## An apple a day keeps the doctor away...but I have 11 of them

- finallyskeptic
- Regular Poster
**Posts:**550**Joined:**Fri Sep 25, 2009 3:05 pm**Custom Title:**----Blank----**Location:**EARTH

### An apple a day keeps the doctor away...but I have 11 of them

AJU,BAJU,CAJU and DAJU are four perfect logicians and members of the perfect logicians club.They were sitting around a table.On the table was a bowl containing 11 apples.Their discussion started.By the end of their discussion the apples had finished.

Each of them had at least one apple and knew how many apples he/she had.They wanted to know how many apples the other had so they asked each others questions.

AJU;Did you have more apples than me BAJU?

BAJU:I dont know.Did you eat more apples than me CAJU?

CAJU:I dont know.Did you eat more apples than me DAJU?

DAJU:I got it.

Daju got the answer.

Question:Like Daju can you workout how many apples did each of them have?

Each of them had at least one apple and knew how many apples he/she had.They wanted to know how many apples the other had so they asked each others questions.

AJU;Did you have more apples than me BAJU?

BAJU:I dont know.Did you eat more apples than me CAJU?

CAJU:I dont know.Did you eat more apples than me DAJU?

DAJU:I got it.

Daju got the answer.

Question:Like Daju can you workout how many apples did each of them have?

If you like anything please thank the poster.

- Gord
- Real Skeptic
**Posts:**24571**Joined:**Wed Apr 29, 2009 2:44 am**Custom Title:**Mister Grumpypants**Location:**Transcona

### Re: An apple a day keeps the doctor away...but I have 11 of them

Ooh, I've never heard of this one before! Let's see what I can come up with.

Let's see. 11 apples. Each of the four had at least one. That means the most anyone could have had is 8.

There are 7 apples unaccounted for. So, if someone had 5 (the first one, plus 4 of the other 7), then no one else could have had more than them (they could have had the first one, plus a maximum of 3 of the other 7). Therefore no one would have to ask anyone else if they'd had more.

Aju asked someone, so he had 4 or fewer apples. Therefore eat ate either 1, 2, 3, or 4 apples.

Baju asked too, so he had 4 or fewer apples. However, he knew he didn't have the same number or fewer, so he had either 2, 3, or 4.

Same thing with Caju, too, except he knew Baju didn't have only 1, so Caju must have eaten either 3 or 4 apples. But then, he asked Daju if he'd had more, so Caju couldn't have had 4 (because he knew no one would have had more than he did -- Aju had at least 1, Baju at least 2, and if he'd had 4, then the most Daju could have had would have been 4, too. Therefore, Caju must have had 3 apples!

And then, since Caju didn't know if that was more than Baju had eaten...uh...then that means that.... Ummmm....

Hmm.

Okay, I need think this through some more.

Baju had at least 2 apples. After Caju asked, "Did you eat more apples than me DAJU?" then Baju knew Caju had eaten 3 apples. Would that let him know if he'd eaten more apples than Aju? Only if Baju had eaten 4 apples. Hmm. I don't see how this helps me.

Hmmmmmmm.

IF Daju had eaten 4 apples, and he knew Caju had eaten 3, and that Baju had eaten at least 2, then he now would know that Aju ate either 2 or 1. (If Baju ate 2, then so did Aju; if Baju ate 3, then Aju ate 1.)

IF Daju had eaten 3 apples, and he knew Caju had eaten 3, and that Baju had eaten at least 2, then he now would know that Aju ate either 3, 2, or 1. (If Baju ate 2, then Aju ate 3; if Baju ate 3, then Aju ate 2; if Baju ate 4, then Aju ate 1.)

IF Daju had eaten 2 apples, and he knew Caju had eaten 3 and that Baju had eaten at least 2, then he now would know that Aju ate either 4, 3, or 2. (If Baju ate 2, then Aju ate 4; if Baju ate 3, then Aju ate 3; if Baju ate 4, then Aju ate 2.)

IF Daju had eaten 1 apple, and he knew Caju had eaten 3 and that Baju had eaten at least 2, then he now would know that Aju ate either 4 or 3 AND that Baju are either 4 or 3. (If Baju ate 4, then Aju ate 3; if Baju ate 3, then Aju ate 4.)

Guess I need to think about it some more.

Let's see. 11 apples. Each of the four had at least one. That means the most anyone could have had is 8.

There are 7 apples unaccounted for. So, if someone had 5 (the first one, plus 4 of the other 7), then no one else could have had more than them (they could have had the first one, plus a maximum of 3 of the other 7). Therefore no one would have to ask anyone else if they'd had more.

Aju asked someone, so he had 4 or fewer apples. Therefore eat ate either 1, 2, 3, or 4 apples.

Baju asked too, so he had 4 or fewer apples. However, he knew he didn't have the same number or fewer, so he had either 2, 3, or 4.

