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How many 'doses' does each jar contain?
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Hmm actually the way I formulated this problem might be problematic, give me a sec to review
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Kinda depends on how much milk you can get the rats to drink.
are we to suppose that we are able to feed rats milk infinitely fast, that it takes no time to open and close the jars of milk?
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can 1 rat drink more than 1 jar of milk? if so only 1 rat will die.
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+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk that was fed to that group was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough.
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Hong Kong20321 Posts
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On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough.
you have a time limit.
(even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong  )
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+ Show Spoiler +
My strategy: assumes that even the smallest dose of the poison will kill the rat, you can mix the milk together and still retain the poison, you can split the milk into enough portions, the time of death is exactly 2 hours (not a single second off) and the rat can drink that bloody much.
1 rat. Feed it very, very small sample of a different jar of milk every 3 seconds and note what time it dies.
If you can't measure the time of death that accurately, then simply add more rats and stagger the milk intake, combined with feeding the different rats with different combination of milks
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On May 17 2008 03:19 travis wrote:Show nested quote +On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough. you have a time limit. (even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong )
The time limit is no problem, you do it simultanously.
An example might be better:
+ Show Spoiler +with 4 jars and 2 rats,
rat 1 drinks jar 2 and 4
rat 2 drinks jar 3 and 4
two hours later...
if no rats die, it was jar 1
if only rat 1 dies, it was jar 2
if only rat 2 dies, it was jar 3
if both rat 1 and rat 2 die, it was jar 4
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On May 17 2008 03:23 Elements wrote:Show nested quote +On May 17 2008 03:19 travis wrote:On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough. you have a time limit. (even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong ) The time limit is no problem, you do it simultanously. An example might be better: + Show Spoiler +with 4 jars and 2 rats,
rat 1 drinks jar 2 and 4
rat 2 drinks jar 3 and 4
two hours later...
if no rats die, it was jar 1
if only rat 1 dies, it was jar 2
if only rat 2 dies, it was jar 3
if both rat 1 and rat 2 die, it was jar 4
yes but u have to wait 2 hours so by the time u get it narrowed down to less jars, you have no time let to do a second wave of experiments
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So the main thing I wanted to avoid was gold rush's answer which utilizes time to figure out when the rats die.
It should be that you cannot really discern any information about when the rats died, and therefore should be unable to figure out when the rat died simply by time.
@travis
The rats have infinite capacity, and you have the ability to feed the rats any amount of milk instantly. The main reason for the time limit is to make sure you can't feed the rats poison after a rat has already died.
@Elements
Congratulations you have solved the problem.
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On May 17 2008 03:25 travis wrote:Show nested quote +On May 17 2008 03:23 Elements wrote:On May 17 2008 03:19 travis wrote:On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough. you have a time limit. (even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong ) The time limit is no problem, you do it simultanously. An example might be better: + Show Spoiler +with 4 jars and 2 rats,
rat 1 drinks jar 2 and 4
rat 2 drinks jar 3 and 4
two hours later...
if no rats die, it was jar 1
if only rat 1 dies, it was jar 2
if only rat 2 dies, it was jar 3
if both rat 1 and rat 2 die, it was jar 4
yes but u have to wait 2 hours so by the time u get it narrowed down to less jars, you have no time let to do a second wave of experiments
Thing is, after the first time, you already know exactly what jar it is. You haven't narrowed down the possibility; you've found the only jar that could be poison.
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On May 17 2008 03:20 goldrush wrote:+ Show Spoiler +
My strategy: assumes that even the smallest dose of the poison will kill the rat, you can mix the milk together and still retain the poison, you can split the milk into enough portions, the time of death is exactly 2 hours (not a single second off) and the rat can drink that bloody much.
1 rat. Feed it very, very small sample of a different jar of milk every 3 seconds and note what time it dies.
If you can't measure the time of death that accurately, then simply add more rats and stagger the milk intake, combined with feeding the different rats with different combination of milks
well given the specificity of the rules I would have to say this is a very clever answer. though it would never workd in the real world cuz digestion doesn't work like that hehe
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I am so confused by what you guys are saying right now. with a 2 hour delay, how can u possibly find out with only 10 rats?
let's say it's the 50th jar out of the 1000 jars. how do you find out with only 10 rats?
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Well, I assumed that if you gave the time limit and the time to die that they would be used...
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+ Show Spoiler +Does the poison take exactly 2 hours to kill a rat?
If so, give a dose from a different jar each 3.6 seconds to the same rat. See when it dies, substract 2 hours and you know exactly at what time it drank the poisoned milk.
I must admit this solution doesn't seem very feasible in a real situation... but nothing in the ridle says it is not =)
EDIT: ouch fuck, it does. Did I misread or was that the part that was edited in the OP?
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@travis
+ Show Spoiler +
Let's say we represent every single jar in binary. This requires 10 binary digits (2^10 = 1024 > 1000). Each of the 10 rats corresponds to one of these digits.
After you have represented all your jars in binary, you take your first rat, and feed it milk from all the jars that has a 1 in the first digit. Take the second rat, and feed it milk from all the jars that has a 1 in the second digit. Do this for all 10 rats.
