Grinstead-Snell-Probability · Problem 3.1.16
Combinatorics
Mathematics · permutations
Problem
Prove that at least two people in Atlanta, Georgia, have the same initials, assuming no one has more than four initials.Intuitive explanation
This is a pigeonhole principle problem: you need to count how many possible initial combinations exist, then compare that to Atlanta's population. Since each person has at most 4 initials (first, middle, middle, last), there are only finitely many ways to arrange letters—far fewer than the number of people in a major city. Once you show that possible combinations < population, you've proven that at least two people must share the same set of initials.
Intuitive explanation
This is a pigeonhole principle problem: you need to count how many possible initial combinations exist, then compare that to Atlanta's population. Since each person has at most 4 initials (first, middle, middle, last), there are only finitely many ways to arrange letters—far fewer than the number of people in a major city. Once you show that possible combinations < population, you've proven that at least two people must share the same set of initials.