M.C. Escher inspired birthday balloon paradox watercolor by Allen West.

A math magician appears before you on the street in a puff of smoke, and he will make you his apprentice if you can but answer one question. You fantasize how you could make your investment portfolio grow if only you knew magic, or how you could star in your own series of blockbuster films–move aside Harry Potter! But before you get carried away, the magician posits his question to you: how many people off of the street do I need to invite to my magic show to have a 50% chance that any two of them celebrate their birthday on the same day? You sweat a little, think a little, then sweat a little more before answering: 183.

You won’t be attending Hogwarts anytime soon, my friend. You’ve been hit by, you’ve been struck by, a Birthday Paradox! Continue reading →