Can someone help me with this question please?

[Award Winning Boss]

Here's a logic question... I hate it.

You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.

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

You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.

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

I think it's something to do with patterns.

Edited May 9, 2012 by Award Winning Boss

[aldld]

The answer is 10.

In short, if you have a set S of slaves and a set W of bottles of wine, you can look at the pattern of deaths resulting from some subset of S testing a bottle of wine (if I remember correctly). If there are n slaves, there are 2^n possible subsets of S with which to associate with a bottle of wine. The smallest number of slaves that works is n = 10, with 2^10 = 1024.

Somebody from my school actually did their EE on this problem, actually worked on extending this problem.

[Award Winning Boss]

The answer is 10.

In short, if you have a set S of slaves and a set W of bottles of wine, you can look at the pattern of deaths resulting from some subset of S testing a bottle of wine (if I remember correctly). If there are n slaves, there are 2^n possible subsets of S with which to associate with a bottle of wine. The smallest number of slaves that works is n = 10, with 2^10 = 1024.

Somebody from my school actually did their EE on this problem, actually worked on extending this problem.

I've seen the answer as 8. But I do not understand what you said. Can you explain further please?

[HiggsHunter]

Yes, a minimum of 10 prisoners have to drink from up to 1024 binary coded wine bottles to identify which one is poisoned.

But there are only 1000 bottles. So you can prevent one possible death by avoiding the binary code for which all the prisoners must drink the wine, and a second possible death by avoiding each of the 10 codes for which 9 of the prisoners have to drink. So that means that the ruler can identify the poisoned bottle by the deaths of no more than 8 prisoners.