Cheryl's Birthday Round-Up

Published on Monday, April 20, 2015 in , , , , ,

normanack's birthday cake photoThanks to a Singapore math exam, the internet is being driven crazy by the biggest problem in birthdays since the birthday paradox!

Here's the problem: Albert and Bernard want to know Cheryl's birthday, but Cheryl isn't willing to tell them directly. Instead, she gives them a list of 10 possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, and August 17. She then whispers only the month to Albert and the date to Bernard. The following discussion then takes place between Albert and Bernard:

Albert: "I don't know when Cheryl's birthday is, but I know that Bernard does not know, too."

Bernard: "At first, I didn't know when Cheryl's birthday was, but I know now."

Albert: "Then I also know when Cheryl's birthday is."

When is Cheryl's birthday? We'll look at how to find the answer in this post!

The simplest and most direct explanation of this puzzle I've found is in Presh Talwalkar's post, When Is Cheryl’s Birthday? Answer To Viral Math Puzzle. The included video makes the answer seem so straightforward:

Another helpful approach is Mark Josef's interactive Cheryl's Birthday page, on which you can click each of the dates to see why that the logic determines that date to be right or wrong. Both Cahoots Malone and The Washington Post have also featured simple and straightforward video explanations of this puzzle.

For a more detailed look at the solution, check out Numberphile's thorough explanation, as well the extra footage:

Ever the intrepid explorer, however, James Grime takes an even closer look at Cheryl's Birthday, and finds that the intended answer may not necessarily be the right answer:

Has this puzzle driven you crazy? Did you manage to solve it? If so, how? I'd love to hear your answers in the comments below!