The number 50 in binary is 0000110010. Each digit of the 10 digit binary number corresponds to one of the 10 rats, so you will feed the 2nd, 5th, and 6th rat some milk from the 50th jar. After 2 hours, these three rats will die, and you will know that it had to be the 50th jar, because no other jar had exactly these 3 rats drink from it.
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On May 17 2008 03:35 KarlSberg~ wrote:+ Show Spoiler +
Does the poison take exactly 2 hours to kill a rat?
If so, give a dose from a different jar each 3.6 seconds to the same rat. See when it dies, substract 2 hours and you know exactly at what time it drank the poisoned milk.
Well I must admit it doesn't seem very feasible in a real situation... but nothing in the ridle forbids says it is not =)
I've fixed the problem description such that you do not know exactly how long it takes the poison to kill the rat.
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On May 17 2008 03:35 Slithe wrote:
After 2 hours, these three rats will die, and you will know that it had to be the 50th jar, because no other jar had exactly these 3 rats drink from it.
ohhh wait i see where I'm off I think
ok I get how you guys did it lol
math is neato
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Elements is 100% right, that's the right answer
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The 3 rats did drink from other jars but...
For example let's take jar 51. binary = 0000110011.
In this case, the 1st, 2nd, 5th, and 6th rat drank from it. Thus if the 51st jar was poisoned, then these 4 rats will die. You know it's not the 50th jar because the 1st rat died. Each jar has a unique combination of rats that drank from it, and as a result you can figure out exactly which jar it is based on which of the 10 rats died.
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the binary is just confusing me lol
but don't worry I get it now, thanks for being patient dude
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lol travis come on XD
i didnt know the answer but i knew which answer to raise my eyebrows to and which to frown and audibly "tch" at
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Yeah the binary is probably just making it harder to understand if you haven't worked with it a lot. My explanations have a natural computer science bias, especially since I get most of my puzzles from other CS majors.
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All you need is one rat. You just have to get really really lucky.
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this was a nice math question 
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the poison takes a nondeterministic amount of time between 2 and 3 hours to kill a rat.
lol. that's so poorly worded: it's possible for none of the rats to die within the 3 hours you have, especially given the fact that your actions don't take ... zero seconds.
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On May 17 2008 03:25 travis wrote:Show nested quote +On May 17 2008 03:23 Elements wrote:On May 17 2008 03:19 travis wrote:On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough. you have a time limit. (even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong ) The time limit is no problem, you do it simultanously. An example might be better: + Show Spoiler +with 4 jars and 2 rats,
rat 1 drinks jar 2 and 4
rat 2 drinks jar 3 and 4
two hours later...
if no rats die, it was jar 1
if only rat 1 dies, it was jar 2
if only rat 2 dies, it was jar 3
if both rat 1 and rat 2 die, it was jar 4
yes but u have to wait 2 hours so by the time u get it narrowed down to less jars, you have no time let to do a second wave of experiments
you dont do a second round :O
you just use exceptions
if you have 2 rats and feed them like so:
rat 1 - jar 2 and 3
rat 2 - jar 3 and 4
if no rats die (and one of those 4 jars has to have poison) then jar 1 (the one not used) was the poison.
if jar 2 is poison, only rat 1 will die
if jar 3 is poison rat 1 and 2 will both die
if jar 4 is poison only rat 2 will die
I think its something like that, but on a larger scale
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On May 17 2008 03:46 Slithe wrote:
The 3 rats did drink from other jars but...
For example let's take jar 51. binary = 0000110011.
In this case, the 1st, 2nd, 5th, and 6th rat drank from it. Thus if the 51st jar was poisoned, then these 4 rats will die. You know it's not the 50th jar because the 1st rat died. Each jar has a unique combination of rats that drank from it, and as a result you can figure out exactly which jar it is based on which of the 10 rats died.
I really like this explanation
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On May 17 2008 04:25 paper wrote:Show nested quote +the poison takes a nondeterministic amount of time between 2 and 3 hours to kill a rat. lol. that's so poorly worded: it's possible for none of the rats to die within the 3 hours you have, especially given the fact that your actions don't take ... zero seconds.
Contrary to what you may think, your actions do indeed take exactly zero seconds. It's pretty awesome.
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You should have used something cute like puppies or bunnies. Rats, I just want to kill them, thus would not be motivated to not feed them all poison.
