From the page: "In probability theory, the birthday paradox states that in a group of 23 (or more) randomly chosen people, there is more than 50% probability that some pair of them will have the same birthday. For 57 or more people, the probability is more than 99%, although it cannot be exactly 100% unless there are at least 366 people. This is not a paradox in the sense of leading to a logical contradiction, but is called a paradox because mathematical truth contradicts naive intuition: most people estimate that the chance is much lower than 50%. Calculating the probabilities above (and related ones) is the birthday problem. The mathematics behind it has been used to devise a well-known cryptographic attack named the birthday attack."