How do you solve this? Without harming anyone?

feed some of ever barrel to the rats and see which died

or do what said

This is so fucking vague! Is this a mathematical problem or does it want a practical solution?

Get 50 servants with 50 rats and have the servants have each rat drink a little bit of each then wait like 2-10 hours for something to die. 1 of the 50 would die and then I would have 10 servants with 10 more rats and pair them with each of the 10 barrels from the original rat that died and have each of the rats drink, one would die and that would be my barrel, and it would take (assuming it took 15 minutes for each rat to drink each round) 4.5-20.5 hours, which is all before 48.

If rats died from alcohol anyway I could just use dogs although that makes me feel bad.

Actually the OP is a practical problem.

You have problem, a desire not to harm and a time limitation, just like real life. Just like real life you don't have enough information to solve without finding more out and leveraging undeclared assets.

>a desire not to harm

not stated in the problem

Without OP's bullshit added rule, the king could just serve the wine.

get 500 peasants and order each one to drink a cup from different barrel.
The one that drops dead, drank from the poisoned barrel.
Other 499 are so fucking jolly, to be invited by the king, to have a cup of wine, that they immediately forget the fact about cruel experiments.

depending on the strength of the poisen just mix them all together and server.

best answer

King could continue to poison all wine in the kingdom with slightly increasing amounts of poison till everyone in the kingdom were immune to the poison

youtube.com/watch?v=N3qmN6pYhi0 Binary

is that a real game?

I am not a man of mathematics and could only come up with the first method. But the second one is amazing. I mean, this is really cool stuff, which just shows how imagination and creativity can help to solve problems in life.

That's an interesting trick but, if you're just going to give it to rats in the first place, why don't you just do it brute force?

Because OP didn't set the problem up correctly.

I think that is just some troll, there would constantly pop up threads with problems which have incomplete set ups or are just ambiguous.
Then he just waits and masturbates.

I could see how it wants a practical solution, but who the fuck has 500 barrells of wine laying around, where one of them is poisoned?

find about 9 rats

then do a binary search for the barrel by mixing wine from each half and feeding it to the rats

>needing a binary search tree
he's a fucking king he can just order 500 people to drink from the casks

nah, it's a thing some artist did for zozzles
>judebuffum.wordpress.com/2012/08/01/the-battle-of-wits-crazy-4-cult-ny/

Me either, just a dude who likes to watch maths YouTubes and masturbate intermittently.

fill a bottle with wine from ten different consecutive barrels, repeat this until you have 50 wine bottles

give tastes of the wine to prisoners or mice

when one of them is affected by poison repeat the same process of each barrel that was used for the wine

The poison could take minutes or even hours to take effect. You'd only know that the barrel was one of the ones the king had drank from.

Have your manservant fuccboi taste all the barrels until he dies.

Isn't this sort of similar to that problem everyone does in diff eq, the brine problem where you have to model equations to describe the rate of flow of clean water into the barrel of brine, and the rate of flow out of the barrel (or something like that)

Not enough information to do this problem obviously though.

>Isn't this sort of similar to that problem everyone does in diff eq, the brine problem where you have to model equations to describe the rate of flow of clean water into the barrel....
Nope

You could dilute the poison until it's no longer harmful

yes, if you had infinite ammount of wine. But then, you could just purge all the barrels.
The problem is entirely different.

For some reason I was thinking about water and not wine

Yeah I've seen this problem before. Let's make it interesting by saying you have two hours instead of one. What's the minimum amount of mice you need then?

So in the first hour you would want to narrow the field down without killing all your mice. Then the second step would be the normal technique with your remaining mice.

You could further generalize this to n hours.

Or maybe just figure out who's selling you poisoned wine and stop buying from him.

Throw away his "wants" and throw away the wine and serve healthy, clean, crisp, clear water. Wine is poison to our bodies anyway: and turns idiots into bigger idiots.

This was covered on infinite series. Something about using a binary sequence to track which barrels kill mice.

Throwing away the blood of our lord savior..

This wouldn't work if all of them were poison and you were trying to find the non poison one.

Pick a barrel at random. Either it's poisoned or it's not, so the probability is 1/2.

