Home Activities Maths problem that’s gone viral: When the hell is Cheryl’s birthday?

Maths problem that’s gone viral: When the hell is Cheryl’s birthday?


Some days ago, Singaporean television host Kenneth Kong posted the above maths problem 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 of 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, this problem so
frustrated so many adults, but when exactly is Cheryl’s birthday? 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”.

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Lets 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 would be 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.
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
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.