Author Topic: Wicked Wine  (Read 6953 times)

Offline Hooman

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« Reply #25 on: December 01, 2005, 05:20:39 PM »
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?
 

Offline Eddy-B

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« Reply #26 on: December 01, 2005, 05:28:57 PM »
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!
« Last Edit: December 01, 2005, 05:29:23 PM by Eddy-B »
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Offline Hooman

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« Reply #27 on: December 01, 2005, 05:41:30 PM »
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.
 

Offline Eddy-B

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« Reply #28 on: December 01, 2005, 05:43:18 PM »
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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Offline Hooman

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« Reply #29 on: December 01, 2005, 05:48:27 PM »
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!
 

Offline Eddy-B

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« Reply #30 on: December 01, 2005, 05:51:59 PM »
modified riddle
Quote
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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Offline Hooman

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« Reply #31 on: December 01, 2005, 06:33:48 PM »
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:  

Offline Eddy-B

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« Reply #32 on: December 02, 2005, 01:47:47 AM »
this works. You've got a solution!
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Offline Hooman

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« Reply #33 on: December 02, 2005, 06:53:20 PM »
Quote
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?
 

Offline Eddy-B

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« Reply #34 on: December 03, 2005, 01:10:09 AM »
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 :)
« Last Edit: December 03, 2005, 01:10:43 AM by Eddy-B »
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Offline Hooman

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« Reply #35 on: December 03, 2005, 02:49:59 AM »
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?