximation, to show that this is approx sqrt(2 ln(2) n), where n is the number of possible birthdays. A book that I have says that the expected number of tries, which can be different (substantially, depending on the probability distribution) from the point at which the probability equals 1/2, is approx sqrt( pi n / 2), which, in this case is fairly close to the above expression, but not equal. I can show that the exact value is 2*(1/n) + 3*(2/n)*n!/(n-2)!/n^2 + 4*(3/n)*n!/(n-3)!/n^3 + ... Apparently, this can be shown to equal Sum_{k=0}^n n!/(n-k)!/n^k It can also be shown to be approximately Int_0^n (1 - t/n)^(t-n) e^(-t) t^2 / n dt I'm not great at finding asymptotic expansions--does anyone know how to show that, say, the integral is approx sqrt( pi n / 2), or that the sums are equal and approx the sqrt expression? Thanks, Bill C.