What is the birthday problem?

The Birthday Problem is a probability problem with results that many find counterintuitive. The problem is formulated as "how many people must you consider such that the probability of at least two people sharing a birthday is at least 50%?". The answer, which many find surprising and counterintuitive, is 23. The answer is lower than most people expect and it is due to the number of pairwise permutations that exists for 23 people.