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:
“I feel like my sixteenth birthday and the time I graduated from high school, and the first time I flew solo all wrapped up in one.”
—Dalton Trumbo (1905–1976)
“The problem of the novelist who wishes to write about a man’s encounter with God is how he shall make the experience—which is both natural and supernatural—understandable, and credible, to his reader. In any age this would be a problem, but in our own, it is a well- nigh insurmountable one. Today’s audience is one in which religious feeling has become, if not atrophied, at least vaporous and sentimental.”
—Flannery O’Connor (1925–1964)