Children’s maths problem is melting people’s brains – can you solve it?
You’re going to really regret asking Cheryl when her birthday is.
A logic puzzle, which was set for some long-suffering 11-year-old schoolchildren, is enough to make you want to throw your phone out the window – even once the answer has been explained to you.
When Albert and Bernard meet villain Cheryl, they simply ask when her birthday is and all hell breaks loose, making it very clear, very quick that Cheryl absolutely does not deserve presents anyway. This is your last chance to turn back.
The question: Albert and Bernard become friends with Cheryl, and they want to know when her birthday is. Cheryl 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.
Cheryl being Cheryl decides to tell Albert only the month of her birthday and Bernard only the day of her birthday. So between them, they have the answer, but separately, they only have half of the information they need. And for some reason they hate sharing.
Albert says: ‘I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know either.’
Bernard says: ‘At first I don’t know when Cheryl’s birthday is, but I know now.’
Albert says: ‘Then I also know when Cheryl’s birthday is.’
So when is Cheryl’s birthday? Before we begin to reveal the answer, try to work it out.
Let’s go through it line-by-line. Albert says: ‘I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know either.’ As Albert only knows the month, and every month has more than one possible date, of course he doesn’t know when her birthday is. Yet.
After listening to Albert, Bernard says: ‘At first I don’t know when Cheryl’s birthday is, but I know now.’ The only way that Bernard could know the full date with a single number, however, would be if Cheryl had told him 18 or 19 because of the ten date options only these numbers appear once, as May 19 and June 18.
For Albert to know that Bernard doesn’t know, either, Albert must have been told July or August, since this rules out Bernard being told 18 or 19. We warned you.
On learning this, Albert says: ‘Then I also know when Cheryl’s birthday is.’ So Bernard has figured out that Albert was told either August or July. To know the full date, he must have been told either 15, 16, or 17. If he had been told 14, then he wouldn’t know whether the month was August or July.
Albert has therefore deduced that the remaining possible dates are July 16, August 15 and August 17. For him to now know, he must have been told July. If he had been told August, he would not know which date for certain is the birthday.
Therefore, the answer is July 16. Did you get it? Nope, us neither.
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