I’ve heard of this ‘prob­lem’ numer­ous times before, as I’m sure many oth­ers have too. Nonethe­less, every­time I do hear it, it fas­ci­nates me.

The birth­day prob­lem (or para­dox, as it’s often referred), looks at the prob­a­bil­ity of two or more peo­ple from a ran­domly cho­sen set of peo­ple shar­ing a birthday.

In a group of at least 23 ran­domly cho­sen peo­ple, there is more than 50% prob­a­bil­ity that some pair of them will both have been born on the same day. For 57 or more peo­ple, the prob­a­bil­ity is more than 99%, and it reaches 100% when the num­ber of peo­ple reaches 367[…]. The math­e­mat­ics behind this prob­lem leads to a well-known cryp­to­graphic attack called the birth­day attack.