Pick another barrel. Again, either it's poisoned or it's not, so the probability is 1/2.

1/2+1/2=1, so one of those 2 barrels is definitely poisoned.

You now just need two mice to test each barrel.

Invite the peasants as they aren't people punish those who get poisoned for defaming GOD.

this is proof that math isn't as smart as history harumpf

Wait. You just need one mouse.

Test one of the two barrels, if the mouse dies then that was the poisoned one, if it doesn't then it must be the other barrel.

Give a glass of wine from each barrel to a different mature sheep. Remove the barrel corresponding to the sheeo that dies, sheer the sheep, and distribute a wool sock to each of the partygoes as comemmoration of the event.

Tell the cleric to prepare Detect Poison and check every barrel until we find the poisoned one.
We will take our reward in wine your majesty, thank you.

The generic algorithm for this is (very) easy high-school level stuff bored guys encounter (figure out for themselves most likely) most of the time while doing programming challenges (and other math based optimization challenges).

1. Divide the barrels you're currently unsure about into two groups. (In the beginning this is all barrels; 250-250.)
2. Make two mixes corresponding to the groups.
3. Check both mixes.
4. Select the group which gave positive result.
5. Is the positive group small enough for individual tests if that's our goal (depending on available resources) or is it consists of only one barrel? If that's the case STOP the algorithm and test the barrel(s).
6. GOTO 1

This will divide the group by 2^n, which converges very quickly.
To simplify for our example let's say that the amount of barrels we have is a power of two. 16384/(2^14) = 1. We will reach conclusion in 14 steps which means 14 test subjects. We can also optimize the algorithm to discard more than one barrel if the group is sufficiently small compared to the whole, like 10%.

>Without harming anyone?
I don't know. I'm not sure that's part of the original problem.
From a quick glance I see multiple solutions:
- You could produce a mix from enough barrels so the poison is no longer harmful.
- Use small animals for testing like rats, mouse, etc. Lot of poisons depend on body weight.
Neither of these two find the barrel though.
- A good trick would be assuming that the king knows who poisoned it (or at least he knows which group of staff has the culprit) is to have his staff (all potential poisoners) taste the wine before serving it. They can't serve from the same barrel twice unless there are no remaining untouched barrels. Obviously the poisoner won't drink the wine, except if he's ready to die for his cause.

Sell these to communists and buy 500 more.

the most realistic answer is that the king just dumps the wine barrels and then gets new ones since he can't harm anyone

nice

this is just stupid enough to work

waterfags get out

>without harming anyone

Serve the barrels anyway.

The king didn't put the poison in the barrels, so technically he did not harm anyone.

The poison will then be discovered anyway, when the barrel is drank from.

Serve beer or mead.

This. Wine is gross anyway.

all of the king's guests leave because he mixed all of the merlot, chardonnay and champagne together and it tastes like shit

try again

I can expend 5 servants and bring our time down to 4 hours.

Also you did the problem wrong. You didn't specify that it takes up to one hour for the poison to take affect.

When they brought out the rats, I immediately thought of that one decision game from ZTD, where Team C had to figure out which phial among 10 had the antidote. Seeing how they described the same algorithm in mathematical terms made me appreciate that one segment a lot more.

I laughed heartily.

Good show. What have the jesters got in store for us tonight?

There's some kind of emergent pattern if you label the bottles in binary, hold up lemme find this video.

here it is

youtube.com/watch?v=N3qmN6pYhi0

its a great channel imo. really, all of the pbs yt channels are good. they tread lightly into popsci but always keep it informative.

also i already claimed kelsey as my waifu.

By using binary numbers and ten small animals, say ten mouse(because small dosage of poison will also be deadly for a small animal). Label a number to every bottle and convert that number to binary. Than make those animals to stand in a row and make those animals which are standing in same position as position of one from left to right in the binary codeb to drink a small amount of wine . After observing which of those animals got poisoned, we can know the binary code of poisoned bottle.

m.youtube.com/watch?v=N3qmN6pYhi0

test a cup of each on prisioners, problem solved. you have 499 happy prisoners, and one less mouth to fee of someone who was goign to be killed anyways

this.

