Incredibly Difficult Logic Problem (Version 2)

[Pan1cMode]

Since quite a few of you liked the first puzzle (found here), here's another one for you.

You are a ruler of a great empire. To celebrate your wealth, you are holding a large party for many important nationals of your empire. This party is to be held 24 hours from now. For this celebration you have purchased 1,000 casks of very expensive wine, which have become a selling point of the whole event. You come to learn through a captured enemy that exactly 1 of the casks of wine has been tainted with a deadly poison that will cause certain death for anyone who consumes it. You must find which cask of wine has been poisoned. Luckily for you, you have a large number of prisoners whose treasonous crimes merit being put to death. Since you are a royal, you want to interact with the least amount of prisoners as possible. What is the minimum number of prisoners required to determine which cask of wine has been poisoned?

Assume the following:
- Anyone who consumes the poison will die
- There is only 1 cask of poisoned wine out of the 1000; you are to dispose of only 1 cask.
- The poison will take effect somewhere between 10 and 20 hours after administration causing death
- You only have 24 hours to determine which bottle is poisoned
- You want to minimise the number of prisoner deaths occurring
- The prisoners are immune to the effects of alcohol poisoning/overdose and are in otherwise good health. They will only die within the next 24 if they are exposed to the poison.
- Only a very small amount of wine (1mL) is required for the effects of the poison to be seen
- The poisoned wine looks, smells and tastes the same as all the other wine and is otherwise indistinguishable.

I'll post clues later if requested and the solution in 48 hours time.

 

[fr stack]

do i have 1000 prisoners ? cause im not risking all my highborn friends when i can just make the peasants drink it for me to find out , tell them they're being rewarded with some wine but they have to guard the cask until tomorow

 

[Pan1cMode]

do i have 1000 prisoners ? cause im not risking all my highborn friends when i can just make the peasants drink it for me to find out , tell them they're being rewarded with some wine but they have to guard the cask until tomorow

You have innumerable prisoners, but 1000 is too many. Remember, you want to minimise the number of deaths.

 

[Rickyraws]

 

[HeroesNZ]

I got it right for the wrong reason lol

 

[fr stack]

hmmm maybe assign 1 man to each ten casks , tell them to drink a shot from each as fast as they can , the dead guys barrels get removed , so you are only losing 10 casks

 

[Mikemetroid]

- The poison will take effect somewhere between 10 and 20 hours after administration causing death
- The prisoners are immune to the effects of alcohol poisoning/overdose and are in otherwise good health. They will only die within the next 24 if they are exposed to the poison.

Which one is it lol 10-20 hours or 24 hours

 

[EGP Wonder_Chef]

I mean if you gave each of 1000 prisoners one sample from each of the boxes, the number of deaths would be one...

I know that isn't the point of the riddle though. Just saying, maybe there should be another reason why the ruler should be trying to use as few prisoners as possible.

 

[Johnny San]

This was done in my Trig class in High School. Good luck to you guys.

 

[EMPEROR PRYCE]

I need a clue

 

[fr stack]

Have 1000 prisoners drink a little bit. The one that dies in the 10-20 hour window is the only one that needs to die. Give the rest to the guests. The answer is one.

yeah exactly cause only one cask is actually poisoned , how eloquent of you mr ricky

 

[EGP Wonder_Chef]

Have 1000 prisoners drink a little bit. The one that dies in the 10-20 hour window is the only one that needs to die. Give the rest to the guests. The answer is one.

The actual question was "the minimum number of prisoners required" not "minimum number of prisoners that need to die" I think.

I think it was just explained kind of strangely.

 

[Pan1cMode]

Which one is it lol 10-20 hours or 24 hours

10-20 hours. It's irrelevent anyways. What I meant was they won't suddenly have a heart attack and die within the next 24 hours.

 

[Solid]

If I have 1000 prisoners, each one will drink a glass of wine from a cask. 1 prisoner for 1 cask. Only 1 prisoner get poisoned.

Edit: gets*

 

[Pan1cMode]

Have 1000 prisoners drink a little bit. The one that dies in the 10-20 hour window is the only one that needs to die. Give the rest to the guests. The answer is one.

