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Stormrider81 #134094 15/12/03 12:20 PM
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Now I don't have a single clue anymore. But I still think it's very important why they jumped on the third day.

Merendrious #134095 15/12/03 12:56 PM
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i thought merdenious had a good sollution <img src="/ubbthreads/images/graemlins/smile.gif" alt="" />
Why was his conclusion wrong?
Because they can't communicate?


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Merendrious #134096 15/12/03 02:14 PM
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or a new answer, i think this one is correct: They decide to go one time to the cliff for every single monk. If they the number of days is equal to the number of monks with dots they see, they have to jump.


Let's take it from here. How do you come to this conclusion - that the number of days is equal to the number of dots seen by the ones who have a dot?

Suppose there are 2 monks with a dot. On day 1, those two monks each see 1 dot. How could either monk know, by seeing one monk with a dot, whether he has a dot or not himself?...

(You're almost there though, you know <img src="/ubbthreads/images/graemlins/winkwink.gif" alt="" /> )


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Kejero #134097 15/12/03 03:27 PM
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=>[color:"#3A495A"]Still asuming the 2 monks: He can only know it if the other monk doesn't jump on the 1st day either (then the both monks have a dot, and they would jump on the 2nd day). If one of both monks jump on the first day, then the one that jumped only has a dot on his head.
Now back to the normal story, there they jump on the third day,so meaning that there are 3 monks having dots on their heads. So they jump when the number of dots that they see, overrides it with one.[/color]

Kejero #134098 15/12/03 03:42 PM
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Man, that's a brain buster, Kejero!

Merendrious #134099 15/12/03 05:09 PM
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=>[color:"#3A495A"]Still asuming the 2 monks: He can only know it if the other monk doesn't jump on the 1st day either (then the both monks have a dot, and they would jump on the 2nd day). If one of both monks jump on the first day, then the one that jumped only has a dot on his head.
Now back to the normal story, there they jump on the third day,so meaning that there are 3 monks having dots on their heads. So they jump when the number of dots that they see, overrides it with one.[/color]


Fair enough, I'll take that as the correct answer <img src="/ubbthreads/images/graemlins/winkwink.gif" alt="" /> I'll post an "extended" explanation now. Well done! <img src="/ubbthreads/images/graemlins/up.gif" alt="" /> <img src="/ubbthreads/images/graemlins/smile.gif" alt="" />

-> [color:"#3A495A"]
Day one. Suppose there is one monk with a dot.

All monks are standing at the cliff. The monk with the dot doesn't see anyone with a dot, so, since he knows there is at least one monk WITH a dot, he knows he's the one, the only one. So, at 12:00 pm, that one monk would jump.

However, no one jumped the first day, so we know one thing for sure now: there are AT LEAST two monks with a dot.

Day two. We know there are at least 2 dots. Suppose there are exactly 2 dots.

Both monks with a dot, only see one monk with a dot. At that moment they KNOW they have a dot as well, since they know there must be at least two dots. No doubt, they are number two. No doubt, they jump at 12:00 pm.

But no one jumped at day two. Conclusion: there are AT LEAST 3 dots.

Day three. We know there are at least 3 dots. Suppose there are exactly 3 dots.

Each of the three monks with a dot only see 2 dots, so they each know they are number three. They will jump at 12:00 pm.

And they jumped, so there were exactly three monks with a dot, leaving the other monks relieved, because they now, finally, know for sure they don't have a forth dot.




Feel free to question this solution, and check if it is really correct <img src="/ubbthreads/images/graemlins/biggrin.gif" alt="" /> Most people don't believe it because there were 3 dots from the beginning, and by the end of day one, the monks with a dot already knew there were AT LEAST 2 dots, and the other monks even know there were at least 3 dots! So they could've jumped on day two! Right? No, wrong <img src="/ubbthreads/images/graemlins/tongue.gif" alt="" /> Figure it out <img src="/ubbthreads/images/graemlins/biggrin.gif" alt="" />

[/color]


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Stormrider81 #134100 15/12/03 05:11 PM
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Man, that's a brain buster, Kejero!


I promised ya one, didn't I <img src="/ubbthreads/images/graemlins/biggrin.gif" alt="" />


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Kejero #134101 15/12/03 08:17 PM
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but they could see that others have dots too on the first day..
SO i dont get it :S
why would they only draw the conclusion on the 3rd day?
on the first day, they saw no one jumped, and also saw that according to you, 2 other monks had a dot.
He could immediatly draw the conclusion that he has a dot himself then according to you, but the other monks don't know about their own dots eiter.

