The Birthday Problem

Not a Coincidence!                      

By Larry Tesler                      

May 25, 1998                      

In "What a coincidence!" (Mathematical Recreations, Scientific American, June 1998, p. 95), columnist Ian Stewart discussed the well-known coincident birthday problem.                       

The author cautions:

“Incidentally, the fact that the answer to the second problem is the same as the number of pairings in the first problem (253 pairings for 23 people) seems not to have any mathematical significance. It seems to be a coincidence.”

I will show that is not much of a coincidence.