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# A merciless emperor

12 replies to this topic

### #1 ujjagrawal

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Posted 26 July 2012 - 09:26 AM

There's a merciless emperor who has 500 bottles of very expensive wine in his cellar.

An assassin infiltrates the wine cellar to poison the wine. Fortunately the emperor’s guards catch the plotter after she has poisoned only one bottle. Unfortunately, the guards don’t know which one of the bottles is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

The emperor decides he will get some of the prisoners in his dungeons to test the wine as he has handful of them about to be executed.

What is the smallest number of prisoners that must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
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### #2 bonanova

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Posted 26 July 2012 - 10:41 AM

Spoiler for first guess

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #3 David_Walker

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Posted 26 July 2012 - 11:08 AM

Spoiler for My thoughts...

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### #4 jim

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Posted 26 July 2012 - 12:20 PM

bonanova would be correct if there were 1000 bottles.
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### #5 MikeD

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Posted 26 July 2012 - 12:45 PM

Spoiler for my try

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hi again, everyone. Nice to be back home.

### #6 bonanova

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Posted 26 July 2012 - 02:06 PM

bonanova would be correct if there were 1000 bottles.

Being an engineer and not a mathematician, I built in some redundancy.
And next puzzle I solve, I'll wear my glasses.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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Posted 26 July 2012 - 04:30 PM

Spoiler for my try

Spoiler for

Edited by TheChad08, 26 July 2012 - 04:31 PM.

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### #8 MikeD

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Posted 26 July 2012 - 04:43 PM

Spoiler for

I think you missed one, 511 bottles were tested, leaving one remaining one. So 512 bottle could have been tested.
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hi again, everyone. Nice to be back home.

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Posted 26 July 2012 - 05:36 PM

I think you missed one, 511 bottles were tested, leaving one remaining one. So 512 bottle could have been tested.

You're right.
I didn't add the 9 choose 9.

It is 512.

You're still right, I just tried to show it in a less convoluted way.
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### #10 jim

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Posted 26 July 2012 - 08:13 PM

bonanova As a math teacher I considered your solution to be correct except for one minor detail. As far as I am concerned you are the one who solved the problem.
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