Confused <img src="/ubbthreads/images/graemlins/confused.gif" alt="" />


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jvb #134102 15/12/03 08:29 PM
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On the second day, the monks without dots see three dots, so know they do not need to jump. The monks with a dot see two dots, so there are two possibilities;

A) they do not have a dot, in which case the two other monks with dots will jump (they would only see one dot, and if that monk had the only dot, he would have seen none the day before and jumped then)

B) they do have a dot, in which case they other monks will not jump, since they will also see two other monks with dots.


On the first day, the monks see 2 or 3 dots, but can not figure out if they have a dot until the 2nd or 3rd day, as above.

Raze #134103 15/12/03 09:01 PM
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I was confused with the answer of Kejero but everything is clear with the answer of Raze.
But next time you ask this riddle say that the monks are fearless and very clever because if one of them is stupid, it's doesn't work !

Barta #134104 15/12/03 09:50 PM
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was it said that they had to jump on the same day as there were dots?
like 3 dots -> day 3??


jvb, royal dragon prince Cheers!
jvb #134105 15/12/03 10:18 PM
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Another one !

You are in a room in which there are two doors A and B.
One of the two doors is the door of Paradise, the other one is the door of Hell.
There is a guard in front of each door.
One of the two guards always says the truth, on the other hand, the other guard lies continuously.
The two guards know each other very well and both of them know which is the Paradise door and which is the Hell door.

You have the right to ask one and only one question to one of the two guards in order to determine with exactitude which is the door of Paradise, door A or door B.

Which is this question ?

Barta #134106 15/12/03 10:37 PM
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That monk one was good, Kejero! Well done!

As for Barta's: [color:"#324372"]"If I asked the other guy if this was the door to paradise, what would he say?"

If it is the door and the guard lies, he'd say "No."
If it is the door and the guard is honest, he'd say "No."
If it isn't the door and the guard lies, he'd say "Yes."
If it isn't the door and the guard is honest, he'd say "Yes."

So if he says "No" you know it's the door to paradise. If he says "Yes", you know it's the other door.

The question forces both a truth plus a lie, leaving nothing left to chance.[/color]

HandEFood #134107 15/12/03 10:45 PM
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Another one:

Two countries are divided by a bottomless chasm. There is a single bridge spanning the chasm. It takes 5 minutes to cross the bridge. There is a guard hut in the centre of the bridge. The guard comes out every 3 minutes to ensure that no one crosses the bridge illegally. Your country is under evil-dictatorship rule and they're out to get you.

  • You cannot legally cross the bridge.
  • You cannot hide from the guard.
  • The guard is armed and a trained athelete. You're not.
  • All other neighbouring countries are under evil-dictatorship rule as well.

How do you escape to the other country and freedom?

HandEFood #134108 15/12/03 10:56 PM
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@HandEfood
[color:"#324372"]Right answer and good explanation.
Mine was : "If I asked to the other guard to tell me which is the door of Paradise, which door would he indicate ?
Each gard would indicate the wrong door.
Congratulations[/color]

Barta

HandEFood #134109 15/12/03 11:12 PM
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How do you escape to the other country and freedom?


you pay the guard 100000 Dollar!


bernhard live and let die!
jvb #134110 15/12/03 11:16 PM
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was it said that they had to jump on the same day as there were dots?
like 3 dots -> day 3??


No, but until the number of days equals the number of dots, there is no way to be sure if you have a dot or not.

To start, you know there is at least one red dot.

Day 1; If you do not see any dots, you know you must have one, so would jump. Nobody jumped, so there are at least 2 dots.

Day 2; If you see one dot you know you also have one (if not, the single monk with a dot would have jumped the day before) and must jump.

Etc.

If you see y number of dots, then you jump on the y+1 day (assuming nobody jumped the day before). Each monk with a dot will see one less dot than monks without a dot, so would jump one day before (revealing to the rest that they do not have a dot and are off the hook).

bernhard #134111 16/12/03 12:36 AM
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How do you escape to the other country and freedom?

you pay the guard 100000 Dollar!

The evil-dictator is the only one with that kind of money. <img src="/ubbthreads/images/graemlins/tongue.gif" alt="" />

HandEFood #134112 16/12/03 12:49 AM
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Assuming walking around the guard hut on the opposite side as the guard or climbing along under the bridge both count as hiding, how about building a hang glider? A forged passport? Kidnap the guard's family?

<img src="/ubbthreads/images/graemlins/silly.gif" alt="" />

Barta #134113 16/12/03 12:58 AM
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@HandEfood - an attempt at The Bridge:
[color:"#324372"]ummm... you scoot across the bridge to just past the halfway point (which takes just over 2 1/2 minutes), and then you turn around and walk slowly back toward the middle, so that when the guard comes out you are going back the way you came. the guard will order you off the bridge, so you obediently turn around again, and continue over to freedom... ?[/color] <img src="/ubbthreads/images/graemlins/question.gif" alt="" />

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