# A monk problem

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

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

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

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.

Spoiler
None of them died, since there is no possible way of them for knowing if they have the disease or not.

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.

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?

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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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.

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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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...

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.

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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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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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Hurkyl
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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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(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?

Hurkyl
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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.

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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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.

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?

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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i've gained 2.3 monks

i've gained 2.3 monks

If that's a joke it just shot right over my head.:tongue2:

Hurkyl
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Science Advisor
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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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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.

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

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?

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

That's true. He's assuming that:

- nobody new gets infected with the disease after the time the messenger arrived?

Why is this?

- all the monks KNOW that nobody new gets the disease?
Never stated. If this had been the case I'm sure the original puzzle which isn't mine obviously would have done so too? but meh...

- 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? Has to be this way
- 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.

All but the first two yes.

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.

I must admit I presented the idea after seeing the solution, I assumed it was the only solution, maybe I was wrong, I would be more than happy to see where?

Um. What?

DaveE

Incubation period, the time in which a disease lays dormant,ie no symptoms present themselves, look it up. This why the simultaneity idea can flounder.

The reason why given this experiment it works because no matter how many monks after the first day it always takes x amount of days for them to figure out they are infected.

A problem with more than one monk being infected is that on the day before last, if you have a situation where all monks have died, and no new monk is infected or two, then one will not die on the last day. Thus the one monk per day infection is a better solution. Although given what you say I would accept others, but again they are conditional. With the one and one situation the monks always have a dead body on the last day at least, assuming their logic is intact and the remaining monks see this pattern of 1 and 1 on every day

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.

That's because you have made a faulty assumption,a) it's not certain that only the first ten are infected or however many,b) I don't make this assertion anywhere but the solution does deal with it.

If you stipulate that one monk is infected after each meal and one dies, then you lose this problem. If however it's possible to have no monks die at any point, you're screwed over, 10 monks die on the 11th meal, then none at all again.

As soon as the monks work out 1 of them per day is infected, they will die on the requisite days to keep the score anyway.But I didn't go this deep, I only state the answer. I think it's the most complete and unconditional answer, if it's wrong then show me where, that's all part of the fun anyway right personally I'm not a huge fan of 2 dimensional problems, if there are dimensions I haven't considered then great.

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davee123 said:
That's true. He's assuming that:

- nobody new gets infected with the disease after the time the messenger arrived?
Why is this?

Because if you don't, the puzzle falls apart and is unsolvable, without even more wildly inappropriate assumptions. The problem is solveable if you assume that that nobody new gets infected.

However, if you assume that new people become infected, then the problem is unsolveable. Well, ok, unsolvable without making even grosser assumptions such as "the messenger comes back and tells them that someone's still infected" or something.

Never stated. If this had been the case I'm sure the original puzzle which isn't mine obviously would have done so too? but meh...

Ok, there's a problem. You're assuming that the puzzle writer is competant. In my experience, people who post word puzzles online are generally incompetant. Even when you see it in print in a word-puzzle book, there's a good chance they're not stating ALL their assumptions.

By and large, that's because the amount of assumptions you have to make is so vast that it's not worth the bother of trying to state them all. Notice that if you were actually quoting the original puzzle, you made a mistake that I corrected right off the bat-- that the messenger has to tell them a CRITICAL piece of information, which is that at least one of the monks is infected.

Also notice the seven assumptions that I posted (which are probably just SOME of the loopholes we can all dream up), which are ALSO not stated, but are necessary for solving the problem uniquely.

I must admit I presented the idea after seeing the solution, I assumed it was the only solution, maybe I was wrong, I would be more than happy to see where?

Well, see my last post. If no new monks are infected, the problem is solveable. Or re-read what Hurkyl posted prior to me. You can also search the forum history for things like "monk" and you'll probably find more re-statements of the puzzle and the solution. I know I've seen it here before at least once.

However, if new monks might be infected arbitrarily, it ruins everything. Monks are no longer able to tell with any certainty the starting point at which to count new infections in terms of number of days, partly because they know that no monk can see themselves, and each monk's status might have changed at any point, or never changed.

I don't understand how you seem to think that the problem is solveable if new monks get infected, but I'm interested in hearing why you think this is so, so we can clear things up.

Incubation period, the time in which a disease lays dormant,ie no symptoms present themselves, look it up. This why the simultaneity idea can flounder.

