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from the it-seemed-like-the-logical-thing-to-do-at-the-time dept.
A couple of months ago, it was a color-changing dress that blew out the neural circuits of the Internet. Now Kenneth Chang reports in the NYT that a problem from a math olympiad test for math-savvy high school-age students in Singapore is making the rounds on the internet that has perplexed puzzle problem solvers as they grapple with the simple question: "So when is Cheryl's birthday?"
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?
Logical puzzles like this are common in Singapore. The Singapore math curriculum, which has a strong focus on logic-based problem solving, has been so successful that it's been adopted around the world. According to Terrance F. Ross, US students have made strides in math proficiency in recent years, but they still lag behind many of their peers internationally, falling at the middle of the pack in global rankings. In the same PISA report the U.S. placed 35th out of 64 countries in math. "And even though the "Cheryl's Birthday" question may be atypical of the average Singaporean classroom, perhaps it's still worth asking: Are you smarter than a (Singaporean) 10th-grader?"
(Score: 2) by TheB on Thursday April 16 2015, @07:42AM
Without assuming that both Albert and Bernard are aware of Cheryl whispering the month to one and the day to the other this puzzle is unsolvable.
Given that the reader is given this information it is reasonable to assume that both Albert and Bernard also know this.
May 15th and 16th are out for the same reasoning you used to eliminate June 17th.
If Cheryl's birthday was May 19th then Albert's statement "I know Bernard doesn’t know, either." would be invalid.
Since there is only one 19th Bernard could deduce it must be May 19th. Albert must know the month is not May for his statement to be correct.
(Score: 4, Insightful) by bzipitidoo on Thursday April 16 2015, @02:16PM
Oh, I see it now. Albert knows that Bernard does not know, not because Bernard or Cheryl told Albert that, but because Albert was told a month for which Cheryl did not give unique days. I was thinking that Albert saw only that Bernard did not know, which eliminates only June. So all of May and June are out. After Albert announces that he knows Bernard does not know, Bernard can also make that connection.
Then, the 14th is out, because Bernard would still not know which month Albert was told if the day was the 14th, and he says he does know after hearing Albert. We're down to July 16, Aug 15, and Aug 17.
Finally, August is eliminated because Albert says that because Bernard now knows, he knows too. If Albert knew the month was August, he still could not tell if it was the 15th or 17th. So Albert must have been told that the month was July, for him to be able to announce (truthfully) that now he knows too.