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Hong Kong20321 Posts
im sorta confused still but then i never really lked math but i half get it so its ok :D cool stuf
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On May 17 2008 04:26 fusionsdf wrote:Show nested quote +On May 17 2008 03:25 travis wrote:On May 17 2008 03:23 Elements wrote:On May 17 2008 03:19 travis wrote:On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough. you have a time limit. (even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong ) The time limit is no problem, you do it simultanously. An example might be better: + Show Spoiler +with 4 jars and 2 rats,
rat 1 drinks jar 2 and 4
rat 2 drinks jar 3 and 4
two hours later...
if no rats die, it was jar 1
if only rat 1 dies, it was jar 2
if only rat 2 dies, it was jar 3
if both rat 1 and rat 2 die, it was jar 4
yes but u have to wait 2 hours so by the time u get it narrowed down to less jars, you have no time let to do a second wave of experiments you dont do a second round :O you just use exceptions if you have 2 rats and feed them like so: rat 1 - jar 2 and 3 rat 2 - jar 3 and 4 if no rats die (and one of those 4 jars has to have poison) then jar 1 (the one not used) was the poison. if jar 2 is poison, only rat 1 will die if jar 3 is poison rat 1 and 2 will both die if jar 4 is poison only rat 2 will die I think its something like that, but on a larger scale
ur like 80 years late
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You could mix all the milk into 1 jar. Then you would only need 1 rat to find out the answer.
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This is a nice way to explain hashing
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United States20661 Posts
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Well I thought it was super cool and it made me wish I knew all these special and cool maths answers because then, probably, I would score with all the hot chicks.
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From the top of my head
+ Show Spoiler +
100 jars
10 x 10 would be
12345678910
11xxxxxxxxx
12xxxxxxxxx
13xxxxxxxxx
14xxxxxxxxx
15xxxxxxxxx
16xxxxxxxxx
17xxxxxxxxx
18xxxxxxxxx
19xxxxxxxxx
20xxxxxxxxx
So each rat would drink 10, but if one got sick you could tell from the way the other rats who drank the same column/row..
So if you did the same with 100 x 10 it would make 110 rats.
EDIT: Sqrt of 1000 ~=32 so if you manage a 32 x 32 grid and you have 64 rats. ?
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nvm my solution si wrong, I forgot the time it takes for the poison to work. My math knowledge is rudimentary, but I think you could create overlapping mixtures, feed them to the rats, and find out which jar it is in one go.
eg with 3 jars, you could create mixtures 12, 23, 13, and feed each to 3 rats. Based on which rats die, the culprit should be identifiable.
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On May 17 2008 06:29 Gandalf wrote:11 rats + Show Spoiler +
split the jars into two groups of 500. mix a small amount of milk from every jar in each group to form a mixture that represents each group, and feed it to two rats. One rat will die and eliminate 500 jars. Then divide the remaining 500 into two groups of 250 and so on.
The rat that doesnt die gets recycled for the next cycle. So we have:
first two rats: 500 jars left
one more rat: 250 left
one more rat: 125 left
one more rat: 63 left
one more rat: 32 left
one more rat: 16 left
one more rat: 8 left
one more rat: 4 left
one more rat: 2 left
one more rat: jar is identified, one rat stays alive, 11 used in all
Does that work with the time limit? It takes 2-3 hours for the poison to work you have 3 hours.
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this is a very clever puzzle. My first thought was also "oh it must be like those weighing problems where you have to keep dividing in half 10 times" so 10, but I couldn't think of any way to make it work, so all i could think of was 999. I'm glad elements explained it so well.
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Fuck the rats, just get one of your friends to drink a small sip of each milk jar until he finds one that tastes funny. Problem solved.
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On May 17 2008 05:12 travis wrote:Show nested quote +On May 17 2008 04:26 fusionsdf wrote:On May 17 2008 03:25 travis wrote:On May 17 2008 03:23 Elements wrote:On May 17 2008 03:19 travis wrote:On May 17 2008 03:17 Elements wrote:+ Show Spoiler +log2(1000) rounded up equals 10 rats.
Each milk is fed to a unique subset of the rats, depending on which subset dies, then you know the milk it came from was poisoned. With 10 rats, there are 2^10 = 1024 different subsets, which is enough. you have a time limit. (even though i think this answer is what he wanted the correct answer to the riddle to be, he just made the time limit wrong ) The time limit is no problem, you do it simultanously. An example might be better: + Show Spoiler +with 4 jars and 2 rats,
rat 1 drinks jar 2 and 4
rat 2 drinks jar 3 and 4
two hours later...
if no rats die, it was jar 1
if only rat 1 dies, it was jar 2
if only rat 2 dies, it was jar 3
if both rat 1 and rat 2 die, it was jar 4
yes but u have to wait 2 hours so by the time u get it narrowed down to less jars, you have no time let to do a second wave of experiments you dont do a second round :O you just use exceptions if you have 2 rats and feed them like so: rat 1 - jar 2 and 3 rat 2 - jar 3 and 4 if no rats die (and one of those 4 jars has to have poison) then jar 1 (the one not used) was the poison. if jar 2 is poison, only rat 1 will die if jar 3 is poison rat 1 and 2 will both die if jar 4 is poison only rat 2 will die I think its something like that, but on a larger scale ur like 80 years late
yeah well Im like 600 years awesome
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log(n) where n is the number of poisoned bottles
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ahh, sweet problem! Me like.
A better formulation may have been that you are allowed to feed each rat only one bowl of milk (in which you then could mix), then you wouldnt have the confusion on the instantaneous milk-mixing.
And cuter things like bunnies wouldnt work very well, since people would just find a safe sort of milk and keep feeding the bunnies (from the infinite amount of milk) and cuddle with them.
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I send my infinite army of rats to take over the world.
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EPT
