A word problem that deals in logic was given to fifth-grade students in Singapore. It has swept the Internet, stumping people even more than the color of the dress.
The New York Times translated it like this:
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?
So what is the answer?
It has as much to do with seeing it through others’ eyes as it does logic. You have to approach the problem based on what Albert and Bernard know, not based on what you know.
Cheryl tells Bernard the day and Albert the month. So Albert says that he doesn’t know (which is obvious because none of the possible months have just one possible day). He ALSO says that Bernard doesn’t know. So all you can logically conclude is that Albert knows Bernard doesn’t know because the month Cheryl told him has days in it that are also in other months. That rules out May and June because Albert wouldn’t KNOW that Bernard doesn’t know, for sure, since May and June both have days in them that are not in other months (18 and 19 don’t appear in any other month.
The fact that Albert doesn’t know will not help Bernard at all (because it’s obvious Albert wouldn’t know–none of the months have just one day as a possibility). However, the fact that Albert knows Bernard doesn’t know will help Bernard figure it out. We know Bernard didn’t know before, which means that it couldn’t have been the 18th or the 19th (these are the only days that are assigned to only one month). Bernard knows that Albert KNOWS Bernard doesn’t know. This means that Bernard can also rule out May and June. Since Bernard says he “knows now,” what it is, that means that the day isn’t 14, since that is the only number that appears in both July and August. If it was 14, Bernard still wouldn’t know. So it has to be 15, 16, or 17.
At this point, Albert knows Bernard has figured it out, so he too can rule out 14 as a possibility. Albert knows the month already, and he says that after he knows Bernard knows, that he now knows as well. The only way he could have figured that out is if there was only one other option than 14, which means the month was July (the only month left with only 2 options). So it has to be July 16.
And there it is!