two people in London with the same number of hairs on their heads as follows. Since a typical human head has an average of around 150,000 hairs; it is reasonable to assume (as an upper bound) that no one has more than 1,000,000 hairs on their head ( m = 1 million holes). There are more than 1,000,000 people in London ( n is bigger than 1 million items). Assigning a pigeonhole to each number of hairs on a person's head, and assign people to pigeonholes according to the number of hairs on their head, there must be at least two people assigned to the same pigeonhole by the 1,000,001 assignment (because they have the same number of hairs on their heads) (or, n &gt; m ). For the average case (m = 150,000) with the constraint: fewest overlaps, there will be at most one person assigned to every pigeonhole and the 150,001st person assigned to the same pigeonhole as someone else. In the absence of this constraint, there may be empty pigeonholes because the "collision" happens before we get to the 150,001st person. The principle just proves the existence of an overlap; it says nothing of the number of overlaps (which falls under the subject of Probability Distribution ). The birthday problem asks, for a set of n randomly chosen people, what is the probability that some pair of them will have the same birthday. By the pigeonhole principle, if there are 367 people in the room, we know