Yeah, I forgot the king. I was wondering if there was one, but I forgot to check into it. Anyways, you should only need to test on 10 people if you intend to get them fairly drunk.
And perhaps you should fine tune the question before I bother spending any more time on it.
Oh, and I went to try and post and answer only to realize it was the wrong thread. Damn you two for confusing me! <_<
Reposted:
Well, I was down to 37 bottles in what I'd said earlier. You can further reduce that by dividing the wine bottles into 6 groups, 5 groups of 6 and 1 group of 7? and have each of the 5 servants taste all the bottles in one group (leave one group out, probably the group of 7). That would reduce the number of bottles left to check down to 6 with one death, or 7 with no deaths (if the group of 7 bottles is the one not tasted). At this point, 3 servants must return, and 5 days are left. If you have one servant to test on and 6 possible bottles... I don't really know. Doesn't seem like there is enough time left to test them all in 5 days, and ensure that you've killed him off. Similar case for having 7 bottles left with 2 people to test them.
So, maybe up the risk of losing two people at once? Instead of having each person taste all the bottles in 1 group, they might share bottles between groups. If both people die, you can't do any more testing, so perhaps 1 bottle shared from each group with two people. If they both die, you know the bottle. If only one of them dies, you now have it down to 5 bottles, with 5 days left and 1 tester. If noone dies, we again have 7 bottles, 2 testers, and 5 days. Same problem as before.
Ok, so that leads me to think maybe the 3 people returning and 2 servants have died just happens to be an outcome in a test where more death was possible (and hence moer information could be determined). So 5 people, consider them the bits of a binary number and label the remaining bottles. Then a variable number of people would die in determining if 32 of the 37 bottles had poison. But, you'd still have tasters left no matter what. I suppose they could be used on the remaining bottles, but it would seem to be a problem if people died after you sent them back, so there is a 2 day period in which people you may want to send back can't taste anything. But, if they were poisoned earlier, then they'll die by the time you send them back, so meh. Next day just do another round with fewer people. 5 bottles left, tested on 3 people in the same binary fashion. The thing is, you could end up killing off all 5 people this way. (If bottle #31 is poisoned).
Or just hand out all 37 bottles in that last round. If it is one of the ones at or above #32, then you'll still have the upper bit people left alive to test the remaining bottles where there is ambiguity. It would be 1 of 2 bottles in that case, and you have at least 1 person left alive. If the upper bit person dies, then for sure there is no ambiguity as to what bottle is poisoned after the first round.
Ahh yeah, that last idea seems to work, but you won't be guaranteed to be sending 3 servants back. Ahh well, sucks to be a servant. :lol:
