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#11 EventHorizon

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Posted 09 February 2008 - 01:50 AM

The puzzle went something like ....

"Queen XXXXXX (can't remember her name) of atlantis said that at least one man was cheating on his wife in atlantis. It was common knowledge that all wives know about whether or not other men were faithful, but not about their husband. She said that once you know your husband cheats, then shoot him at midnight. After 49 nights of silence, gunshots were heard. How many men were cheating? What was Queen XXXXXX's great accomplishment?"

Obviously not verbatim, but that's the gist of it.

As for your follow-up...

Spoiler for oops....

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#12 roolstar

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Posted 09 February 2008 - 02:03 AM

They would all get off the bus at the 6th station thinking there were 6 and they were the sixth.



Spoiler for HAHA

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#13 Jkyle1980

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Posted 09 February 2008 - 02:03 AM

Don't the five with dirty faces get off after the second stop. Isn't the number of faces completely irrelevant and all monks with dirty faces will get off at the second stop?
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#14 roolstar

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Posted 09 February 2008 - 02:09 AM

What about:

Spoiler for They know more than you think they know.



Spoiler for Something doesn't add up here

Edited by roolstar, 09 February 2008 - 02:14 AM.

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#15 roolstar

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Posted 09 February 2008 - 02:13 AM

As for your follow-up...

Spoiler for oops....


Spoiler for Or

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#16 Jkyle1980

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Posted 09 February 2008 - 06:16 AM

This is very similar to another puzzle that I believe I saw on here a while back.

Spoiler for Those monks are so smart....


The 1st - 3rd stops above tell the monks nothing new. When they get to the first stop they all already know that there are at least 4 with dirty faces. So you can remove the first three stops in the above answer and rename "Fourth stop" and "Fifth stop" as "First stop" and "Second stop".

"Why would the 5 monks get off thinking they are number 5 and not the rest of them get off thinking they are number 6? (a)

What is the difference between the 5 monks and the rest? NOTHING (b)

For all they know (the 5 monks), the other 4 may be wondering if they are number 4! ©

Remember they don't know what everybody else is thinking!" (d)


(a) Good question. Let me come back to that.

(b) The difference is that some know there are at least 4 dirty faces and some know that there are at least 5.

© All 5 dirty faces will be wondering if they are number 5 because all 5 will see the other 4.

(d) All of the monks are thinking, "I count x amount of dirty faces. The total possible amount of dirty faces is x+1, because I do not know about mine." Since they are all supposed to be smart enough to figure this out, I assume they all know that every monk is thinking this same thing.

(a, again) Hmmm...let me get back to you. Roadblock.
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#17 catchgeekay

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Posted 09 February 2008 - 11:24 AM

Simple....

If the controller told me so, & if i was one amongst them, I'd have just covered my face with my cloth... :D

Since everyone out there is smart, we can expect everyone to cover their faces...

The legend says that monks expose only the face & palms while everything else is covered.... hence covering the face wouldnt be an issue...

Another possiblity is that, I'd just close the windows....

Possibility 3, I will sit in the direction opp to the wind flow.... :D

In the worst case scenario, I'll turn my back to the wind/window.... whatever.... Hence face is still clean.... :D
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#18 roolstar

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Posted 09 February 2008 - 04:50 PM

The 1st - 3rd stops above tell the monks nothing new. When they get to the first stop they all already know that there are at least 4 with dirty faces. So you can remove the first three stops in the above answer and rename "Fourth stop" and "Fifth stop" as "First stop" and "Second stop".

"Why would the 5 monks get off thinking they are number 5 and not the rest of them get off thinking they are number 6? (a)

What is the difference between the 5 monks and the rest? NOTHING (b)

For all they know (the 5 monks), the other 4 may be wondering if they are number 4! ©

Remember they don't know what everybody else is thinking!" (d)


(a) Good question. Let me come back to that.

(b) The difference is that some know there are at least 4 dirty faces and some know that there are at least 5.

© All 5 dirty faces will be wondering if they are number 5 because all 5 will see the other 4.

(d) All of the monks are thinking, "I count x amount of dirty faces. The total possible amount of dirty faces is x+1, because I do not know about mine." Since they are all supposed to be smart enough to figure this out, I assume they all know that every monk is thinking this same thing.

(a, again) Hmmm...let me get back to you. Roadblock.


(a) The answer lies in the small flaws in (b) (c ) & (d) will come back to that later!

(b) Even if some of them think there may be 5 & others think there might be 6, Nobody knows what everybody else is seeing or thinking (d)
==> There will be no way of agreeing on deleting the stops from 1 - 4 and starting from 5. They may be deleting 1 - 3 and starting at 4. See (a) below for illustration.

(c ) This means that if there were only 4 faces dirty, 4 people will see 3 dirty faces and will be wondering if they are number 4 and 36 see that there are 4 dirty faces and will be wondering if they are number 5!
==> This scenario is no different than the 5 dirty faces scenario and the monks cannot tell if it's this scenario or the other. See (a) below for illustration.

(a) Let me put it this way:
The different scenarios all haved a possibility in common (Two by Two) and the doubt cannot be eliminated except by missing the stops.

Scenario $: 4 Dirty Faces
- 4 people see 3 and wonder if they are number 4
- 36 people see 4 dirty faces and wonder if they are number 5 <=

Scenario 5: 4 Dirty Faces
- 5 people see 4 and wonder if they are number 5 <=
- 35 people see 5 dirty faces and wonder if they are number 6

And as 1 monk not knowing the other people thinking, you cannot tell if you are part of the group of 36 in scenario 4 or part of the group of 5 in scenario 5

The same in Scenario 5 & Scenario 6...

Ans that's why they cannot do it by stop #2
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#19 unreality

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Posted 09 February 2008 - 06:20 PM

This is similar to the Josephine problem :D good one though ;D
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#20 GIJeff

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Posted 10 February 2008 - 02:24 AM

(a) The answer lies in the small flaws in (b) (c ) & (d) will come back to that later!

(b) Even if some of them think there may be 5 & others think there might be 6, Nobody knows what everybody else is seeing or thinking (d)
==> There will be no way of agreeing on deleting the stops from 1 - 4 and starting from 5. They may be deleting 1 - 3 and starting at 4. See (a) below for illustration.

(c ) This means that if there were only 4 faces dirty, 4 people will see 3 dirty faces and will be wondering if they are number 4 and 36 see that there are 4 dirty faces and will be wondering if they are number 5!
==> This scenario is no different than the 5 dirty faces scenario and the monks cannot tell if it's this scenario or the other. See (a) below for illustration.

(a) Let me put it this way:
The different scenarios all haved a possibility in common (Two by Two) and the doubt cannot be eliminated except by missing the stops.

Scenario $: 4 Dirty Faces
- 4 people see 3 and wonder if they are number 4
- 36 people see 4 dirty faces and wonder if they are number 5 <=

Scenario 5: 4 Dirty Faces
- 5 people see 4 and wonder if they are number 5 <=
- 35 people see 5 dirty faces and wonder if they are number 6

And as 1 monk not knowing the other people thinking, you cannot tell if you are part of the group of 36 in scenario 4 or part of the group of 5 in scenario 5

The same in Scenario 5 & Scenario 6...

Ans that's why they cannot do it by stop #2


In reality, they can't do it at stop 5 either...these monks are WISE, so why in the world would the thought "If a monk saw no other dirty faces, he'd get off at the first stop" EVER cross his mind? He knows FOR A FACT that there are only two possibilities...either a) there are 4 dirty faces, and mine isn't one of them, or b) there are 5 dirty faces, and mine is one of them. There is not a single way to logically deduce which scenario it is (and the same goes for the Josephine one)
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