Outpost Universe Forums
Off Topic => Test/Spam Forum => Forum Games => Topic started by: Eddy-B on November 30, 2005, 03:52:55 PM
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A king has 1000 bottles of wine. He drinks 1 bottle of wine each weekend. He always selects a new bottle every friday evening. A neighboring evil queen plots to kill the king, and sends a servant to poison the wine during that sunday, right after the king finished his bottle. The king's guards catch the servant after he has only poisoned one bottle. They put him in the dungeon, but the guards don't know which bottle was poisoned.
The kings alchemists tell him the poison could kill a man within three days. The king does not want to stop drinking his weekly wine, so he comes up with a brilliant plan. He throws a party the very next day, inviting the evil queen and her king. She shows up, bringing 25 of her best servants.
After three days, the queen informs the king that one of her servants died misteriously, and sends 5 of her servants to the king's castle to help in the investigation.
The next day (friday), the king was drinking his wine again, and right after the weekend, on monday morning, he sends back 3 of her servants, along with a note that the other servants she sent died.
By the end of the week, on saturday, he sends a bottle of "his best wine" to the queen, and a note stating he wants to settle the problems between their nations. Three days later, the wicked queen died, after drinking from the bottle of wine.
Now, how did he do this ?
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What's with the alcohol obsession lately?
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he poisoned the bottles himself
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no .. he found out which bottle was the poisoned one, and sent it to the queen.
now, you guys tell me how to do it, using the info & dates described above
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he only used x number of bottles for the party. Only a certain number of these were for servants. when one of the servants died, he set those bottles aside, knowing his main ammount were safe.
when the five servants came, he gave them each a different combination of different bottles The one the two had in common was the one sent to the queen
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Hmm, very interesting.
Well, he was drinking on Friday again, so I assume he knew of at least 1 bottle that wasn't poisoned. He probably didn't know which of the 25 servants died, only that 1 of them died. So, use the number of servants that die to somehow mark the bottles so you know at least one is safe, and hopefully gain a bunch of info about the other bottles. Now of the 5 servants that were sent, he should know which of the 2 died, so there is much better potential for gaining information on which bottle was poisoned here.
I'm a bit curious about the last part where he waited till the next week on a saturday. I'm guessing he made sure those 2 servants died while tasting bottles, but not necesarily before he told her they were dead.
Am I correct in all of my assumptions so far?
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interresting reply - but i'd like to see you do the math
i'd like to add the king's margin of error is zero.
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hooman his lead me to something: the fact he waited means that he had more time to test the wine on servants
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correct.
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so, either the two did not die, or only one died at first
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hehe .. IM being honest here ... i can't vouch for the king.
HE may be lieing in what HE says. IM stating the facts only.
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I think the remaining tests were designed so that both servants were guaranteed to die. He doesn't want to say 2 servants died, and then have one of them return.
Sounds like there were 4 more rounds of tasting after the 3 servants were sent back. But that's assuming no rounds of tasting ever overlap. I guess it's certainly possibly that they do. Ok, so I count 12 days from when the servants are sent back from when the king sends the bottle.
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no .. only 5 days between them. I should've been more clear:
he sends them back to her, and the same week (on saterday) he sends her the 1 bottle (poisened) wine.
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Ahh ok, I thought that part seemed wrong.
Does any of the tasting overlap? Or will you not tell use that. I kinda seems like it would if there is 5 days in there.
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if overlapping, you'd be testing bottles that may not be poisened .. but you won't know this until the previous "test" is complete, now would you ?
So you could overlap, but that would cause unnecessary deaths, and you ARE short of testing victims..
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Ok, I'm gonna assume 1000 bottles were there originaly, and the king drank one at the start, so one of 999 bottles was poisoned. Now, there were 25 servants and the queen at the party, so if the wine was tested on those people, there are 0 - 25 (26 possibilities) servants that could have died, plus the queen (27 possible outcomes), so by dividing the bottles up among the people evenly to determine the maximum information, that's 999/27 = 37. (I find it possibly leading that it divided evenly here). Basically that means divide the bottles up into 27 groups of 37 bottles each, and every bottle in group i is tasted by exactly i people. Thus, if the poisoned bottle is in group i, i people will die. The queen telling you how many people died will tell you what group the poisoned bottle is in.
Of course, if we knew WHO died, and not just how many people, we could have figured this out in fewer people. Which is why I think the assumption that we only know how many people died and not who died is important. (See other thread on poisoned bottles. ... this forum is becomming pretty morbid. :unsure: )
Ok, so at this point, we're down to 37 bottles that could be poisoned. The king can simply avoid drinking one of those for his Friday drink. We also have 5 servants comming by to test the remaining bottles on. I'll think about this last part a little more.
I don't suppose you can confirm or deny the top part? :D
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I still think only one died and he kept the other around to test the remaining possibilities on
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hooman: you're on the rite track, but you're forgetting someone :)
since i've just written this riddle myself -after reading horus' riddle - it needs fine-tuning still :P the queen gave the name of the person who died to the king, so he'd know. besides the 5 servents could be asked to give this information. The queen also wants to know what happened, so i don't believe that information would be classified.
CK9: uhm.. yea - at first. :)
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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. :P
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:
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Still, the margin of error is to great. This king is 100% sure he sends the right bottle to the queen, and he's also 100% sure he can drink all the other 999 (or 998 if you like) bottles.
You are forgetting he has 1 servant in jail :D
put him to good use!
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you're evil!
