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        riddles >> hard >> Criminal Cupbearers - right answer
        
(Message started by: utgrad on Feb 26^th, 2003, 5:38pm)

Title: Criminal Cupbearers - right answer
Post by utgrad on Feb 26^th, 2003, 5:38pm

Ok, let's examine the question. It says that the king will need to murder no more that 10 prisoners. This is not to say that he ONLY uses 10--just that 10 die.

I think all this crap about the binary method is really absurd. Who would waste time trying to figure out what combination of wine to get the prisoners to drink??? I mean, come on.

Here's the most validated solution. The king has 1000 prisoners test the wine. They each drink from 10 bottles. Prisoner 1 drinks drops of bottles 1 through 10. Prisoner 2 drinks from 2 through 11...etc So prisoner 992 will drink bottles 992 through 1 (prisoner 1's first bottle). Doing this will ensure that 10 prisoners drink wine from the same bottle. Number all the prisoners 1 through 1000. If prisoners 10 through 19 die, then the king can deduce that bottle 19 is the poisoned one. See, simple answer and there's no need for the stupid binary code crap.

Title: Re: Criminal Cupbearers - right answer
Post by Icarus on Feb 26^th, 2003, 7:45pm

1) If you are going to reply to a thread (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1027806173), reply to the thread! Don't start a new one!

2) If the king uses 1000 prisoners, a much simpler solution is the one mentioned in the puzzle. Each prisoner drinks from one bottle, and whichever one dies, throw that bottle out! You solution is just a way to needlessly kill more prisoners, and even worse, waste more good wine on them! :o

3) The whole point of the puzzle is to figure out how to do it with only a few prisoners. The solutions given in the thread (at least, those that are correct) optimize certain variables (least number of prisoners used. Least number killed.)

4) Even if your answer were right, it would not be "the" right answer. Any answer that meets the conditions and spirit of the puzzle is right - whether or not you like it.

Title: Re: Criminal Cupbearers - right answer
Post by Chronos on Feb 28^th, 2003, 6:17pm

I still say that given the parameters of the riddle, 1000 prisoners with one bottle each is the best answer. We're told that the king wants to minimize the number of deaths (so he can put the prisoners to other use later), but we're not told that he wants to minimize the number he uses. The only reason he would do that is if he has a limited number of prisoners available, but all we know about the number of prisoners available is that his dungeons are "vast", which suggests to me that he has plenty. In addition to minimizing the number of deaths, this method has a number of other advantages. While either method will identify the poison bottle if all goes right, evil kings are naturally suspicious, and will not assume that all will go right. What if one of the prisoners kills himself in the four week period? The king won't be able to choose between two of the bottles. Or even worse, what if a prisoner has access to some of that poison, and uses it to kill himself? The king wouldn't even know that the prisoner died by his own hand, and would have a 50% chance of discarding the wrong bottle (and thereby dying). For that matter, the king also doesn't trust his guards who caught the infiltrator: What if he poisoned two or three bottles, before he was caught? Likewise, he doesn't trust the court physician who assured him that the poison was 100% deadly. Maybe one of the prisoners is naturally immune to it. Et cetera. The binary method allows no room for "what-if"s, but the 1 to 1 method does. If more than one prisoners die (by any means), then you throw out all the wine corresponding to those prisoners. If no prisoner dies (the one who drank is immune), then you know that you don't have any information, and can call off the party (which is better than ignorantly going on with it, and having a 50% chance of dying, should one of the 10 binary prisoners be immune). If you want even more of a margin of safety, you could use more prisoners, and assign 2 or 3 to each bottle, but this would increase the final death toll.

So the advantage of the 1 to 1 method is that it minimizes the number of deaths (exactly one), and provides failsafes and redundancies. The sole advantage of the binary method is that it only uses 10 prisoners. But that's not what the riddle wants.

Title: Re: Criminal Cupbearers - right answer
Post by Cage Hiu on May 18^th, 2003, 10:15pm

<img src="http://www.geocities.com/gihiu/winesolution.jpg">

the above chart show that you have Prisioner 1 drink from bottles:

1,2 101,102 201,202 301,302 401,402 501,502 601,602 701,702 801,802 901,902 on the first day. (20 samples daily)

Until the week is over Prisioner 1 ends on 13th and 14th bottle of each Interval.

