# Game Theory: Tough Puzzle

**URL:** <https://boards.straightdope.com/t/game-theory-tough-puzzle/264532>\
**Category:** Factual Questions\
**Created:** [September 15, 2004, 9:11am UTC](https://boards.straightdope.com/t/game-theory-tough-puzzle/264532 "2004-09-15T09:11:55Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![JKilez](https://avatars.discourse-cdn.com/v4/letter/j/e5b9ba/32.png) [@JKilez](https://boards.straightdope.com/u/JKilez)\
**Post date:** [September 16, 2004, 1:28am UTC](https://boards.straightdope.com/t/game-theory-tough-puzzle/264532/21 "2004-09-16T01:28:34Z")

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The solution that **PVirtanen** and **Chronos** provide makes sense as far as I can see.

On day X, if a monk sees X-1 other monks infected, he would know that he too is infected and should kill himself. On day X+1, there is no plague.

The “you are a writer” bit appears to be there to justify the one piece of knowledge that is given to the monks–that at least one of them has the plague. We are also making the assumuption that these monks are a logical order.

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**Author:** ![Trunk](https://avatars.discourse-cdn.com/v4/letter/t/87869e/32.png) [@Trunk](https://boards.straightdope.com/u/Trunk)\
**Post date:** [September 16, 2004, 1:55pm UTC](https://boards.straightdope.com/t/game-theory-tough-puzzle/264532/22 "2004-09-16T13:55:09Z")

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> [@SoulSearching](#):
>
> There is absolutely no form of communication between the monks, directly or indirecty. For instance, a monk who see another monk having the plague cannot and does not make a facial gesture, any form of ostacizing infected monks is also impossible. In short, a monk who is infected cannot determine if he is infected based on the behaviour of other monks. No communication.

The “communication” is the combination of

1. the knowledge that at least one monk has the disease
2. observing the other monks

If you want to be picky, interprety “no communication” as “the only communication is observing other monks”

> [@SoulSearching](#):
>
> To the poster who says that D = n^0, I am curious as to your conclusion as you are basically stating that D is 1. I am quite eager to solve this and rid the headaches it has caused. Maybe you could post the explanation under a spoiler warning so those who wish to still work on the problem may do so.

He was wrong.

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