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# Poisoned Wine

## Question

I heard this puzzle the other day; sorry if it's been posted before.

You are the chief sommelier for a massive kingdom. The king wants to throw a banquet tomorrow, and as a result he's asked you to bring out all one thousand bottles of wine you have in the cellar. So you walk into the cellar when suddenly one of your assistants comes running up to you: "Boss! Boss! This is terrible! Someone's gone and put poison in the wine!" After calming him down a bit, you manage to squeeze some useful information out of him:

There is exactly one bottle of poisoned wine.

The poison is completely undetectable and fatal in any quantity.

The poison takes exactly one night to work, so that the next morning anyone who drank the poisoned wine will be found dead.

You rush off and tell the king. Naturally, he's very displeased: "If you can't separate that poisoned bottle from the 999 good ones, your head's gonna be on the chopping block!"

You lament, "But how can I find just the one bottle by tomorrow morning without any resources?"

The king relents, and tells you that he has ten criminals who have been sentenced to death. You may use them as guinea pigs to test the bottles of wine. Each criminal can test an unlimited number of bottles.

How can you find the one poisoned bottle in one thousand with just ten testers? Think quickly, or perhaps the wine won't be the only thing running red tomorrow...

## Recommended Posts

• 1

I think…

Spoiler

Each wine tester could take a small sip from a different half of the thousand bottles, in such a way that the poisoned bottle is uniquely specified by which of the ten testers are found dead the following morning.

For example, consider the bottles to be indexed from 0 to 999. This range would require ten binary digits (bits) to express. You could have Tester #1 sip from every bottle whose lowest bit is a "1", Tester #2 sip from every bottle whose second-lowest bit is a "1", and so on.

Edited by ThunderCloud

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Let number bottles from 1 to 1000

10 firt bottle are drinked by each crimals

45 bottles next art drinked by 10C2 group of criminals

...

So on..

=> actually, 10 criminals can find 1 poison bottle in 1024 bottles

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Yup, you both got it! I'm gonna mark Thundercloud as best answer since he was first by a couple of hours, but Aiemdao's answer is just as good and the one I had in mind (although I'm fairly sure both methods are identical).

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