Nope. The question is phrased as how many prisoners are required. Your solution requires 1000. It can be done with much less than that. True, it leads to the least amount of deaths, but the question specifically asks for the least amount of prisoners required, not least amount of deaths.

 

[EMPEROR PRYCE]

I mean if you gave each of 1000 prisoners one sample from each of the boxes, the number of deaths would be one...

I know that isn't the point of the riddle though. Just saying, maybe there should be another reason why the ruler should be trying to use as few prisoners as possible.

U know. thats what I thought as well. This would require having to give each cask a number and the corresponding prisoner the same number to insure its the right one. If this is possible, that'd be the way to go.

 

[roosTakk]

Iv always been more of a beer guy

 

[Pan1cMode]

Have 500 prisoners drink two different casks. Who ever dies, you then narrow it down to the two. Then have one more drink one of the possible 2. 501


I've narrowed it down to this so far. Gonna try some more.

You don't have the time. What if the first one doesn't die till 19 and a half hours after drinking the wine?

 

[Pan1cMode]

I mean if you gave each of 1000 prisoners one sample from each of the boxes, the number of deaths would be one...

I know that isn't the point of the riddle though. Just saying, maybe there should be another reason why the ruler should be trying to use as few prisoners as possible.

I came up with another reason ._. good enough?

 

[EGP Wonder_Chef]

Have 500 prisoners drink two different casks. Who ever dies, you then narrow it down to the two. Then have one more drink one of the possible 2. 501


I've narrowed it down to this so far. Gonna try some more.

couldn't you lower that down further? like 100 prisoners drink 10 each? Then those 10 would have a max of 9 in common, so that would take 109 prisoners, etc. Not sure what the lowest you could get this is.

EDIT: Nevermind.

 

[RiBBz22]

Guys, it is about the minimum amount of people required to test...not the minimum amount of causalities.

 

[Youphemism]

Ooh time for the maths nerd to come out to plaaaaaaayyyyyyy

*mumbles to himself* Ok, 1000 casks, x prisoners to taste these casks, 1 poisoned. Find the minimum number required to find the poisoned cask.

I'm going to say that it's got something to do with an array kind of layout, ie instead of 1 prisoner getting super drunk and dying it'll be

Cask...........1.......2......3........4......5.....1,000
Prisoner 1....Y......N......Y.......N......Y.......N
Prisoner 2...N......Y......N.......N......Y.......N
...
Prisoner n...Y......Y......N.......N......Y.......N

Where Y = prisoner drinks this barrel, N = prisoner doesn't drink this barrel.

Each casket will have a different combination of people drinking from it, you can find which cask it is from the combination of prisoners that dies...

I'm going to work out a formula for 'n' now, but this is how I think it works amirite @Pan1cMode ?

 

[Pan1cMode]

Ooh time for the maths nerd to come out to plaaaaaaayyyyyyy

*mumbles to himself* Ok, 1000 casks, x prisoners to taste these casks, 1 poisoned. Find the minimum number required to find the poisoned cask.

I'm going to say that it's got something to do with an array kind of layout, ie instead of 1 prisoner getting super drunk and dying it'll be

Cask...........1.......2......3........4......5.....1,000
Prisoner 1....Y......N......Y.......N......Y.......N
Prisoner 2...N......Y......N.......N......Y.......N
...
Prisoner n...Y......Y......N.......N......Y.......N

Where Y = prisoner drinks this barrel, N = prisoner doesn't drink this barrel.

Each casket will have a different combination of people drinking from it, you can find which cask it is from the combination of prisoners that dies...

I'm going to work out a formula for 'n' now, but this is how I think it works amirite @Pan1cMode ?

Lol, not even an hour hahaha.

Now all that's left is to calculate the amount of prisoners required. There's a simple way to figure it out without brute forcing through the necessary combinations.

 

[MidTierHarley]

Buy new wine...never mind buy beer or SunnyD you dumbasses

 

[RiBBz22]

Yeah Youphemism pretty much has the idea. Each cask would be marked with some sort of unique number based on a binary sequence formed by the Y/N's (or 1's and 0's) that reflect which prisoners did and didn't drink from it. The number of prisoners that actually die will then point to the exact cask that all of them drank from that the others did not. I am at work now and don't have time to work out the exact answer. But you can trust my logic as I am an engineer