In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are 366 possible birthdays, including February 29). However, 99% probability is reached with just 57 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally probable for a birthday.
The mathematics behind this problem led to a well-known cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of cracking a hash function.
Read more about Birthday Problem: Understanding The Problem, Calculating The Probability, Approximations, An Upper Bound, Partition Problem
Famous quotes containing the words birthday and/or problem:
“Age is a limit we impose upon ourselves. You know, each time you Westerners celebrate your birthday you build another fence around your minds.”
—Robert Riskin (1897–1955)
“I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
—Jean Giraudoux (1882–1944)