Yes, I know what an incubation period is, and I understand that a majority of diseases have them, but I fail to understand why you think *all* diseases have them with periods of 1 day or more (and not less than 1 day) and why you would assume that this necessarily affects the problem. It adds unnecessary complexity to the problem and makes it unsolveable. So, why assume it? The problem doesn't explicitly say that new monks will be infected, and it doesn't say anything about an incubation period-- why make that assumption?

Oh yeah-- look at the problem again, too. Notice how it says that the disease isn't contagious? Now, if the problem were still solveable if new monks are infected, why bother saying that it's not contagious? Wouldn't that be an unnecessary statement on behalf of the puzzle writer? The very clear message that I get from that statement is "nobody new gets the disease".

In general, this is why you need to choose your word problems EXTRAORDINARILY carefully. This particular statement of the problem is stupid, because it's talking about a disease, which is spreadable, has incubation periods, can be counteracted by antibodies, or whatever. One of the better restatements of the problem is blue-eyed vs brown-eyed monks. In this version:

A group of monks live in a monestary where no communication whatsoever is allowed. Furthermore, no reflective surfaces are allowed, so no monk is able to see himself. Also, each monk who knows they have blue eyes is sworn to kill himself at midnight on the day he discovers that it is true of himself. And the monks have perfect logic ability. Also, the monks gather once a day to embrace each other (so they all see every other monk every day). One day, a visitor comes to the monestary, and spends a few hours with the monks. Upon leaving, the visitor addresses all the monks of the monestary, and tells them in passing that while there, he noticed a monk with blue eyes. 12 days later, a group of monks kill themselves at midnight. How many died?

Actually, that's not quite true. Usually, the problem tells you exactly how many days took place, and exactly how many died, but asks you why they died, or how they knew they had blue eyes.

Now, that's a bit better statement of the problem, because eye color doesn't change, unlike being infected with a disease, which may or may not change with time. So it's a little bit less error-prone in interpretation.

DaveE

Because if you don't, the puzzle falls apart and is unsolvable, without even more wildly inappropriate assumptions. The problem is solveable if you assume that that nobody new gets infected.

However, if you assume that new people become infected, then the problem is unsolveable. Well, ok, unsolvable without making even grosser assumptions such as "the messenger comes back and tells them that someone's still infected" or something.

Ok, there's a problem. You're assuming that the puzzle writer is competant. In my experience, people who post word puzzles online are generally incompetant. Even when you see it in print in a word-puzzle book, there's a good chance they're not stating ALL their assumptions.

By and large, that's because the amount of assumptions you have to make is so vast that it's not worth the bother of trying to state them all. Notice that if you were actually quoting the original puzzle, you made a mistake that I corrected right off the bat-- that the messenger has to tell them a CRITICAL piece of information, which is that at least one of the monks is infected.

Also notice the seven assumptions that I posted (which are probably just SOME of the loopholes we can all dream up), which are ALSO not stated, but are necessary for solving the problem uniquely.

Well, see my last post. If no new monks are infected, the problem is solveable. Or re-read what Hurkyl posted prior to me. You can also search the forum history for things like "monk" and you'll probably find more re-statements of the puzzle and the solution. I know I've seen it here before at least once.

However, if new monks might be infected arbitrarily, it ruins everything. Monks are no longer able to tell with any certainty the starting point at which to count new infections in terms of number of days, partly because they know that no monk can see themselves, and each monk's status might have changed at any point, or never changed.

I don't understand how you seem to think that the problem is solveable if new monks get infected, but I'm interested in hearing why you think this is so, so we can clear things up.

Yes, I know what an incubation period is, and I understand that a majority of diseases have them, but I fail to understand why you think *all* diseases have them with periods of 1 day or more (and not less than 1 day) and why you would assume that this necessarily affects the problem. It adds unnecessary complexity to the problem and makes it unsolveable. So, why assume it? The problem doesn't explicitly say that new monks will be infected, and it doesn't say anything about an incubation period-- why make that assumption?

Oh yeah-- look at the problem again, too. Notice how it says that the disease isn't contagious? Now, if the problem were still solveable if new monks are infected, why bother saying that it's not contagious? Wouldn't that be an unnecessary statement on behalf of the puzzle writer? The very clear message that I get from that statement is "nobody new gets the disease".

