Puzzle Quiz #2

[Syterion]

We used to have a thread with logic and math puzzles, and I thought it was a lot of fun(except when Perfection put up that stupid paperfolding triangular prism one). So I'm starting another one.

The rules are simple.

1) This a quiz for puzzles, generally of a logic/math nature. Other topics are not allowed.

2) A puzzle will be posted by me, and the first person to solve the problem will be able to post a puzzle of their own. If they choose not to, anyone can post a puzzle.

3) A solution, to be valid, requires an explanation of how the answer was ascertained.

4) If there is no present puzzle for 24 hours, anyone can post a puzzle.

5) No spamming random answers without backup.

The first puzzle:

Four perfect logicians who all knew that each other was a perfect logician, were talking around a plate of 11 apples. After a while, all the apples were eaten. Everyone knew that each person had at least one apple, and each knew how many apples they ate, but they did not know how many apples the others had. They agreed to only ask questions that they did not know the answer to.

Al said, "Did you eat more apples than I did, Bert?"
Bert said, "I don't know. Did you George, eat more apples than I did?"
George said, "I don't know."
Ed said, "Aha!"

Ed now knew how many apples each person ate. Can you figure it out?

 

[andrewgprv]

Ed ate 1 apple.

One would know for sure if they did not eat more apples then another if they ate one. So one can answer either no (if they ate one apple) or i dont know (if they ate two) they cant answer yes for sure because they do not know if the person asking them ate one apple.

Using that criteria we can eliminate bert and George from having ate one apple since they answered i dont know.

Al would not have asked Bert if bert ate more apples if al only ate 1, because al would already know that answer was yes.

So we can elimate AL.

So Ed ate one apple.

 

[Syterion]

You need to figure out how many they each had, not just Ed.

 

[andrewgprv]

You need to figure out how many they each had, not just Ed.

oops i assumed they distributed equally expet one so, 2 2 2 2 1 silly me

EDIT: Please ignore this my head is not screwed on right today

 

[andrewgprv]

EDIT: oops nevermind, god im spacey today

 

[Juka The Dumb]

george 4,al and bert 3,ed 1...

 

[Syterion]

You're all wrong.

 

[betazed]

eh styreion. you got to ask stuff harder than that in this forum.

al must have eaten at least 1 apple. This is givn
bert must have had at least 2 otherwise he would have answered no.
george must have had at least 3 otherwise he too would have answered no.

hence between the three of them they must have ate 6 apples at least. But none of them could have eaten more than 4. So Ed must have eaten 5.

Hence Ed ate the rest. so Ed -5 , george - 3, bert - 2, al - 1

 

[Juka The Dumb]

then al 4,bert and george 3,ed 1?

 

[Mise]

Ed had eight, he knew that already, so figured the rest of them had 1 each.

EDIT: oh wait 1 = 1 .... doh!

 

[Yom]

Bert - 4, Al and George - 3, Ed - 1?



(Just in case Juka is wrong )

 

[Yom]

Ed had eight, he knew that already, so figured the rest of them had 1 each.

No, Ed had 5, the rest had 2 each. Otherwise they wouldn't all say that they didn't know if they had more apples than the others.


Edit:

eh styreion. you got to ask stuff harder than that in this forum.

al must have eaten at least 1 apple. This is givn
bert must have had at least 2 otherwise he would have answered no.
george must have had at least 3 otherwise he too would have answered no.

hence between the three of them they must have ate 6 apples at least. But none of them could have eaten more than 4. So Ed must have eaten 5.

Hence Ed ate the rest. so Ed -5 , george - 3, bert - 2, al - 1

That way works too, but my way works as well (I think). Bert must have eaten 2, but George could have eaten 2 (but not 1). George doesn't know how many Bert has, so he can answer "I don't know" unless he has 1 or 4+. Thus, he has either 2 or 3. Bert can also have 3, while George has 2 (since, in each case, it is possible for another to have 4, as they don't know each other's apple count).

 

[Juka The Dumb]

Bert - 4, Al and George - 3, Ed - 1?



(Just in case Juka is wrong )

that was gonna be my next guess

edited:dumb guess

 

[ainwood]

Moderator Action: Moved to All Other Games.

And there is a fine-line between playing the game and spamming the game. I "suggest" that each person be required to post their answer with appropriate reasoning. If the reasoning is missing, the post may go missing as well.

 

[Mise]

But the HAD to answer "I don't know", cos they wouldn't know how many apples the other people had. (I know I'm wrong about the 1 each though)

 

[Syterion]

Betazed is right, of course.

[mutters expletive]

So he can post a puzzle.

 

[Renata]

edit: nevermind, Betazed got it. And I overlooked something silly.

Renata

 

[BasketCase]

I think I've got it.

Spoiler :

If Bert ate only 1 apple, he would have answered "no" to Al. So Bert ate at least 2. Since Bert answered "no" to Al, George also knows Bert ate at least 2.

If George had only eaten 2, he would have answered "no" to Bert. So George ate at least 3.

At this point, Ed knows Bert ate at least 2 and George ate at least 3. Since this is enough information for Ed to figure out how many apples everybody ate, we know he ate 5, otherwise Ed wouldn't have known if Al had eaten 1 or 2.

So Al ate 1, Bert ate 2, George ate 3, and Ed ate 5.

Edit: Bah, posted too slow.

 

[Syterion]

Al ate only 1. Bert must have had at least 2 otherwise he would say no. George must have more than two or he would also say no. The only way Ed would know the answer at this point is if he had 5 apples. So Al-1, Bert-2, George-3.

 

[betazed]

Betazed is right, of course.

[mutters expletive]

So he can post a puzzle.

Actually, I like answering puzzles more than asking them. So I will pass the oppurtunity to someone else.

Ask away.