[Guest]

In a far away land, there is a king who is known for throwing huge banquettes. The largest banquette of the year was coming up and the king spent weeks gathering 1000 casks of very expensive wine for the celebration. Exactly 5 days before the party, a peasant who hated the king snuck into the wine cellar of the palace and poisoned one of the casks. The guards caught him as he was fleeing, but they never saw which casks he poisoned and it is impossible to tell just from looking which casks was poisoned.

The king does not want to cancel the banquette but there is not enough time to replace all the casks. The poison is designed to be incredibly powerful and even if diluted 10,000,000 times it is still lethal. It is also designed so that it doesn't kill immediately, rather the victim dies 3 days after drinking it. The king decides he will use prisoners to test the wine. Now if he had 1000 prisoners it would be easy, just have one prisoner drink from each and see who dies 3 days later. But the king doesn't quite have 1000 prisoners.

What is fewest number of prisoners needed to figure out exactly which cask contains the poison, and have the other 999 ready for the banquette?

[akaslickster]

ZERO.

[Guest]

Just one. Does the person taking the wine die EXACTLY in 3 days, as in, if he took it at 3:00 on monday, he dies at 3:00 on thursday? If that's the case, you could have him drink samples from all of the caskets, and mark down at what time he drank them. When he dies exactly three days later, you would know what casket to dump. If that's not the case.... Well, then I'll still have quite a bit of work ahead of me....

Good riddle, by the way.

[Guest]

Good riddle, by the way.

Just one. Does the person taking the wine die EXACTLY in 3 days, as in, if he took it at 3:00 on monday, he dies at 3:00 on thursday? If that's the case, you could have him drink samples from all of the caskets, and mark down at what time he drank them. When he dies exactly three days later, you would know what casket to dump. If that's not the case.... Well, then I'll still have quite a bit of work ahead of me....

i didnt think of that but lets say its not quite exactly 3 days

[Guest]

Assuming that the person who drinks poison dies not before 48 hrs and not later than 72 hrs!!

Now take A,B,C,D,E as 5 days, where banquet is on the eve of E. Also number the prisoners as 1-333. And number the casks from 1-1000, where each day 333 casks would be consumed.

The king can have 333 prisoners to take wine on A day, so the contaminated wine would show reaction by C day. Then the same prisoners would be numbered from 334-666 n they would drink from next set of 333 wine casks on day B, whose reaction would be on day D. Similar on day C, which would show reaction at max early morning of dat E!!! If no one dies, the remaining one cask is poisoned. Else if the one prisoner who dies, the cask can be found by the day (from C,D,E) & prisoner number who has died(e.g. if prisoner number 566 dies on day D, then cask 556 is the poisoned!!)

Hence the visitors can enjoy the banquet which surely would have been planned for the 'E' night!!

N this way the 333 prisoners can make party for the first 3 days!!

[Guest]

10? Mark each person 1-10. 1 drinks from cask 1, 2 drinks from cask 2, both 2 and 1 drink from cask 3, 3 drinks from cask 4.. and so on. Basically convert each cask number to binary (1->1, 2->10, 3->11, 4->100 and so on). Find out who all have died after 3 days, and convert the resultant number combination back to decimal, that should give you the poisoned cask. Makes sense?

[Guest]

10? Mark each person 1-10. 1 drinks from cask 1, 2 drinks from cask 2, both 2 and 1 drink from cask 3, 3 drinks from cask 4.. and so on. Basically convert each cask number to binary (1->1, 2->10, 3->11, 4->100 and so on). Find out who all have died after 3 days, and convert the resultant number combination back to decimal, that should give you the poisoned cask. Makes sense?

correct!

[Guest]

10? Mark each person 1-10. 1 drinks from cask 1, 2 drinks from cask 2, both 2 and 1 drink from cask 3, 3 drinks from cask 4.. and so on. Basically convert each cask number to binary (1->1, 2->10, 3->11, 4->100 and so on). Find out who all have died after 3 days, and convert the resultant number combination back to decimal, that should give you the poisoned cask. Makes sense?

You can do it with 8. 3 days means you can run the experiment 3 times on 333 barrels. 2^8 gives you 512 results.