Prisioner 2 picks up from where Prisioner 1 WILL leave off (it is important that Prisoner 2 samples his drinks at the same time as one due to time restriction) and so on and so forth until you get to the 97th and 98th bottles done by the 7th prisioner

You then have prisioner number 8 drink half of the 99th and 100th bottles on each interval and 9 drink the other half. That leaves 6 more days left which they both will divide evenly drinking 100 sample a day.

IT IS CRITICAL THAT 8 SAMPLES THE SETS OF 100S THAT ARE OPPOSITE WHAT HE DRANK THE DAY BEFORE. !!!!!

The 10th Prisoner shall then drink all the ODD numbered bottles on the first day.

After the first week, comes a three week waiting period , after the waiting period comes the 5th week where 2 -3 people will INEVITABILY DIE. The days that they die on GIVES YOU THE ANSWER.

PICK A RANDOM NUMBER, IF YOUR IN DOUBT AND YOU SHALL SEE THAT THE METHOD ABOVE USES EXACTLY 10 PEOPLE, TO ISOLATE EXACTLY ONE BOTTLE!

C.H

Title: Re: Criminal Cupbearers - right answer
Post by Cage Hiu on May 18^th, 2003, 10:54pm

http://www3.sympatico.ca/impreeza/winesolution.jpg

lets hope the chart works this time!!!

Title: Re: Criminal Cupbearers - right answer
Post by Chronos on May 19^th, 2003, 12:45pm

That assumes that the poison takes exactly four weeks to work. But if that's the case, then we can just use one prisoner, and serve him a different bottle every minute. Then, at the end of four weeks, have a clock handy to see exactly when he dies, and you've got your answer.

Title: Re: Criminal Cupbearers - right answer
Post by phobos on May 19^th, 2003, 6:47pm

Would it be better if the question is that there're only 10 prisoners?

Title: Re: Criminal Cupbearers - right answer
Post by Cage_Hiu on May 20^th, 2003, 7:56pm

the riddles says:

"Furthermore, the effects of the poison take one month to surface"

Therefore if I assume that the poison is accurate to the day it is not unreasonable. If we assume that the poision is accurate right down to the hour, that's pushing it, Why not mintues then, seconds?

If we were to make it so that the poison is + or - serveral days after the month, then what is the significance of the riddle of telling us:

"...will still be able to drink the rest of the wine in 5 weeks time. "

Title: Re: Criminal Cupbearers - right answer
Post by Chronos on May 20^th, 2003, 11:26pm

I think that the five weeks is just some random time longer than a month. He couldn't use four weeks, because that's less than a month.

Title: Re: Criminal Cupbearers - right answer
Post by Cage_Hiu on May 22^nd, 2003, 1:27am

Chronos I'd hate to say it but your right!!!

But I worked out another sloution:

if you have 1 person you can reduce your odds by 50%, meaning if he drinks bottles (501-1000) and doesn't die, you will know its within 1-500

if you have 2 people you can reduce the odds by another 50% if you have an overlap in the ranges:

A:250-750
B:500-1000
(25% chance they both live, both die, A or B dies )

for 3 people you can still reduce the odds by 50%, only its not as obvious

0----125---250---375---500---625---750---875---1000

______________________AAAAAAAAAAAAAAAAAAAAAA

___________BBBBBBBBBBBBBBBBBBBBBBBB____________

CCCCCC____CCCCC______CCCCC______CCCCCC______

C, everyone lives , B+C, B , A+B+C , A+B, A+C , A
(8 possiabilities) =12.5%

Therefore by induction the 10th person would generate 2^10 possiabilities, which is 1024.... which is more than 1000. IT WORKS!!!!! we just have to work out the correct RANGES and determine who dies.

THIS SLOUTION AGAIN USES ONLY 10 PEOPLE, TO ISOLATE EAXACTLY ONE BOTTLE.

Title: Re: Criminal Cupbearers - right answer
Post by Icarus on May 22^nd, 2003, 5:02pm

You will find that solution first posted here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1027806173;start=2) on the original thread for this puzzle.