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Emperor, wines, and accomplice- with a nod to meciless emperor


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14 replies to this topic

#1 bushindo

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Posted 26 July 2012 - 11:00 PM

This is a variant of ujjagrawal's excellent puzzle Merciless emperor.

Suppose that like ujjagrawal's puzzle, an assassin infiltrates a king's cellar and poisons 1 of the king's 500 wine bottles. Upon being detected and cornered, the assassin takes a suicide pill and dies.

Anyone who consumes even the most minute amount of the poisoned wine will die between 12 and 24 hours. Consumers of the poisoned wine exhibit no other symptom besides death, and the poison can not be detected by any other means.

The emperor decides to use some prisoners to taste the wine in order to determine the poisoned bottle. There is one catch, however. It is known that the assassin has precisely one accomplice among the prisoners. The accomplice has access to the same poison that the deceased assassin used to envenom one of the king's bottle. If the accomplice is chosen as one of the tasters, he will surreptitiously consume the poison regardless of which bottle he is given to drink in the hope of corrupting the deduction process.

The emperor does not know which of his prisoners is the assassin's accomplice. The emperor is intrigued by this logical puzzle, and he figures that he can simply use some extra prisoners to compensate for this unknown unreliable taster. What is the minimum number of prisoners (and the tasting procedure) that he would need to use in order to correctly find the poisoned bottle among the 500 bottles within 24 hours?
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#2 jim

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Posted 27 July 2012 - 12:13 AM

You can do it with 18. In place of each prisoner in the solution to the previous problem, use a pair. It counts as dying only if both prisoners die--otherwise it counts as survival. Now do as before. It may be possible to do with less than 18, but i would not no how.
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#3 phaze

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Posted 27 July 2012 - 01:57 AM

In any circumstance will the accomplice not take poison to pevert the decision making process?

Edited by phaze, 27 July 2012 - 01:57 AM.

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Perfecting Mafia suicide since August 2008

#4 TheChad08

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Posted 27 July 2012 - 02:04 AM

You can do it with 18. In place of each prisoner in the solution to the previous problem, use a pair. It counts as dying only if both prisoners die--otherwise it counts as survival. Now do as before. It may be possible to do with less than 18, but i would not no how.

So he will drink the poison no matter what?
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#5 bushindo

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Posted 27 July 2012 - 02:08 AM

You can do it with 18. In place of each prisoner in the solution to the previous problem, use a pair. It counts as dying only if both prisoners die--otherwise it counts as survival. Now do as before. It may be possible to do with less than 18, but i would not no how.


That's a good start. It is possible to require a few prisoners less than that though.

In any circumstance will the accomplice not take poison to pevert the decision making process?


If selected as a taster, the accomplice will definitely commit suicide by drinking his own supply of poison. However, keep in mind that the emperor has many prisoners, and in the random selection procedure it is very possible that the accomplice is not chosen as a taster.
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#6 phaze

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Posted 27 July 2012 - 03:39 AM

Spoiler for


Edit:
Spoiler for

Edited by phaze, 27 July 2012 - 03:43 AM.

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#7 bushindo

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Posted 27 July 2012 - 03:56 AM

Spoiler for


Edit:
Spoiler for


I'll just note that the intent of the puzzle is that all prisoners have to sample the wine at the same time. Since the deadline is 24 hours and the poison will take effect randomly between 12 and 24 hours after consumption, it is not possible to wait and see the effects of one wave of wine drinking before applying another.
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#8 bonanova

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Posted 27 July 2012 - 04:18 AM

Spoiler for looks like

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#9 bushindo

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Posted 27 July 2012 - 06:22 AM

Spoiler for looks like



All correct there, except for one detail
Spoiler for detail


The emperor would also like to request more details on this drinking scheme for the sake of completeness. You see, back in college the emperor majored in Political Science, which does not require any course in Computer Science, so concrete details on how to go about doing it would be very much appreciated.
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#10 phil1882

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Posted 27 July 2012 - 04:21 PM

i believe i can do it with 13.
Spoiler for tastes good

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