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:
“the birthday of my life
Is come, my love is come to me.”
—Christina Georgina Rossetti (1830–1894)
“Our political problem now is “Can we, as a nation, continue together permanentlyforever—half slave, and half free?” The problem is too mighty for me. May God, in his mercy, superintend the solution.”
—Abraham Lincoln (1809–1865)