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posted by cmn32480 on Thursday April 16 2015, @01:24AM   Printer-friendly
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?"

 
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  • (Score: 2, Insightful) by hoeferbe on Thursday April 16 2015, @04:50AM

    by hoeferbe (4715) on Thursday April 16 2015, @04:50AM (#171387)
    TheB (1538) [soylentnews.org] wrote [soylentnews.org]:

    "Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either."
    Since there is only one 18th and 19th.
    This eliminates May and June from the possible months.

    OK, I understand how this eliminates June as a possible month from Albert's point of view, but I don't understand how it removes May.

    Taking away 18 as a candidate would leave June 17th as the only June choice. If Albert had been told "June" by Cheryl, then Albert would now know her birthday is June 17th. But since Albert doesn't know that, it removes June as a candidate.

    In Albert's mind, these should still be the possibilities:

      May    15 16
      Jul 14    16
      Aug 14 15    17

    What is the reasoning that Albert can eliminate the entire month of May before Bernard says "I didn’t know originally, but now I do"?

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  • (Score: 4, Informative) by KilroySmith on Thursday April 16 2015, @05:48AM

    by KilroySmith (2113) on Thursday April 16 2015, @05:48AM (#171404)

    Well, if you ignore my comment above and assume that Bernard knows that Albert knows the month, and Albert knows that Bernard knows the day, then...

    Following TheB's analysis,

    "Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either"

    If Cheryl had told Bernard a unique date (i.e. the 18th or 19th which only occur in one month), then Bernard would immediately know both the month and date. With this statement, Albert is telling Bernard that the Month that Albert was told doesn't have a unique possible birthday date - that for the month he was told, each of the possible dates also occur in a second month. That tells Bernard that Albert must have been told either July or August, because both May and June have unique dates (the 19th of May or the 18th of June).

    I think you're getting a bit confused at this step. Albert couldn't make his statement "I know Bernard doesn't know either" if it's possible that Bernard was given either the 18th or 19th. Albert knows, based on the month he was given, that Bernard couldn't possibly have been given a unique date, so Albert must have been given a month that doesn't have a unique date.

    Bernard now knows two pieces of information - a date that occurs in at least two different months, and the fact that May and June have been eliminated. The 14th occurs in both July and August, but can't be the right date - if it was, Bernard wouldn't be able to make the statement that "I didn’t know originally, but now I do". If the date was the 14th, the information that Albert has given him wouldn't be sufficient to choose one or the other. So, we can eliminate the 14th.

    July 16 is a possibility. The 16th occurs in both May and July, so Bernard wouldn't be able to tell the difference originally, but would be able to by using Albert's revelation to eliminate May 16.

    August 15 is a possibility. The 15th occurs in both August and May, and Bernard should be able to eliminate May using Albert's revelation.

    August 17 is also a possibility. The 17 occurs in both August and June, and Bernard should be able to eliminate June using Albert's revelation.

    So how do we choose between these three possibilities?

    Bernard reveals the next clue - "Well, now I know too". So, of the three possibilities, only one can be possible

    If Albert had been told August, then he couldn't determine whether Aug 15 or Aug 17 was the correct one, so it can't be either of those or he couldn't make the statement.

    If Albert had been told July, then he could make the statement. This is the only possibility left, so it must be the correct date.

  • (Score: 4, Informative) by Ryuugami on Thursday April 16 2015, @05:50AM

    by Ryuugami (2925) on Thursday April 16 2015, @05:50AM (#171406)

    If B was told "18th", he would know it was May 18th.

    If A was told "May", there would still be a possibility of the day being May 18th, so he wouldn't know B has insufficient information.

    In other words, as the first step you can strike all months that have any unique days.

    --
    If a shit storm's on the horizon, it's good to know far enough ahead you can at least bring along an umbrella. - D.Weber