Same thing with Caju, too, except he knew Baju didn't have only 1, so Caju must have eaten either 3 or 4 apples. But then, he asked Daju if he'd had more, so Caju couldn't have had 4 (because he knew no one would have had more than he did -- Aju had at least 1, Baju at least 2, and if he'd had 4, then the most Daju could have had would have been 4, too. Therefore, Caju must have had 3 apples!

And then, since Caju didn't know if that was more than Baju had eaten...uh...then that means that.... Ummmm....

Hmm.

Okay, I need think this through some more.

Baju had at least 2 apples. After Caju asked, "Did you eat more apples than me DAJU?" then Baju knew Caju had eaten 3 apples. Would that let him know if he'd eaten more apples than Aju? Only if Baju had eaten 4 apples. Hmm. I don't see how this helps me.

Hmmmmmmm.

IF Daju had eaten 4 apples, and he knew Caju had eaten 3, and that Baju had eaten at least 2, then he now would know that Aju ate either 2 or 1. (If Baju ate 2, then so did Aju; if Baju ate 3, then Aju ate 1.)

IF Daju had eaten 3 apples, and he knew Caju had eaten 3, and that Baju had eaten at least 2, then he now would know that Aju ate either 3, 2, or 1. (If Baju ate 2, then Aju ate 3; if Baju ate 3, then Aju ate 2; if Baju ate 4, then Aju ate 1.)

IF Daju had eaten 2 apples, and he knew Caju had eaten 3 and that Baju had eaten at least 2, then he now would know that Aju ate either 4, 3, or 2. (If Baju ate 2, then Aju ate 4; if Baju ate 3, then Aju ate 3; if Baju ate 4, then Aju ate 2.)

IF Daju had eaten 1 apple, and he knew Caju had eaten 3 and that Baju had eaten at least 2, then he now would know that Aju ate either 4 or 3 AND that Baju are either 4 or 3. (If Baju ate 4, then Aju ate 3; if Baju ate 3, then Aju ate 4.)

Guess I need to think about it some more.

"Knowledge grows through infinite timelessness" -- the random fictional Deepak Chopra quote site

"You are also taking my words out of context." -- Justin

"Nullius in verba" -- The Royal Society ["take nobody's word for it"]

#ANDAMOVIE

"You are also taking my words out of context." -- Justin

"Nullius in verba" -- The Royal Society ["take nobody's word for it"]

#ANDAMOVIE

- finallyskeptic
- Regular Poster
**Posts:**550**Joined:**Fri Sep 25, 2009 3:05 pm**Custom Title:**----Blank----**Location:**EARTH

### Re: An apple a day keeps the doctor away...but I have 11 of them

You need to think a bit more you were quite right in the beginning.

If you like anything please thank the poster.

- Gord
- Real Skeptic
**Posts:**24571**Joined:**Wed Apr 29, 2009 2:44 am**Custom Title:**Mister Grumpypants**Location:**Transcona

### Re: An apple a day keeps the doctor away...but I have 11 of them

Yes, I see. Daju never asked anyone. I need to consider that he's eaten at least 5 apples.

If he ate 5, and he knows that Caju ate 3, that's 8 already. He knows Baju had at least 2 and Aju had at least 1. That's a total of 11 already.

So I would guess that Daju had 5 apples, Caju had 3, Baju had 2 and Aju had 1.

Is that correct?

If he ate 5, and he knows that Caju ate 3, that's 8 already. He knows Baju had at least 2 and Aju had at least 1. That's a total of 11 already.

So I would guess that Daju had 5 apples, Caju had 3, Baju had 2 and Aju had 1.

Is that correct?

"Knowledge grows through infinite timelessness" -- the random fictional Deepak Chopra quote site

"You are also taking my words out of context." -- Justin

"Nullius in verba" -- The Royal Society ["take nobody's word for it"]

#ANDAMOVIE

"You are also taking my words out of context." -- Justin

"Nullius in verba" -- The Royal Society ["take nobody's word for it"]

#ANDAMOVIE

- finallyskeptic
- Regular Poster
**Posts:**550**Joined:**Fri Sep 25, 2009 3:05 pm**Custom Title:**----Blank----**Location:**EARTH

### Re: An apple a day keeps the doctor away...but I have 11 of them

Sure it is....Guess thinking about delicious apples is what that pushed you off track...

If you like anything please thank the poster.

- Gord
- Real Skeptic
**Posts:**24571**Joined:**Wed Apr 29, 2009 2:44 am**Custom Title:**Mister Grumpypants**Location:**Transcona

### Re: An apple a day keeps the doctor away...but I have 11 of them

Yay!

(Actually, it was probably a combination of watching TV and not being smart enough to get it the first time. )

(Actually, it was probably a combination of watching TV and not being smart enough to get it the first time. )

"Knowledge grows through infinite timelessness" -- the random fictional Deepak Chopra quote site

"You are also taking my words out of context." -- Justin

"Nullius in verba" -- The Royal Society ["take nobody's word for it"]

#ANDAMOVIE

"You are also taking my words out of context." -- Justin

"Nullius in verba" -- The Royal Society ["take nobody's word for it"]

#ANDAMOVIE

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