The Birthday Problem

There is a famous problem in Probability Theory that is phrased in terms of birthdays: What is the smallest number such that a randomly selected group of people of that number will have the same birthday (that is, month and day, ignoring the phenomenon of leap years)? People guessing the answer usually greatly over-shoot the mark. The number is surprisingly small: 23. This answer is so counter-intuitive that the ‘birthday problem’ is sometimes referred to as the ‘birthday paradox’.
Here is the Wikipedia article on this.