In general, this is why you need to choose your word problems EXTRAORDINARILY carefully. This particular statement of the problem is stupid, because it's talking about a disease, which is spreadable, has incubation periods, can be counteracted by antibodies, or whatever. One of the better restatements of the problem is blue-eyed vs brown-eyed monks. In this version:

A group of monks live in a monestary where no communication whatsoever is allowed. Furthermore, no reflective surfaces are allowed, so no monk is able to see himself. Also, each monk who knows they have blue eyes is sworn to kill himself at midnight on the day he discovers that it is true of himself. And the monks have perfect logic ability. Also, the monks gather once a day to embrace each other (so they all see every other monk every day). One day, a visitor comes to the monestary, and spends a few hours with the monks. Upon leaving, the visitor addresses all the monks of the monestary, and tells them in passing that while there, he noticed a monk with blue eyes. 12 days later, a group of monks kill themselves at midnight. How many died?

Actually, that's not quite true. Usually, the problem tells you exactly how many days took place, and exactly how many died, but asks you why they died, or how they knew they had blue eyes.

Now, that's a bit better statement of the problem, because eye color doesn't change, unlike being infected with a disease, which may or may not change with time. So it's a little bit less error-prone in interpretation.

DaveE

One question, does the solution given solve the problem given my criteria, and I admitted my fault, why bring that up? Your assumptions?

Nothing else matters.

If we accept the solution as the only one? Is there another, really don't need to get bent out of shape about this, it isn't my problem and I would genuinely like to see if there is another solution? Sorry if that's a problem. Again I am reminded of the last one where I presented a solution and you felt the need to go on for pages and pages about x and y that aren't specified? Now if you have indeed pulled out the flaws with this solution, I'd be happy to see them. I haven't yet.

Again your unavoidably assuming that given the criteria the original solution fails because you say it does, and because you've made up new ideas? I never claimed it was 100% correct only that someone else did, but apparently this is a faux pas. We have to invent new ways to get round the only solution, if so what are they? Again I feel I'm getting more out of this than you, but that's possibly because you wont accept the criteria. Please quote my post and the original solution and show how it is wrong, 1 day I never said I said 1 to x days, x is in days the original constant is in? But what does it matter you're nitpicking.

The onus is on you to prove your solution correct given my criteria and the solution I present(or the aholes who gave it as the solution as wrong) I aint gonna go round searching for anything until you do it. Think about it.

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Hurkyl
Staff Emeritus
Science Advisor
Gold Member
You haven't presented a solution. You've asserted an answer, but have given no justification for it.

You haven't presented a solution. You've asserted an answer, but have given no justification for it.

Er I have, considering the fact that your reading all sorts of x into y, I think I've pretty much done that, now explain how your mistaken assumptions would actually work given that, they aren't viable? hehe this is great thanks fellas explain how any of your solutions would work, given the fact that you've basically used sophistry? As I said before: now you know the criteria explain how your solutions work, given they don't. If not then why should I respond?:tongue2:

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One question, does the solution given solve the problem given my criteria? And not your assumptions?

Wait, what solution? My solution does, I don't see how yours does.

For starters, why do you say that 2 monks die on the first day? And why does another one die on the 2nd day? And after which meals do they die? What is the reasoning of the first two monks who kill themselves, and that of the 3rd monk that dies? How do they successfully deduce that they each have the disease, and how many monks are infected at each stage, given that you seem to be claiming that that state changes?

I guess-- here's one thing I'd like to see: Make me a little table that shows how many monks you're saying are infected at each mealtime. Something like this:

Meal 1: Monks infected: 2 Monks who learn they are infected: 0
Meal 2: Monks infected: 2 Monks who learn they are infected: 2
2 monks die.
Meal 3: Monks infected: 1 Monks who learn they are infected: 0
Meal 4: Monks infected: 1 Monks who learn they are infected: 1
1 monk dies.
Meal 5: Monks infected: 0 Monks who learn they are infected: 0
Meal 6: Monks infected: 3 Monks who learn they are infected: 0
Meal 7: Monks infected: 3 Monks who learn they are infected: 0
Meal 8: Monks infected: 4 Monks who learn they are infected: 4
4 monks die.
etc.

Again I am reminded of the last one where I presented a solution and you felt the need to go on for pages and pages about x and y that aren't specified?

The truth is I want us both to be on the same page here. From what I can see, you posted a solution that was incorrect, and I'm not sure where you went astray. I'm interested in hearing you explain your position so that I can help clarify the point. And if I AM making a mistake in my assumptions, I'd like to know how and why. If that takes pages and pages, I'm fine with that. Understanding is worth taking time.

