A (probably) exact solution to the Birthday Problem
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- Brink, D. Ramanujan J (2012) 28: 223. doi:10.1007/s11139-011-9343-9
Given a year with n≥1 days, the Birthday Problem asks for the minimal number Open image in new window such that in a class of Open image in new window students, the probability of finding two students with the same birthday is at least 50 percent. We derive heuristically an exact formula for Open image in new window and argue that the probability that a counter-example to this formula exists is less than one in 45 billion. We then give a new derivation of the asymptotic expansion of Ramanujan’s Q-function and note its curious resemblance to the formula for Open image in new window.
KeywordsBirthday Problem Ramanujan’s Q-function Asymptotic analysis
Mathematics Subject Classification (2000)41A60 60C05 65D10
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