Wine bottle puzzle !
You are a logician turned mad scientist,and decide to have a Party ONE MONTH from today. You have one thousand bottles of wine. Suddenly, you remembered about a "small" experiment you did, which POISONED one of the wine bottle. Ofcourse you don't remember which one.
The poison takes a LITTLE Less than a month to take effect.
You have a LOT of "guinea pigs" at your disposal. The puzzle is to find the SMALLEST number of rodents that must drink from the bottles to find the poisoned one?
HINT: There is one !
The poison takes a LITTLE Less than a month to take effect.
You have a LOT of "guinea pigs" at your disposal. The puzzle is to find the SMALLEST number of rodents that must drink from the bottles to find the poisoned one?
HINT: There is one !
Labels: friday special, logic, puzzle
posted by Rajesh Lal at
9:56 AM
25 Comments:
The answer is 10
I was confused at first, but the hint gave it to me, there is one. That brought me back to my programming classes and I remembered that this was a series of binaries to represent each of the guinea pigs.
Each tester represents a binary from 1 to 10. Each wine bottle is numbered to the select testers.
For example, wine bottle 1, the binary representation is 00000001, so tester 1 only tries it.
For bottle 19, the binary is 0000010011, so testers 1,2 and 5 try it.
Each tester's drink has a little bit of wine from each bottle which has a one in their digit.
After 20 hours you note which testers died. You then construct a number with '1's for the testers that died, '0's for others. That is the number of the poisoned bottle.
So, if testers 4,5 and 6 die, the bottle that is poisoned is
0000111000 = 48
The daddy is ingenious!
I wonder if drinking a small amount from each of 500 bottles would kill a rodent even without the poison :)
On average 5 rodents will die from the poison assuming you don't give them an antidote.
It will take almost a month before you'll know which bottle is poisoned. Life expectancy for a guinea pig is 5 years, so you shouldn't have to worry about it dying from natural causes. However, if one does die from other causes, then you're guaranteed to serve the poisoned bottle at the party.
One bottle can be labeled #0 and no rodents need taste it.
(I got the same answer, if someone is counting.)
0000111000 = 32+16+8 = 56 btw
Ha! After all that I can't even add right... brain fart. Thanks for the catch....
And in the news...
"Several people were killed today when logician turned mad scientist, The Daddy, had a brain fart and accidentally served tainted bottle '#56' of wine to his guests."
Any lucky Irish logician/mad scientist could drink from 999 bottles, throw the last (obviously tainted) bottle away, and still have the time and sobriety to hire a piper for the party.
Another suggestion (although I don't have a solution):
Is there a fair way to keep score of who gets the right answers? It would be nice if people that know the answer, like The Daddy here, can get credit for the right answer without posting it so early that everyone else can claim they had the answer. [Hopefully my previous posts convince you I really did know the answer (and I used the binary system Daddy used), but realistically you don't have any way of knowing.]
I'm thinking of a % correct to allow newcomers to compete. Something weighted on # of answers but % correct also counts (so newcomers that happen to get one question right don't move to the top of the pack.)
A little competition is good for sites. I could send email to Rajesh, but some ideas from everyone else would be helpful, so I post it here.
I had fun with this on, here it goes.
At first my response was normal, 1000 thousand! But as I thought about it more; it wasn't fun.
The question stated “[I am a] logician turned mad scientist” (don’t know ‘bout you, but being logical and being mad is a dangerous mix).
There are 1,000 bottles and one of them are poisoned.
I have guinea pigs at my disposal, but I need to use the least bit.
The poison take little less then a month to bring an irrevocable reaction on the victim; leaving them to die a slow, horrible, painful death wondering if I can save them…
*evil laugh
I wouldn’t use any of the guinea pigs!
I would invite 1,000 people.
As a gift to my party, I would give them a bottle of wine (that I have been marking with codes for the last month), that corresponded to ticket they would receive upon entrance to this extravagant affair.
Each ticket corresponds with a subject matter (of course).
And I will eventually find which bottle was poisoned with using the least amount of guinea pigs…
I am mad and logical, right!?!
*evil laugh
I had fun with this on, here it goes.
At first my response was normal, 1000 thousand! But as I thought about it more; it wasn't fun.
The question stated “[I am a] logician turned mad scientist” (don’t know ‘bout you, but being logical and being mad is a dangerous mix).
There are 1,000 bottles and one of them are poisoned.
I have guinea pigs at my disposal, but I need to use the least bit.
