A monk problem

  • #1

Main Question or Discussion Point

I saw this the other day, it's quite an interesting little problem :smile:

300 monks live together in a monastery. They have very strict rules which are followed by all of the monks at all times. One of the rules is, that absolutely no communication between monks is allowed. Another is, that mirrors are forbidden. The monks have their three meals a day together in a large hall, the rest of their day is spent with individual contemplation and chores.

One morning, a messenger comes to the monastery and addresses the monks at breakfast. He tells them, that a rare disease is spread throughout the country, and that the monks may have the disease as well. The main symptom of the disease is a large red spot on the head of the afflicted. The disease kills everyone who knows they have it within two hours. The disease was transmitted by a bad shipment of rice, but is not contagious.

On the morning of the eleventh day after the messenger arrives, some of the monks don't turn for breakfast and are found dead in their beds.

Question: How many monks died?
If you already know it then wait 'til others have got it, in any case use spoiler tags.

So no one knows who doesn't want to ie &{/COLOR]
 
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Answers and Replies

  • #2
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Just a quick addendum:

The messenger, while addressing the monks at breakfast (where he can see them all), tells the monks that he can see that at least one monk already has a dot!

DaveE
 
  • #3
Just a quick addendum:

The messenger, while addressing the monks at breakfast (where he can see them all), tells the monks that he can see that at least one monk already has a dot!

DaveE
Oh yeah thanks DaveE.
 
  • #4
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0
Spoiler
None of them died, since there is no possible way of them for knowing if they have the disease or not.
 
  • #5
Spoiler
None of them died, since there is no possible way of them for knowing if they have the disease or not.
Not right, as the messenger tells them at least one monk has it, therefore one of them at least must have a dot on his head. They can all see the man in question, this means that the man who sees no red dot would be the infected one, and he'd know it.
 
  • #6
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this means that the man who sees no red dot would be the infected one, and he'd know it.
That much is easy, but why did he take 10 days to figure it out?
 
  • #7
That much is easy, but why did he take 10 days to figure it out?
They don't, each man dies within two hours of knowing he has the disease. After 10 days x amount of monks have died. Your making the assumption that they only die on the tenth day which is obviously not true, given the 2 hour criteria.

Mind you I made the same assumption when I first read it.
 
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  • #8
Hurkyl
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They don't, each man dies within two hours of knowing he has the disease. After 10 days x amount of monks have died. Your making the assumption that they only die on the tenth day which is obviously not true, given the 2 hour criteria.

Mind you I made the same assumption when I first read it.
Er, all the people who die do so simultaneously.
 
  • #9
Er, all the people who die do so simultaneously.
Er no, all the people who die, die from day 1 to day 11. After they realise they are infected.

Put it this way the priests know that someone at least is infected if two are infected, how many die? Then subsequently at each meal time how many die? Give the answer as any number you like. How many of the monks would know they had the disease?

With 3 infected on the first morning? With 4, with 5 and so on. You have to think carefully about what the monks would think. There is only one answer.
 
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  • #10
Hurkyl
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Er no, all the people who die, die from day 1 to day 11. After they realise they are infected.

Put it this way the priests know that someone at least is infected if two are infected, how many die? Then subsequently at each meal time how many die? Give the answer as any number you like. How many of the monks would know they had the disease?

With 3 infected on the first morning? With 4, with 5 and so on. You have to think carefully about what the monks would think. There is only one answer.
This is my favorite new-knowledge problem. :tongue: If N people are infected, then all N will die shortly after the N-th time that the monks congregate.

There's actually a very simple argument that proves all the people that die will have to die at the same time: symmetry. There is no relevant difference between any of the infected monks, so if any one if them is capable of figuring out e's infected, then all of them can.


If two monks are infected, then nobody dies the first meal: each of the infected monks can see someone else with a dot, and thus is unsure about his own status. Then, when nobody dies after the first meal, they learn there is a second dot, and they both die after the second meal.

If three monks are infected, then nobody dies after the second meal: at that point they know there are at least two infected people, but they all see two dots. But after the third meal...
 
  • #11
This is my favorite new-knowledge problem. :tongue: If N people are infected, then all N will die shortly after the N-th time that the monks congregate.

There's actually a very simple argument that proves all the people that die will have to die at the same time: symmetry. There is no relevant difference between any of the infected monks, so if any one if them is capable of figuring out e's infected, then all of them can.


If two monks are infected, then nobody dies the first meal: each of the infected monks can see someone else with a dot, and thus is unsure about his own status. Then, when nobody dies after the first meal, they learn there is a second dot, and they both die after the second meal.

If three monks are infected, then nobody dies after the second meal: at that point they know there are at least two infected people, but they all see two dots. But after the third meal...
2 people have it, they assume that they maybe safe as only one person may have it, so one person seeing one person with the dot, may assume what if no one died? 'tis the key.:smile:
 
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  • #12
Hurkyl
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All of the other monks see the two people with dots die after the second meal, and conclude that they are not infected.

