This is a repost from two years ago. That post had become inundated with splogger comments, so I'm reposting it. I’ve taken the liberties (or perhaps you view it as an injustice if you are the original author) to rewrite a puzzle I once heard. I can find no reference to it online, so here goes.
Tale of the Diseased Monks
One Sunday evening after working in the fields, the secluded monks of the Kaetorsian order gathered for evening prayers. After the usual somber songs and pious prayers, the high priest said, “I have a grave announcement. It appears a horrible disease has fallen on our community this fine spring day. I know this because the disease results in a purple spot on your forehead, and I can see that some of you have this. From what I know of this most evil disease - you will remain unharmed for 14 days. After which, the disease will spread to others, and you will experience a most painful passing that may last months. If we are not careful, this disease will completely destroy our peaceful monastery. Therefore, I ask that those of you who have this spot to please remove yourself from our community immediately. I pray (for my sake!) that this matter will be resolved before these two weeks are over. Despite the fact that all of you have taken a vow of silence, and a vow of humility, and thus will not be able to inform one another of the forehead spot, and even though we lack mirrors and the lake is choppy and you are unable to see for yourself whether you have this spot, you are all trained highly in the ways of logic and will be able to deduce on your own whether or not you have become infected. In this way, we will carry on as we always have: working solitarily all morning and congregating here every evening to share in this holy life. Some of you would prefer that I simply point out those of you who are diseased and while I have not taken the vow of silence that you have taken, my vow of humility prevents me from calling attention to your dysfunctions. Good night”
The next few days passed as they always have. The monks that had been infected seemed as good natured as the others, and no one treated one another any differently. However, after more than a week, as the two week deadline approached, an air of nervousness crept in. The second Saturday after the high priest’s announcement was particularly tense. The next day marked the two week deadline before the disease was to spread again, and the diseased monks were still working and praying along side the healthy ones. After the congregation disbanded from the Saturday evening prayers, the monks returned to their private quarters. On Sunday, two weeks after the high priest announcement, all of the diseased monks were gone. Through their highly tuned logic skills, they were able to determine that they had been affected and sacrificed themselves for the good of the monastery.
How many monks were infected (the actual number, please)? And how did they determine it?
My only hint is the following. What would you notice if you were the only one infected?
13 comments:
Very interesting puzzle. I've love to know the solution
Okay, I'll add something. If you were part of this conflict and you saw no mark on anyone's head, you would deduce that you were the only one infected, and you had a duty to 'off' yourself immediately. Now, if you were one of the others and saw this person with the mark - what would it mean if they didn't kill themselves immediately. Well, it'd mean that they saw the mark on someone else (that someone being you)!
Okay, I realized a subtle point that made the puzzle confusing. I've rewritten a small bit - but not telling which part. :)
Interesting Puzzle..!
Is the answer 7?
very close. you probably have the logic correct. I suppose I was trying to hint the cycle repeated quicker than every other day but...
My logic was that if I (a monk) see the same number of people infected for 2 consecutive days then I am infected and would kill myself. Am I heading in the right direction?
Please ignore my previous email:
I think the answer is 5. The monk who leaves thinks what the rest of them are thinking. I worked it backwards by considering that 2 of them have to be infected on the 14th day for getting 0 infected on th 15th day. Working backwards we get 3 infected for 3 consecutive days, before one of them figures out that he is infected and so on.
So:
Days 1,2,3,4,5: 5 are infected
Days 6, 7, 8, 9: 4 are infected
Days 10, 11, 12: 3 are infected
Days 13, 14: 2 are infected
Day 15: 0
Now, you've confused me. You are making it more complicated than it needs to be. The answer is (#of days) = (# of infected monks)
my answer would be 14..as many as the number of days to pass on the dieases...
Logic being - if 1 monk is infected he would realize it the next day and would leave immdeiately..
if 2 are diseaseed the..both waite for 2 days until both realize and then leave...
carrying the same logic ahead...if all the diseased monks are to leave on the 15th day..14 monks should have been diseased...
its 105...right?
15 monks
the answer can be explained comfortably using mathematical induction
fact:infected monks leave on the
14th day
suppose only 1 monk was infected
now dis man wud not see anyone with a mark and wud leave immediately after the speech..
if 2 were infected
they would wait for 1 day and then would realize they can see only 1 with a mark
both would know that there are 2 men and thus other must be he/she himself
they woul leave on second day or 1st day after announcement...
thus 15 men at end of 14th day would leave
15 monks
the answer can be explained comfortably using mathematical induction
fact:infected monks leave on the
14th day
suppose only 1 monk was infected
now dis man wud not see anyone with a mark and wud leave immediately after the speech..
if 2 were infected
they would wait for 1 day and then would realize they can see only 1 with a mark
both would know that there are 2 men and thus other must be he/she himself
they woul leave on second day or 1st day after announcement...
thus 15 men at end of 14th day would leave
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