Again your unavoidably assuming that given the criteria the original solution fails because you say it does, and because you've made up new ideas?

I'm saying there are multiple ways of stating the same problem, and some are better than others. In this instance, I very strongly believe that there's a particular logical method which is attempting to be demonstrated. I can explain that point in very abstract terms, if desired, but it's boring. So usually we like to dress these up as word problems. Hypothetical situations which are interesting to us because there are people and things involved we can relate to. But as soon as you make that leap from purely logical to "realistic", assumptions of all kinds jump out and haunt you.

For example: In your original problem, you did not explictly state that the disease does not infect anyone else. So, I'm *forced* to assume something. I can assume that the disease does not infect anyone else, or I can assume that it MIGHT infect someone else. Either way, it's an assumption. I utterly HAVE to assume something. And it's pretty unclear which way I should assume things! However, the clue about the disease not being contagious tells me that the author *probably* intended to clarify my assumption by stating that nobody else is infected.

If you'd like to dispute which assumptions are acceptable and which aren't, that's fine, and we can even talk about what other solutions might present themselves if we make other assumptions. But it gets really sticky when we *don't know* what the other person's assumptions are.

Please quote my post and the original solution and show how it is wrong,

Heh, alright, I'll try. But keep in mind that 90% of my problem is that I don't understand what your solution is! You may do better not to even read this, but here goes:

===================================================
BEGIN POST SNIPPIT OF SOLUTION
===================================================

Schrodinger's Dog said:
Assuming that the only time the monks can be sure that they have it is if only one monk has it

This is wrong, because, as I showed, if only two monks are infected, they are capable of discovering at the 2nd meal that they are infected. Each monk knows that there is at least one monk with the disease, and each monk has seen one monk with the disease. If they had NOT seen any monks with the disease, they would know they were infected. If that had been the case, the monk they were looking at would have died. Quite clearly, that has not happened, and so they realize that it was NOT the case that ONLY the other monk was infected. Therefore, they know that the only other possibility is that THEY are infected.

Schrodinger's Dog said:
ergo he dies on the second meal. We then say one more has it

Ok, clarification please. "One more has it"? One more has it when? After the 2nd meal? On the very first day? Has the other monk you just mentioned died, or not?

Schrodinger's Dog said:
and one monk is dead and so on untill the 11th day after the messenger arrived.

You appear to be suggesting that the only way for monks to die is if they are, at any time, the only monk to have the disease. Hence, you appear to be stating that in between EACH meal, one monk dies, and one new monk becomes infected. This is clearly wrong, because after the first monk(s) die, the remaining monks are not assured again that at least one monk is still infected.

Schrodinger's Dog said:
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,

This is actually correct!

Schrodinger's Dog said:
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.

While possible if assuming that the disease can infect new people, the remaining monks have lost their valueable piece of knowledge that at least one monk is infected, and therefore will be unable to make any conclusions after the number of monks infected begins to change, or after any infected monks die.

Schrodinger's Dog said:
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.

Again, this is not possible, because as soon as a single monk dies who was infected, the remaining monks are deprived of the information they had. Part of their information derives from the fact that known infected monks are somehow not killing themselves, and the REASON they're not killing themselves is due to what they can observe. If they can no longer relay that information, the remaining monks' information source is drained.

Schrodinger's Dog said:
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.

Ok, so, you just sort of solved the problem, but dismissed it due to its being unlikely?

Schrodinger's Dog said:
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.

Again, this solution is unclear. Days are rather irrelevant-- only meals are particularly relevant. Which meals for which days do you mean?

Also, this is incorrect. If one dies on the morning of the 11th day, that would have to be *AFTER* breakfast (because if they died from knowing, it would have had to have been after DINNER, which would be in the evening of the 10th day), and the question quite clearly stipulates that the monks do not appear for breakfast on the 11th day, so they are already dead, making the total be 32 instead of 33.

Schrodinger's Dog said:
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,

Ok, that's correct, but ONLY if no other monks have died yet, and no new monks have been infected. If new monks have been infected, or if other monks have died, they CANNOT realize they have it.

Schrodinger's Dog said:
and you have to assume no one else gets it. Otherwise the system is screwed

Wait, why is it screwed at this point, instead of earlier?

===================================================
END POST SNIPPIT OF SOLUTION
===================================================

Schrodinger's Dog said:
The onus is on you to prove your solution correct given my criteria and the solution I present as wrong, I aint gonna go round searching for anything until you do it. Think about it.

