Logic problem given to 15 yr old Singapore students

[Ichingcarpenter]

Here's the problem Singaporean high school students were asked to solve, reworded slightly for clarity:

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl marks 10 possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, or August 17.

Then Cheryl tells Albert the month of her birthday, but not the day. She tells Bernard the day of her birthday, but not the month. Then she asked if they can figure it out.

Albert: I don't know when Cheryl's birthday is, but I know Bernard doesn't know either.

Bernard: At first I didn't know when Cheryl's birthday is, but now I know.

Albert: If you know, then I know too!

When is Cheryl's birthday?


hint
I had to make a grid to solve it but if you want a explanation you can google it.


This is why their math scores are so high analytically problem solving

[silverweb]

1. Not hard, actually.

[font color="navy" face="Verdana"]Recognizing patterns is integral to analytical thinking.

[William Seger]

16. Um, yes it is hard

... and deliberately so. It was the 24th of 25 questions asked in the 2015 Singapore and Asian Schools Math Olympiad. There were 28,000 contestants (presumably all of whom had shown some aptitude for math and logic), and according to SASMO's organisers, the quiz was aimed at the top 40% of the contestants and aimed to "sift out the better students".

The key to solving it is not simply "recognizing patterns." Like most logic puzzles, the solution lies in eliminating the incorrect answers, but in this one, that requires correctly interpreting the precise meaning of each statement, in the exact order they are given.

[silverweb]

17. Then I must be a freakin' genius.

[font color="navy" face="Verdana"](Which I'm clearly not.)

It took me 15 seconds, no grid, to see the one date that was unique - because I saw the duplications in the components of the other dates, i.e. pairs (as in patterns).

Must have been that semester of logic in high school, back when they actually taught thinking skills.

[William Seger]

18. Then I have to think you don't have the right answer

The correct month has 2 possible days, and the correct day appears in 2 possible months. How long ago was that logic class?

[silverweb]

19. A looooong time ago.

[font color="navy" face="Verdana"]I'll review the problem and my answer when I get back home later today.

[eridani]

2. Dell crossword puzzle books used to have those kinds of problems with grids

Being online has kept me from picking them up for a few years. I still do Sudoku and crosswords in the newspaper when I pick it up, though.

[bvf]

3. Did you ever do

the cryptic crosswords? Just asking...

[eridani]

4. Yes! Loved them. And I usually didn't have to use the cheat about where 1 across started

The trick is to figure out where the middle line is from the number of across clues divided by 2., and it's almost always an odd number.

[Yo_Mama]

5. Very simple logic problem.

For those who like them, there are some online logic puzzle sites. Here's one:
http://www.logic-puzzles.org/

[Ichingcarpenter]

6. yes, but

not for 15 year old american students.

[Yo_Mama]

9. Well, I've been out of school for a long time, but

it would not have posed much of a challenge for the kids I went to school with.

Maybe modern kids would have to have their cell phones confiscated so they could pay attention. They'd solve it to get the phones back.

[Ichingcarpenter]

10. International Math and Science scores

http://www.businessinsider.com/pisa-rankings-2013-12?IR=T

[eppur_se_muova]

7. Every month is duplicated; every date but the 19th is too.

It looks very frustrating at first, but then you realize there must be some unique "giveaway" that only one of the boys knew. So it must be the 19th, and May 19th is the only such date.

[Thor_MN]

8. The 18th isn't duplicated either.

[eppur_se_muova]

12. Oops, so it isn't.

I had thought there was *too much* info in the problem -- maybe not.

[Thor_MN]

13. It also relies on knowing if the other person knows. Neither knows right away.

I had to look it up, but I'm blaming it on having to do some work while thinking about it.

[William Seger]

20. That's what makes it a cool puzzle

When Albert says, "I know Bernard doesn't know either," he is correct -- or he was correct, up until he says that! And then when Bernard says he now knows, we still can't figure it out until until Albert informs us that he now knows, too. It's very clever.

[Fumesucker]

11. They haven't solved the problem of their ridiculously authoritarian government

For instance one party has been in power since 1959...

http://en.wikipedia.org/wiki/Politics_of_Singapore

Human rights activists, foreign scholars and opposition party members have pointed out that members of the opposition parties often suffer "misfortunes" of various kinds, including arrest, sued into bankruptcy especially in defamatory lawsuits, and imprisonment,[30] with the convictions and bankruptcy in turn barring the opposition candidates from standing in elections.[31]

Kenneth Paul Tan[32] has said that "Singapore's formal institutions of representative government are a colonial legacy, fundamentally based on the Westminster system of parliamentary government. In Singapore, the executive has greater power than the legislature. Regularly held political elections since 1959, run according to the simple plurality voting system, have seen the PAP remain in power and a very small number of elected opposition parliamentarians. With an overwhelming majority in parliament, the PAP government has been able to amend the Constitution without much obstruction, introducing multi-member constituencies, unelected parliamentary membership, and other institutional changes that have, in effect, strengthened the government's dominance and control of Parliament.

[AlbertCat]

14. Feb 29th?

I'm too tired to think this much!

Does Cheryl want a birthday party or not.... what an ass she is!



(Actually. after reading the comments, eliminating the unique #'s must be the 1st step...since nobody knows for sure at 1st. There must be a way of eliminating the months too.... like May and June.... because the unique days fall in those months.... I have a headache!)

[struggle4progress]

15. a grid as suggested by the OP

[Yo_Mama]

21. Easy way - don't read this if you want to work it out yourself!

Albert got the month, Bernard got the day.

Albert, knowing only the month, knows that Bernard cannot know what Chery's birthday is. Therefore, Bernard knows the the month is not May or June, because each of those months has a unique date.

Bernard didn't know the month, but after hearing Albert say he can't know Cheryl's birthdate, Bernard is able to figure out Chery's bday. Therefore the day Bernard was told can't be the 14th. The possible dates left are July 16th, August 15th, and August 17th

After hearing Bernard say that now he knows Cheryl's birthday, Albert realizes that he does know Cheryl's bday - it is July 16th.

We know that, without knowing the month as Albert does, because if Albert had been told that the month was August, he still would not know whether it was the 15th or the 17th, although Bernard would know Cheryl's birthday.

[Ichingcarpenter]

22. correct solution and explanation

I honestly didn't get this kind of problem until I took Logic 201 and wished it had been introduced to me earlier.

[Yo_Mama]

24. My mother at one point started her 2nd graders on logic problems

They were a solid class with an excellent group dynamic, so they moved along quickly, and toward the end of the year she needed a little something extra to keep them pepped up without encroaching on the third grade curriculum. So she stretched it with more math and science.

They did quite well, and very much enjoyed it. After that she added a bit of this sort of thing to her Gifted and Talented classes, and then added it to her Remedial classes if the student was at least a third grader.

I think this is a natural way of thinking, but like language, it is easier to learn it young. American education probably neglects this to the extreme. A very little exposure while young and locked in learning/playing mode goes a long, long way.

[Ichingcarpenter]

25. I used logic problems with my special ed inner school math 9th graders

but not at this level of complexity.

It made them think more than doing the usual math problems.

[Yo_Mama]

26. They must have loved you. n/t

[AlbertCat]

23. OMG... I was on the right path!

I knew that who knew what, when, had to be important because they included this info in the problem. But imagine if (like in the real world) there was also a bunch of superfluous info also given!

YIKES!