Mass spectroscopy of each wine barrel

damn

there was nothing in the question by OP about rats REEEE

Binary Search Tree

Find the open one?

Kek this guy, MS on each barrel in 48 hours. You will destroy our kingdom!

depending on the column, method, and the mass spec itself it is definitely possible. it's just under 6 minutes per run, and that's assuming you have to run all 500 which you very likely won't.

Haha so first do the right research for the right method and than analyze all the compounds in all barrels. No just find the open one, its a lot easier.

he doesn't. He simply dilutes every barrel down to 0.2% of it's original content. That should be workable.

Alcohol is a poison
All the barrels are poisoned by technicality.

explain how any mathematical system helps find a random barrel in a more efficient manner than checking them 1 by 1

>>without harming anyone
show me where do you see this proposition in op's picture
else
choke on cock

Two words: Molecular Analysis

can you prove me wrong?

>pro tip: you can't

>Without harming anyone?

remove wine, drink water instead.

that's also assuming you only have one mass spec. if you have 500 that's not a problem.

I'd mix one drop for each bottle with all of the other bottles so every bottle had a small amount of poison. By drinking that diluted poison mixture, everyone would get immune to the poison. Homeopathy, bitches.

it's possible to find the solution with 9 rats, each of them only drinking once and at the same time

Mix all of the 500 barrels.
The poison Is diluted by at 500 times.
The king should feel safe to serve the wine knowing that no poison known to man is able to kill if diluted to such degree.

>It's a homeopathic poison
>It's still far too strong
>Everyone dies
Well done

binary search.
mix samples of 250 barrels together, check for poison.
Then 125.
Then 63/62

etc.

This is the fastest way. Of course the question doesn't give us anything to work with, so the 48 hours bit is useless information. It should just read "as fast as reasonably possible"

You could test 500 barrels for poison in 8 hours, its literally what QA people do.

You get 500 prisoners on death row. You offer them a pardon if they each drink from 1 barrel of wine.

Technically you haven't harmed anyone. You have saved 499 lives. The poisoned guy was going to die anyway. You just moved up his execution date.

In op's actual post. Can you even read?

How much poison are we talking about? Is there enough poison in the wine barrel to be at a lethal concentration?

Why even bother finding the poisoned barrel if there isn't even enough poison in the wine to kill someone?

except for the people harmed by the marauding horde of 499 rapists and murderers pardoned.

>Check the mass spec for anything not wine.
>Because all wines are the same and wine has a well behaved mass spectrum

boi...

Easy, mix it all together. The poison will be so diluted that it does not matter now.

no the other barrel is 1/2 poison so u have to check it

what if the poison takes a long time to act.....

This is a classic OR (operations research) / DOE (design of experiments) question.

Usually it is phrased better, with it asking the fewest number of tests needed to pick the correct barrel.

Say you are a consultant and are paid big bucks to come in and determine the absolute minimum number of trials to absolutely determine the poisoned barrel. To test for the poison may cost a lot and it is best to do it cheaply. Also assume the wine/poison is fully mixed, so sampling from the barrel will yield a poisoned sample.

The correct answer is log_base2 (n) where n is the number of barrels. It is set up like
said.

Fun problem, hope I get to do this some day at my job because so many dumbshits would just brute force this problem and test all of the barrels because "muh 50% probability, test them all"

>tfw peasant and live in the hinterlands

>2017
>still calling it spectroscopy
Fuck off

I'd be more concerned about who keeps poisoning my fucking barrels of wine.

I'd gather all the potential suspects, the delivery men, the caskers, the farmers, everyone.

I would make them select a cask to drink from
The ones who drop dead were most likely innocent
The ones who are alive are still suspects

You narrow the suspects down to 400
You have one hour to find the poisoner
You can only kill one, and the chamber torture Barron is on vacation
the suspects are not prone to bribery and they all claim innocence
If you don't find the poisoner the villagers will become unruly and capture you, and the Barron of torture returns from vacation immediately

What do?

...

obviously just have luck maxed out and where the amulet of good fortune (+2 to luck)