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All of Singapore is Arguing Over the Answer to this Impossible Math Problem

First everyone on the Internet argued over the colors of dress that some saw as white and gold but others thought was black and blue. Now a crazy word problem from Singapore is starting another online debate, and this one requires a little more brain power.

Apparently a question on a math test given to high school students in the country proved so difficult that people posted it online asking whether rational adults could figure out the answer. Here’s the problem in question:

Gawker

Gawker

Uh…how the heck is someone supposed to answer that?

The New York Times has restated the question to make it a little (emphasis on a little) more understandable:

Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl.
Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 dates:
May 15 — May 16 — May 19
June 17 — June 18
July 14 — July 16
August 14 — August 15 — August 17
“My birthday is one of these,” she said.
Then Cheryl whispered in Albert’s ear the month — and only the month — of her birthday. To Bernard, she whispered the day, and only the day.
“Can you figure it out now?” she asked Albert.
Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!
When is Cheryl’s birthday?

Ok, so now that it’s been restated, can you figure it out? Well we sure as hell couldn’t. So we had to rely on Gawker to help answer the problem. Here’s their explanation:

Albert knows that Bernard can’t know the answer just by knowing the day. So we have to rule out May and June, both of which have days (the 18th and 19th) unique to them. Knowing those months have been ruled out, Bernard’s knowledge of the day suddenly gives him the answer. How? Well, it can’t be the 14th. It’s the only repeated number, and it wouldn’t give him any information about the correct month. That leaves only three choices: July 16, Aug. 15, and Aug 17. Now we’ve exhausted all of Bernard’s information about the day, and we still don’t have an answer. This is where some people, like Jianwen, probably gave up and declared the problem a trick. Bernard seemingly doesn’t have enough information to answer the question. Hold up, though. Bernard knows one more thing: that Albert got the correct answer by knowing the month. Albert couldn’t do that if Cheryl’s birthday were in August, because there are still two August dates for him to choose from. And that means there’s only one possible birthday left: July 16.

So…yeah. That’s the answer. Unless it’s not. Apparently a lot of people believe the answer is August 17th. The Singapore and Asian School Math Olympiads released a two page document explaining how the answer is July 16th (if you’re really passionate about math, you can find the document here).

Here’s the real question: Why the hell can’t Cheryl just tell people the date of her f*&%ing birthday?

Serious, Cheryl. Grow up.


Joseph Misulonas is an editorial assistant for Playboy.com. He has not taken a math class since high school. He can be found on Twitter at @jmisulonas.

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