Singapore maths question: How to solve the problem for school children that has stumped the world

[jhungary]

To people who still don't know and can't access to youtube.

Albert know the months so he would have know it could only be July 14 or July 16.

When he check against the possible date, that mean he guessed Bernard could only have know it was either August 14, July 14, May 16 and July 16. So he concluded Bernard did not know this.

What Bernard know is, the month cannot be May or June, if that is May, then it would be May 19 (An unique date) and June 18 (Another Unique Date) and thus the month can only be either July or August, but since he was told the date (16) and there were no August 16 in the list, he knew the date would be July 16. And declare that he did not know it before, but he knows after albert saying that.

While albert now know the date could not be 14, as albert know it is duplicated with August, and since Bernard knew, the number have to be unique. So he knew it is July 16.

By deductive reasoning.

 

[Kloitra]

To people who still don't know and can't access to youtube.

Albert know the months so he would have know it could only be July 14 or July 16.

When he check against the possible date, that mean he guessed Bernard could only have know it was either August 14, July 14, May 16 and July 16. So he concluded Bernard did not know this.

What Bernard know is, the month cannot be May or June, if that is May, then it would be May 19 (An unique date) and June 18 (Another Unique Date) and thus the month can only be either July or August, but since he was told the date (16) and there were no August 16 in the list, he knew the date would be July 16. And declare that he did not know it before, but he knows after albert saying that.

While albert now know the date could not be 14, as albert know it is duplicated with August, and since Bernard knew, the number have to be unique. So he knew it is July 16.

By deductive reasoning.

By day does it means date? If so than the question is not properly worded hence confusing.

 

[jhungary]

By day does it means date? If so than the question is not properly worded hence confusing.

the date is the master group of all 10 days. Don't look at it like Day/Time format. it would have easier and less confusing if you think about it as 2 sets of digit.

You have

5-15 5-16 5-19
6-17 6-18
7-14 7-16
8-14 8-15 8-17

Now, albert know the first digit, he knew it is either 7-14 or 7-16

now given what he knew, he can guess that Bernard was given either 14 or 16, so the possible set would down from 10 set to just 4 (7-14 8-14 7-16 5-16), and Albert's subset is 7-14 or 7-16

Now, as Bernard know, the first digit cannot be 5 or 6 as 5-19 and 6-18 both unique, if the first number is either 5 or 6, Albert would have said I could have know but giving an unique second number (If Bernard was given 18 or 19, Bernard would instantly know the number is 5-19 or 6-18), so when Bernard was given the second digit of 16, Bernard knew by negating the mutually exclusive condition, the first digit cannot be 5.

Then by saying he does not know before, but now he know, that means the number Cheryl gave to Bernard is also mutually exclusive (Otherwise Bernard could not have known) Given the second number 14 is duplicated in both 7 and 8, 14 could be ruled out as the second digit. Hence it could only be 7-16

The first thing when people encounter this kind of problem, the first thing those problem did is to confuse you with words and selections. Just look at the number itself and you can figure out.

 

[thesolar65]

Anyone wants to befriend Cheryl??

 

[Levina]

The problem doesn't mentions the two can't consult among themselves!

Exactly!!
Since they don't discuss it, how would one know that other knows a particular month or date??
The question is vague, we 've to make many assumptions.
@thesolar65 I seriously think some teachers enjoy giving tough questions to their students, and this is one of them .
(I know this question was asked in a competition but keeping it so vague was intentional). Lol

 

[500]

Its very simple:

5-15 5-16 5-19
6-17 6-18
7-14 7-16
8-14 8-15 8-17

Albert: I know Bernard doesn’t know

This eliminates:

5-15 5-16 5-19
6-17 6-18

Remains:

7-14 7-16
8-14 8-15 8-17

Bernard: I didn’t know originally, but now I do.

This eliminates:

7-14 and 8-14

Remains:

7-16
8-15 8-17

Albert: Well, now I know, too!

This eliminates:

8-15 8-17

Remains:

7-16

 

[jhungary]

Exactly!!
Since they don't discuss it, how would one know that other knows a particular month or date??
The question is vague, we 've to make many assumptions.
@thesolar65 I seriously think some teachers enjoy giving tough questions to their students, and this is one of them .
(I know this question was asked in a competition but keeping it so vague was intentional). Lol

actually, this question is not really hard, maybe a bit extreme with 11 yos learning logic but it's not especially hard within the topic of logic

 

[Kloitra]

the date is the master group of all 10 days. Don't look at it like Day/Time format. it would have easier and less confusing if you think about it as 2 sets of digit.

I was thinking in terms of days - week. That is Bernard was given a day. That would make 5-19 and 6-18 both 'not unique'.

 

[lightoftruth]

 

[William Hung]

@jhungary @500

Can you solve this problem, it is the same type.

I put both of you and levina in a room and put a sticker on each of your guy's forehead. I tell each of you it is either a black or white sticker. I also tell you all that at least one of you have a black sticker, but I won't tell how many has a black sticker. You guys can see each other's sticker but can't see your own and you cannot communicate with each other.