Here's the timeline:

: Messenger arrives.
(everybody knows there is at least one dot)
: Next meal happens.
(everybody knows there is at least two dot)
: The two people with dots die.
: Next meal happens
(everybody knows there were exactly two dots, and thus the remaining people are not infected)
 
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  • #13

All of the other monks see the two people with dots die after the second meal, and conclude that they are not infected.

Here's the timeline:

: Messenger arrives.
(everybody knows there is at least one dot)
: Next meal happens.
(everybody knows there is at least two dot)
: The two people with dots die.
: Next meal happens
(everybody knows there were exactly two dots, and thus the remaining people are not infected)
If everyone assumes there are two dots? Why? The puzzle says there are at least one person with the disease, why would they assume two and if they did what would happen? think carefully. What is the only logical solution? Considering someone at least dies on the last day in the morning?
 
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  • #14
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(Admittedly my last post is sloppy)

If there are two people with dots, they will die simultaneously two hours after the second meal, and nobody dies. (I count the messenger's arrival as the first meal) Are you trying to dispute this?
 
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  • #15
(Admittedly my last post is sloppy)

If there are two people with dots, they will die simultaneously two hours after the second meal, and nobody dies. (I count the messenger's arrival as the first meal) Are you trying to dispute this?
Not at all, just wondering about your prognosis for the disease? What is the only logical solution?
 
  • #16
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Exactly what I said in post #10. And the only reason I stated the answer is because you told jimmysnyder that, in fact, the N people do not die simultaneously, which indicates you do not know the solution to the problem.
 
  • #17
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I finally figured it out: 29 died simultaneously.
If there were only one dot, he would have missed lunch. If there were two, they would both have missed dinner. At the end of the 10th day, all 29 dotted monks came to dinner and realized their predicament. None of them showed up for breakfast the next day.
 
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  • #18
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I found n-1 monks dying before repast n. Since breakfast on the eleventh day is the 31st repast, 30 monks will miss breakfast and be found dead in their beds. They all die simultaneously.
 
  • #19

Exactly what I said in post #10. And the only reason I stated the answer is because you told jimmysnyder that, in fact, the N people do not die simultaneously, which indicates you do not know the solution to the problem.
No I never said x monks don't die simultaneously I simply told him that they wont all die necessarily on the 10th day, think about why?

OK since your assuming I don't know the answer for some reason, here it is. Why would I put up a problem I didn't know the answer to? :confused:

Hurkyl, your guilty of making assumptions that don't exist. or not accounting for something, I'm not sure which: Spoiler below.

Here's a hint:-

Clues


1)Don't assume the disease doesn't have an incubation period.
2) bearing this in mind in what situation would make you know that your answer is always correct?
3)can you assume when and on which day the disease will show up in a new person?
4) Hurkyl does this conflict with your idea of simultaneity?


Spoiler


Assuming that the only time the monks can be sure that they have it is if only one monk has it ergo he dies on the second meal. We then say one more has it and one monk is dead and so on untill the 11th day after the messenger arrived.

However if you have 2 monks then they find out after 2 meals, if 3 after 3 meals and so on with subsequent deaths leaving potentially no monks infected, however the disease may continue to show up after the first day if it has an incubation period of 1 to x days,which of course all diseases do.

Since we cannot be sure when the disease presents the symptoms, the only way we can be sure that at least one monk dies on the last day is if one monk dies after every meal with one infected.

It is possible that 33 are infected but then no one else must present with the disease, 33 would then die on the last day but then the answer is the same anyway not to mention this is unlikely.

The total is therefore the number of meals:-

2 die on the first day
3 for the following 10 days
1 on the morning of the 11th day after the messenger arrives.

Total 33.

You have two bits of information here that you should adhere to, at least one monk has it,at least one monk dies on the last day, if 3 monks have it then it will take 3 meals before they realise that they have it, and you have to assume no one else gets it. Otherwise the system is screwed

Essnov you're technically right like Hurkyl but you miscounted the meals.
See above. On the morning of the 11th day after the messenger arrives.


Spoiler part 2:-

Your answer is technically right Hurkyl but only if 33 are infected in a precise way, otherwise you can't be sure that any more will present with the disease, so there is no way of knowing absolutely,in other words it's conditional, the other solution is much better. But well done anyway.
 
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  • #20
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i've gained 2.3 monks :rolleyes:
 
  • #21
i've gained 2.3 monks :rolleyes:
If that's a joke it just shot right over my head.:tongue2: :smile:
 
  • #22
Hurkyl
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Hurkyl, your guilty of making assumptions that don't exist
I'm guilty of reading a logic puzzle as if it were a logic puzzle. (As opposed to a "how can I subvert the apparent intent of the question?" problem)

That said, I have considered the modification of the original puzzle to allow people to develop symptoms after the messenger makes his announcement, and I'm virtually certain that it's irrelevant: only the people who were showing symptoms when the messenger made his announcement will be able to figure out they're diseased, and they will figure it out at exactly the predicted time.

I'm completely at a loss as to why you think it's possible for one person to die after each meal for 33 meals.
 