Done.

But I fail to see why the onus isn't on whoever wants to do the understanding. If you want to understand where the disagreement is, the onus is on you to try and understand it-- ask questions, make points, whatever. If you don't care about understanding, then you can do whatever you want. But if you geninuely want to understand, you'll try and put some effort in.

DaveE

Your assuming the monks who cannot possibly know don't figure out the pattern 1 on 1, anyway, I haven't the time to address your questions. anon.

I'll try and think about it on the morrow. You still haven't answered how you can with no ability to predetermine a causal pattern in the disease, or otherwise having no prognosis determine your answer is right.

Suffice to say I think we're getting somewhere here, maybe the aholes who presented the problem are indeed wrong, and by default so am I, frankly I'd be happier with not being right than being right. Not my problem but no time to consider it, hope we're all having fun.

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
For example, suppose only one monk displayed symptoms at the beginning. He dies two hours after the first meal.

You then assert:

We then say one more has it and one monk is dead​

but you give no reason why we can say another one has become infected, nor have you given a reason why that monk can determine he is infected.

Put yourself in the monk's place: you saw one red spot at the first meal. At the next meal, you found out he has died, and you see no other red spots. What can you possibly glean from this information to distinguish between the case that nobody has the disease during the second meal and the case that you have the disease during the second meal?

The classical solution, which still works with a spreading disease, is a simple inductive argument on the number of meals.

At the N-th meal, if M people displayed symptoms at the beginning, exactly one of the following is true:
(1) M < N, and all of the people who displayed symptoms at the beginning have died, and nobody else has died.
(2) M = N, nobody has died yet, but all of the people who displayed symptoms at the beginning will die in two hours.
(3) M > N, nobody has died, and nobody will die before the next meal.

The base case is obvious. The inductive step is straightforward: each monk (who saw that k other monks had a red spot at the beginning) considers whether the following hypotheses are consistent with his observation:

(1) I am infected
(2) I am not infected

And it's easy to see from the inductive hypothesis that the only time that (1) is consistent with observation and (2) is inconsistent with observation is if k = N-1, and nobody has died yet.

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For example, suppose only one monk displayed symptoms at the beginning. He dies two hours after the first meal.

You then assert:

We then say one more has it and one monk is dead​

but you give no reason why we can say another one has become infected, nor have you given a reason why that monk can determine he is infected.

Put yourself in the monk's place: you saw one red spot at the first meal. At the next meal, you found out he has died, and you see no other red spots. What can you possibly glean from this information to distinguish between the case that nobody has the disease during the second meal and the case that you have the disease during the second meal?

The classical solution, which still works with a spreading disease, is a simple inductive argument on the number of meals.

At the N-th meal, if M people displayed symptoms at the beginning, exactly one of the following is true:
(1) M < N, and all of the people who displayed symptoms at the beginning have died, and nobody else has died.
(2) M = N, nobody has died yet, but all of the people who displayed symptoms at the beginning will die in two hours.
(3) M > N, nobody has died, and nobody will die before the next meal.

The base case is obvious. The inductive step is straightforward: each monk (who saw that k other monks had a red spot at the beginning) considers whether the following hypotheses are consistent with his observation:

(1) I am infected
(2) I am not infected

And it's easy to see from the inductive hypothesis that the only time that (1) is consistent with observation and (2) is inconsistent with observation is if k = N-1, and nobody has died yet.

To be honest I've kind of given up on this, it's obvious that the problem although not mine is deeply falwed and the answer given by the particular web site is completely wrong. Let's just leave it at that, I really don't know why they have specified that as the answer.

I have suposed this is because given there are 1-34 number of monks present with systems on the first day and then x for the next few days, ie there is no reason to assume they all have the symptoms on the first day, if this is the case then the only solution I can see is if the monks use the counting method, but this doesn't gel with the answer. So I guess either the problem is deeply falwed, or there is something missing from the presented problem, either way there's obviously something wrong here so I suggest we just forget about it, I was misnformed by some dubious web site.

To be honest I've kind of given up on this, it's obvious that the problem although not mine is deeply falwed and the answer given by the particular web site is completely wrong. Let's just leave it at that, I really don't know why they have specified that as the answer.

Could you perhaps post a link to the place where you found it? As it is, the problem isn't deeply flawed, it's just badly worded. And it's not without a solution-- it just kind of sounds like your interpretation of the answer isn't quite right.

DaveE