Here's the scenario. Suppose I've put black stickers on all of you (but still only say "at least one has a black sticker" ).

Then I ask, raise your hand if you know you have a black sticker on your forehead (you have to respond immediately without first looking at the other's response, and you can't lie either). None of you will be able to raise your hand cause none of you will know.

I then let you guys know that none raised their hand, then ask again the same question. Again, none of you will raise your hand cause you cannot know.

Then I let you know that none have raised their hands and ask a third time the same question. If you are smart, all three of you will now be able to figure out that you have a black sticker on your forehead and all raises your hand. The question is how?

 

[Thorough Pro]

her hint and questions have six words each. the date is sixth in sequence.

Singapore Cheryl’s Birthday: Impossible Math Question Is Tearing Apart The Internet

“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?”


Answer : July 16
But the way to answer just went above my head!!

@levina @Skull and Bones @Indo-guy @janon
Singapore maths question: How to solve the problem for school children that has stumped the world - The Times of India
Singapore Cheryl’s Birthday: Impossible Math Question Is Tearing Apart The Internet

 

[Kloitra]

@jhungary @500

Can you solve this problem, it is the same type.

I put both of you and levina in a room and put a sticker on each of your guy's forehead. I tell each of you it is either a black or white sticker. I also tell you all that at least one of you have a black sticker, but I won't tell how many has a black sticker. You guys can see each other's sticker but can't see your own and you cannot communicate with each other.

Here's the scenario. Suppose I've put black stickers on all of you (but still only say "at least one has a black sticker" ).

Then I ask, raise your hand if you know you have a black sticker on your forehead (you have to respond immediately without first looking at the other's response, and you can't lie either). None of you will be able to raise your hand cause none of you will know.

I then let you guys know that none raised their hand, then ask again the same question. Again, none of you will raise your hand cause you cannot know.

Then I let you know that none have raised their hands and ask a third time the same question. If you are smart, all three of you will now be able to figure out that you have a black sticker on your forehead and all raises your hand. The question is how?

The first time no one raises hand, it confirms that at least 2 of them have black stickers. No one is sure which two. What changes after you tell them no one raised hand?

 

[William Hung]

The first time no one raises hand, it confirms that at least 2 of them have black stickers. No one is sure which two. What changes after you tell them no one raised hand?

Partially correct. They can already all see that the other two has black stickers. None of them raises their hand because they don't know whether it is only 2 of them or all 3 of them having black stickers. e.g. Levina can see that the 2 boys has black stickers but don't know if she also has them or not.

When I told them that no one have raised their hands, they know that at least 2 has black stickers, but still don't know if all three has black sticks.

So when I ask them the second time, they still won't know.

I will tell them again that after my second time asking, no one raised their hands. But then when I ask them the third time, they will then know and will all raise their hands.

You still have to figure out how lol.

It is actually the same type of question as that Singapore Cheryl birthday puzzle, just in a different setting with an extra player.

 

[500]

There are two options:

My sticker is white.

- Levina sees one black and one white.
- jhungary sees one black and one white
- I see two blacks

jhungary knows that Levina sees one white and another X
And that I see one black and another X

Since first time no one rose his hands we all understood that no one can see 2 white stickers.

Now jhungary knows that Levina sees one white (mine) and one black (his).

So when he asked second time he will rise his hand.

Since it does not happen it is impossible and I have black sticker too.

 

[William Hung]

There are two options:

My sticker is white.

- Levina sees one black and one white.
- jhungary sees one black and one white
- I see two blacks

jhungary knows that Levina sees one white and another X
And that I see one black and another X

Since first time no one rose his hands we all understood that no one can see 2 white stickers.

Now jhungary knows that Levina sees one white (mine) and one black (his).

So when he asked second time he will rise his hand.

Since it does not happen it is impossible and I have black sticker too.

Correct!!!!!!!

Have you come across this muddy children puzzle before or did you just figure it out yourself? I shall call you Akira:

The first time no one raises hand, it confirms that at least 2 of them have black stickers. No one is sure which two. What changes after you tell them no one raised hand?

@Kloitra, this problem is solved like the Cheryl’s Birthday puzzle by the process of eliminations to get to the final answer.

Basically, when I first declared that at least one of them has a black sticker, they will know that there are 3 possibilities:

-First possibility: only one of them has a black sticker.

-Second possibility: only 2 of them has black stickers.

-Third possibility: all 3 had black stickers.

After the first question, everyone can eliminate the first possibility. Basically, say if 500 and jhungary has a white sticker, Levina will figure out that it must be her with the black and will raise her hand after the question. Well everyone will eliminate this possibility anyway since they can see that there are at least 2 black stickers.

After the second question, when they see that still no one has raised their hands, they can eliminate the second possibility. @500 has already explained this elimination process.

So if you eliminate the first and second possibility, the only option left is that all three has black stickers.

So when I ask them again for the third time, they will know by now and will all raise their hands. Basically, they had to wait after the first and second questions to confirm that one or two black stickers are not possible. Hence it is at the third questions that they can all know for sure.