A Math Problem From Singapore Goes Viral: When Is Cheryl’s Birthday?
By KENNETH CHANGAPRIL 14, 2015
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By KENNETH CHANGAPRIL 14, 2015
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A couple of months ago, it was a color-changing dress that blew out the neural circuits of the Internet. Though it may not have quite the mass appeal, this week it is a math problem that is making bushels of brains hurt.
It started with a posting on Facebook, by Kenneth Kong, a television host in Singapore.
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From there, people around the world have been trying to figure out Cheryl’s birthday, or at least wondering why she couldn’t just save everyone a lot of trouble and be more direct with Albert and Bernard.
The wording of the problem is terrible, so here is a clearer version, which makes some of the assumptions more obvious but which does not change any of the underlying logic of the problem:
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?
Originally, Mr. Kong said this was a problem inflicted on fifth-graders, leading to hand-wringing that Singapore children were way better at math than everyone else in the world and worries that Singapore children were being mentally abused with convoluted logic at a young age.
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RELATED COVERAGEIt turned out the problem actually came from a math olympiad test for math-savvy high school-age students.
How would you fare in a room full of adolescent math competitors in Singapore?
How to Figure Out Cheryl’s Birthday
By KENNETH CHANGAPRIL 14, 2015
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By KENNETH CHANGAPRIL 14, 2015
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If you have not already, read about the question first.
Otherwise, this answer will be even more confusing.
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This genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful, for instance and no one gets offended and walks off when strangers insist on making basic communication so complicated. Students who compete in math competitions are generally familiar with the conventions of logic puzzles, but people who have not taken a math class for more than a decade generally say, “Huh?”
This puzzle is particularly convoluted. Why don’t Albert and Bernard just blurt out what Cheryl has told them? Why is Cheryl so coy about revealing the month and day, but not year, of her birthday? What else is Cheryl trying to hide?
But if you are willing to play, here’s how the logic unwinds.
It helps to put the list of 10 dates into table form:
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Now let’s examine what Albert and Bernard say. Albert goes first:
I don’t know when your birthday is, but I know Bernard doesn’t know, either.
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RELATED COVERAGEThe first half of the sentence is obvious — Albert only knows the month, but not the day — but the second half is the first critical clue.
The initial reaction is, how could Bernard know? Cheryl only whispered the day, so how could he have more information than Albert? But if Cheryl had whispered “19,” then Bernard would indeed know the exact date — May 19 — because there is only one date with 19 in it. Similarly, if Cheryl had told Bernard, “18,” then Bernard would know Cheryl’s birthday was June 18.
Thus, for this statement by Albert to be true means that Cheryl did not say to Albert, “May” or “June.” (Again, for logic puzzles, the possibility that Albert is lying or confused is off the table.) Then Bernard replies:
I didn’t know originally, but now I do.
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RECENT COMMENTS
JMU
42 minutes ago
First thing about logic puzzles - you assume everyone in them to be perfectly logical and to be telling the truth. The answer in the article...
thebeorn
43 minutes ago
grrrrr so many bad assumption on such a basic logic question...no wonder there are so many bugs in software lol...ok so yet another...
authenticPisces
44 minutes ago
I messed up. July 16 is the only possible date that ensures that all of the statements made by Albert, Bernard and Cheryl are true. If...
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Now there are only three possibilities left: July 16, Aug. 15 and Aug. 17. Albert again:
Well, now I know too!
The same logical process again: For Albert to know, the month has to be July, because if Cheryl had told him, “August,” then he would still have two possibilities: Aug. 15 and Aug. 17.
The answer is July 16.
Cheryl is a Cancer, which still does not explain her behavior.
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