## A math problem that’s gone viral: When the hell is Cheryl’s birthday?

Kenneth Kong, a television host in Singapore posted the above maths question on his Facebook page. This math problem that went viral is making millions of brains hurt. The high school maths question which was meant for 15 to 17 year olds has managed somehow to bowl over half the Internet. It has even come on the New York Times science page. In addition, it has inspired a blog from British author and numbers expert, Alex Bellos over at The Guardian.

People around the world have been trying to figure out when is Cheryl’s birthday. First let’s clear up the vagueness with the terrible wording before we go to the solution. So, here is a clearer version, which makes some of the presumptions more obvious but which does not change any of the underlying reasoning of the problem:

To start with, Cheryl (who we assume has set her birthday to private on Facebook) will only give Albert and Bernard 10 possible dates for her birthday.

May 15, May 16, May 19

June 17, June 18

July 14, July 16

August 14, August 15, August 17

Then Cheryl whispers in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispers the day, and only the day. The information Albert receives convinces him that Bernard does not possibly know the answer. However, the information given to Bernard is enough for him to find the answer. In turn, Bernard’s confidence assures Albert of the answer, too.

So what’s the answer? It’s not actually as hard as it seems, you just need to break it down logically, as Bellos explained at over at The Guardian.

In order for Albert to be sure that Bernard can’t work out Cheryl’s birthday after being told the date, it means that he must be certain the number Bernard was told appears in more than one option. In other words, it cannot be 18 or 19, which are only mentioned once – May 19 or June 18.

As Bellos explains: “For Albert to know that Bernard does not know, Albert must therefore have been told July or August, since this rules out Bernard being told 18 or 19.”

“And after Bernard has worked this out, he quickly becomes certain of Cheryl’s date of birth, which means that he’s been told a number that only appears in one of these months.

That rules out 14, and leaves only three potential birthdays: July 16, August 15 or August 17.”

On knowing this, makes Albert certain of the birthdate too, which means that July 16 must be Cheryl’s birthday. “Since if he had been told August, he would not know which date for certain is the birthday,” writes Bellos.

Chang stated at The New York Times: “Cheryl is a Cancer, which still does not explain her behavior. Seriously, we hope she was not expecting a gift.”

Note: There’s also a strong camp of redditors who believe Cheryl’s birthday is really August 17. You can read more about other theories here.