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  • #23
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answer?


they all show up to breakfast. cause if at least 1 has the disease but more than 1 have it, every monk will always find some1 else infected and he will think he has no disease. so as long as they don't know they are infected, then no1 will die.
 
  • #24
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they all show up to breakfast. cause if at least 1 has the disease but more than 1 have it, every monk will always find some1 else infected and he will think he has no disease. so as long as they don't know they are infected, then no1 will die.
But suppose that exactly two monks have dots. At breakfast, each one will see 298 clear heads and one dot. Each one will say to himself, "He sees the same 298 clear heads that I see, the only question is what does he see on my head." When the other fellow shows up for lunch, he says to himself "If he had seen 299 dots he would have died before lunch. It must be that he sees a dot on my head. Oh dear! Both say the same thing, both die before dinner. If there are exactly 3 people with dots, then at dinner each one of the three wonders why the other two are still alive. etc.
eom
 
  • #25
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Ok, Schrodinger's Dog, you've let realism into a logic puzzle where it doesn't belong. Logic puzzles are logical, not real. A disease that only kills people who know they have the disease? Come on. Monks who don't communicate? Yeah, right. No mirrors or reflective surfaces at all? Not bloody likely.

The problem is unrealistic, but logical.

Why would I put up a problem I didn't know the answer to? :confused:
Happens sometimes, certainly-- especially if you've got a Brain Teaser that you're looking for help with.

This one is fairly common, and it's been posted here before with different variations. That said, you left out a phenomenal chunk of stipulations given your interpretations.

Hurkyl, your guilty of making assumptions that don't exist.
That's true. He's assuming that:

- nobody new gets infected with the disease after the time the messenger arrived
- all the monks KNOW that nobody new gets the disease
- the monks have perfect logic which functions instantly, so they WILL know instantly when they are capable of doing so that they have the disease
- no monks die from any causes OTHER than the disease
- no monks play practical jokes by putting red dots on other people's foreheads (IE all red dots are symptoms of the disease)
- all monks see all other monks ONLY at mealtimes, and are 100% incapable of seeing all 299 other monks at any time of day
- monks will NECESSARILY see ALL 299 other monks at mealtime
- the only reason that monks would NOT show up for the mealtime is if they're dead
- monks cannot communicate with ANYONE, not just other monks

Now, you didn't state these stipulations (and maybe more) in your problem, but I think they're pretty safe to imply.

Assuming that the only time the monks can be sure that they have it is if only one monk has it ergo he dies on the second meal.
Alright. Slow down for a second and type in complete sentences. You just made an assumption that's incorrect and therefore an incorrect conclusion. But I can't see where your mistake was because you tried to jump 3 steps at once. Actually, your post kind of does this a lot. Take smaller steps.

It's quite easy for a monk to be sure that he has a dot without being the only one to have a dot. Let me try to explain:


Let's suppose only 1 monk was infected at the time the messenger shows up. Now, at the next meal, the infected monk shows up and sees that NOBODY ELSE has a dot. Therefore, since the infected monk KNOWS that at least ONE person has a dot, and he knows that nobody else has the dot, that HE must have the dot. He is instantly infected, and dies two hours later, and doesn't make it to the next meal.

Alright, now let's pretend that 2 monks are infected. The two infected monks show up at the first meal and each one of them sees that there's someone else with a dot. Ok, they each think, that guy ought to be dead before the next meal, if he figures out that he has a dot. So NEITHER of them concludes that they have a dot. Next, they show up at the *second* meal, and each infected monk sees that the OTHER monk who had a dot isn't dead! If that other monk was the ONLY one who was infected (as we already saw), they would be dead. But they're not! So that means that at least TWO monks are infected. Hence, since each infected monk sees only ONE other monk with a dot, they instantly figure out that THEY have a dot, and will be dead before the next meal.

So, now it gets bigger. Let's pretend that 3 monks are infected. They show up to the 1st meal, and see 2 other monks with dots. Ok. So they conclude that if those other 2 monks are the ONLY ones with dots, they should die before the *3rd* meal, thanks to the logic above. However, when it comes time for the 3rd meal, both the infected monks show up. What this means is that the infected monks now KNOW that there are at least *3* infected monks, and they know that THEY are the ones to have the 3rd infection dot. Therefore, all 3 realise simultaneously at the beginning of the 3rd meal that they are infected, and are dead two hours later.

Et cetera. If 4 monks are infected, they learn this at the 4th meal. If 5 monks are infected, they learn this at the 5th meal. And so on.

Now, normally, this riddle is done in days, not meals, because counting by meals is more confusing, and this puzzle doesn't really need any more complexity. But anyway. You said the morning of the 11th day. So because the day the messenger arrived is the 0th day, and not the 1st day, that means 11 full days have transpired since the messenger came as we're starting the 11th day. So that means 33 meals have transpired. Therefore, 33 monks died, because if 33 were infected, they would learn that on the 33rd meal, and would die before the 34th meal, which is breakfast on the 11th day.


however the disease may continue to show up after the first day if it has an incubation period of 1 to x days,which of course all diseases do.
Um. What?

DaveE
 

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