Yesterday, a math problem went viral on the Internet —that’s not a joke — and after you read the problem, you’ll immediately understand why.
At first glance, it seems like a cruel joke. Why did Cheryl have to make things so complicated? Is this some sort of friendship initiation game? The logical reasoning problem was originally included in the Singapore and Asian Schools Math Olympiad (SASMO) held last week, a competition that about 28,000 teenagers across Asia took part in — but it spread like wildfire after a TV presenter in Singapore shared it on Facebook last Friday. It seemed like no one could solve the problem, and those who did couldn’t agree on the solution.
“Being Q24 out of 25 questions, this is a difficult question meant to sift out the better [students],” Henry Ong, Executive Director of SASMO, told Mothership.sg. “SASMO contests target the top 40% of the student population and the standards of most questions are just high enough to stretch the students.”
We think “stretch” is an understatement — but there is an answer to the problem, and SASMO has officially released the solution. Think you know how to figure it out? We explain how on the next page! (In case we need to clarify: SPOILER ALERT.)
Let’s start with what we know: Albert only knows the month, and Bernard only knows the day. Therefore, when Albert explicitly says that Bernard doesn’t know Cheryl’s birthday, we can deduce that the day can’t be a number that only appears once within our options (because, if that were the case, Bernard would have been immediately able to figure out the month without Albert’s help). Of the 10 dates given, the only two numbers not repeated twice are 18 and 19 — so we can now rule out their corresponding dates: June 18 and May 19.
The only way Albert can know for sure that Bernard doesn’t know Cheryl’s birthday is if he can also know without doubt that it’s not on the 18th or 19th. (For some reason, this part was the hardest for me to grasp, so I’m going to try to explain it in the most obvious way possible.) Since Albert only knows the month, the only way that would be possible is if the month is neither June nor May — because if it had been either of those, he couldn’t have known for sure that Albert didn’t know Cheryl’s birthday. Therefore, we can rule out May 15, May 16, and June 17.
Now, Bernard’s sentence comes into play. Like Albert, he originally didn’t know Cheryl’s birthday, but has figured it out after Albert’s (totally convoluted and not that helpful, in my opinion) clue. Since Bernard only knows the day, we can apply the same logic as step one: it can’t be a day of the month that appears twice, otherwise he would still be guessing between two months. This means we can cross out July 14 and August 14.
Final stretch! From here, Bernard has figured out Cheryl’s birthday (which makes sense, because he knows the day of the month and there are no repeat dates amongst our final three options). After Bernard states that he knows Cheryl’s birthday, Albert deduces what it is, too. This means that the month can’t be August, because if it were, then Albert would still be guessing between two dates — so we can cross out August 15 and August 17.
Therefore, Cheryl’s birthday must be July 16!
In case you want to question our logic some more, check out the official solution from the test makers themselves right here.
Cheryl is a super smart girl who doesn’t like birthdays very much.