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Lol, nice Eddy. But as you said, if I know who died, I only need 10 people in one round to find the bottle.
I think you need additional restrictions on the problem to force the use of that last person. Like perhaps a maximum amount of wine that each person can drink. Or some way of stopping me from using all the bottles at once on 10 people in a way of my choosing.
And what did you mean the margin of error was too great? That last idea would have worked. (There was more than one idea listed above. Kindof an interative approach to solving the problem).
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Okay - i don't think this is necessary, but each person drinks no more then 1 glass of wine :P (they can drink again - if they survive, after 3 days).
want me to explain it already ?
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killing too many servants would look suspicious..
the king done it with the least amount of fatalities.
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Can you mix wine from multiple bottles into each glass? And if so, is there a limit to the number of bottles that can be mixed into each glass?
And no, I'm not ready to give up on this. I just need a properly phrased problem to work from. <_<
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hehe.. it is phrased they way i phrase .. im not english!
and yes, you could put a small amount from each bottle... i guess u could fit upto about 50 bits into a glass without a problem.
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You do realize my binary numbering scheme uses about 37 bottles mixed per glass, and only requires 10 people in one round. If that's all your restrictions, the problem is very easy to solve. Perhaps more restrictions?
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10 people : fine ... you don't HAVE 10 people..
it's just you, your prisinor and the 5 "guests", and i suppose you don't want to test ANY bottle at this time!
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You're forgetting the dinner party. There were 25 servants there. More than enough. And that's assuming I'm not testing on the evil queen and her king.
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okay: amuse me. tell me how you find the 1 poisoned bottle, during the party, if they drink 1 glass full each, and with killing 1 person only (after 3 days)
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Well there was no guarantee of killing just 1 person. That's what I was saying earlier. But then, I also was working with the assumption that we didn't know who died, only how many people died. I guess if we know who died, we can drop the assumption that we can kill more than one person. It sounded more like an outcome than a requirement the way it was phrased. But yes, this gives me something to work with!
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modified riddle
A king has 1000 bottles of wine. He drinks 1 bottle of wine each weekend. He always selects a new bottle every friday evening. A neighboring evil queen plots to kill the king, and sends a servant to poison the wine during that sunday, right after the king finished his bottle. The king's guards catch the servant after he has only poisoned one bottle. They put him in the dungeon, but the guards don't know which bottle was poisoned.
The kings alchemists tell him the poison could kill a man within three days. The king does not want to stop drinking his weekly wine, so he comes up with a brilliant plan. He throws a party the very next day, inviting the evil queen and her king. She shows up, bringing 25 of her best servants. They all drink 1 glass of wine
After three days, the queen informs the king that one of her servants died misteriously (she gives him the name of the person), and sends 5 of her servants to the king's castle to help in the investigation.
The next day (friday), the king was drinking his wine again, and right after the weekend, on monday morning, he sends back 3 of her servants, along with a note that the other servants she sent died.
By the end of the week, on saturday, he sends a bottle of "his best wine" to the queen, and a note stating he wants to settle the problems between their nations. Three days later, the wicked queen died, after drinking from the bottle of wine.
Now, how did he do this ?
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Ok, I think I got what you were thinking now.
Mix 40 bottles of wine into 1 glass, so each of the 25 visiting servants are trying 40 different bottles. Since there is no sharing a bottle between servants, at most one of them will die. Also, since the poisoned bottle is guaranteed to be used in one of those glasses, there will be eactly one dead servant. Knowing which servant died, we will know it was one of those 40 bottles. (That's 1000 bottles / 25 servants = 40 bottles per servant). Now, the king has 1000-40 bottles to choose from for his weekend drinking. No problems there.
Now, he has 5 guests, the prisoner, and 40 bottles to test. Divide the 40 bottles among 5 glasses, with 8 bottles in each. One person will die. It's now down the 8 bottles. If the 3 people are sent home, we only have 2 test subjects left for 8 bottles, se we'd be kinds screwed here since we could end up with 1 of 2 bottles with a 50% chance provided we had 6 days left. Ok, so a more even division seems to be required somewhere.
If the 40 bottles are divided among the 6 servants, with 6 bottles each, and 4 bottles left over, then we'd either have it be one of 6 bottles with 1 dead servant, and 2 testers left, or 3 testers left and 4 bottles. The 3 testers left with 4 bottles case is easy, you'd need to kill at most 2 to figure it out and can be done in 1 round of tasting. (Use that binary method). If 6 bottles are left for 2 tasters in 6 days, then give 2 bottles to each of the two tasters. If one of them dies, it's one of two bottles, and you have 1 taster left and 3 days to determine which one is poisoned. If they both live, you have 2 bottles left and two tasters. You only need to have one person taste one bottle to be sure and 3 days left. In all cases, you know what bottles is poisoned by saturday. (Tasting is on Friday, Monday, and Wednesday, finishing at Saturday when the queen "tastes" the wine).
And of course, you can just excute anyone left over that you don't want around to tell the story. :whistle:
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this works. You've got a solution!
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this works. You've got a solution!
I can't help but notice the "a" solution part. Did you have another? Anything interesting in it?
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i solved it without using a binary.. as i said: least amount of victims
PS: ur very observent .. i was actually wondering i'f you'd notice/reply :)
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Hmm, the only binary I used was when there were 4 bottles left. But in that case it shouldn't affect the expected number of deaths. You could kill 2 people either way, or you might get an answer without killing anyone, or maybe you hit average and kill 1 person. Or is there somewhere else where you can gain some efficiency?