# The Maths Problem That’s Gone Viral: When The Hell Is Cheryl’s Birthday?

FIONA MACDONALD
15 APR 2015

A few days ago, Singaporean television host Kenneth Kong posted the below maths question on his Facebook page, and it went viral. The high school maths question was aimed at 15- to 17-year-olds, but somehow it managed to stump half the Internet. It even appeared on the New York Times science page, and prompted a blog from British author and numbers expert Alex Bellos over at The Guardian.

So when exactly is Cheryl's birthday, and why is the problem so frustrating for so many adults? Before we get to the solution, let's clear up any ambiguity with the wording, which Kenneth Chang over at The New York Times calls "terrible".

To start with, Cheryl (who we can only imagine 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

She then whispers only the month of her birthday to Albert, and nothing but the date itself to Bernard. The information Albert receives convinces him that Bernard can't possibly know the answer.

But knowing that is enough for Bernard to figure it out. In turn, Bernard's certainty convinces Albert of the answer, too.

So what's the solution? As Bellos explains over at The Guardian, it's not actually as hard as it seems, you just need to break it down logically.

For Albert to be certain that Bernard can't possibly work out Cheryl's birthday after being told the date, it means that he must be sure the number Bernard was told appears in more than one option. In other words, it can't be 18 or 19, which are only listed once each - 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.

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.

As Chang adds over at The New York Times: "Cheryl is a Cancer, which still does not explain her behaviour." Seriously, we hope she wasn't 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.

Sources: The New York Times, The Guardian