The poison take little less then a month to bring an irrevocable reaction on the victim; leaving them to die a slow, horrible, painful death wondering if I can save them…
*evil laugh
I wouldn’t use any of the guinea pigs!
I would invite 1,000 people.
As a gift to my party, I would give them a bottle of wine (that I have been marking with codes for the last month), that corresponded to ticket they would receive upon entrance to this extravagant affair.
Each ticket corresponds with a subject matter (of course).
And I will eventually find which bottle was poisoned with using the least amount of guinea pigs…
I am mad and logical, right!?!
*evil laugh
Wouldn't the smallest number be zero, look for the open bottle of wine through the 1000 bottles and throw it away
I almost feel guilty busting out the samantics, but like steve said a few questions back: if raj is going to be so ambiguous in his questions, I think we ought to continue to put up different types of answers.
That said, here goes:
The poison is going to yield noticeable effects in "LITTLE LESS THAN a month," the question is how little? How many days are there between the poison results and the party if we start feeding rodents wine today? If it's mere hours, then the binary solution of ten is of course correct, however if it's something more, then the number of course is less, and I think you all know where I'm going with this one.
Let's say the poison takes effect 2 days before the party. Instead of using base 2 (binary) we can use base 3, and feed the guinea pigs wine cocktails in 2 waves, which will of course have 2 waves of symptom-showing, and in turn require 7 guinea pigs instead of ten. In this scenario if pigs 3 and 6 show signs of poisoning in the first wave, and pigs 2,5,and 7 show signs in the second wave, we get a solution of 0210212, which translates to bottle #590.
Similarly, if there are 3 possible days of death, we can use base 4 and knock our required number down to 5.
Ultimately, this number can continue to change until you as a logician feel that we're not using a number of days which is defined as "A LITTLE."
If "a little less" means something like "within a few days of the party", then you can't count on a rodent getting sick exactly on a particular day, so Daniel's idea doesn't work.
--
If any initial symptoms show before the rodent actually dies, you may be able to have even more waves (Daniel's explanation).
--
If the Mad Scientist is one of the testers, you can save one rodent. After all, it was his fault he forgot.
--
The problem assumes that an incredibly small amount of poison will kill (to allow a rodent to test 500 bottles at one sitting without bursting or dying from alcohol poisoning).
--
Having said that, I thought the level of detail in this question was fine. There comes a point when you just can't eliminate every concievable interpretation. As long as the intent of the problem is clear, I think Rajesh's posts are fine.
test succesfull :)
that first guy is a genius!!!!!!!!!!!!!!!
There isn't a puzzle, and you do not have to wait for a month! If you are a scientist... you are smarter then most! And if you are logical.. well then use logic!
If I did an experiment, there should be wine MISSING from one bottle, and it should be OPEN!
So I would find that bottle, discard it, needed ZERO rodents!
Which is the least amount of rodents.!!
:)
And there is one, meaning one poisoned bottle.
Not everything is to be so overlooked gentlemen!
and btw....
("You have a LOTS of "guinea pigs" at your disposal. The puzzle is to find the SMALLEST number of rodents that must drink from the bottles to find the poisoned one? ")
LOTS should be LOT, since there is "a" infront of it!
and I am just a house wife! lol
Thanks angie ! for the correction (lots to lot)
0 rodents: provided that you have enough money to buy 1000 bottles of wine as well as enough guinea pigs to test them (bearing in mind that guinea pigs need to be fed, watered, and otherwise taken care of), you've most certainly got enough money to purchase a Gas Chromatograph (GC) machine, which, using a small sample from each of the bottles, could correctly determine precisely which bottle had the poison. It most certainly could be done without harming any innocent rodents :-)
only one will die, because only one bottle is poisoned
Logically speaking the most simple answer tends to be the correct one. This being said, It would take 1000 guinea pigs. Each one could only be allowed to drink from one bottle due to the time restriction. Then wait and see.
Also ... If you are indeed "mad" you wouldn't care about having to sacrifice 1000 rodents.
GET TRASHED! :D
The bottle whKeeping in mind that if you have all of these rodents drinking your wine, you will have no full bottles of wine left to serve your party guests and will then have to buy more wine or invite less people, the more rodents try each bottle.
The bottke that is poisoned will have a broken seal and supposing it was a liquid poison will have more liquid in the bottle, so just throw away that bottle. Still no rodents.
why did i ruin the wine by poisoning it? that's just shameful but since i really don't care...now there should be a less than full bottle of wine somewhere and i'll test that one on the rodent first....if that one is not the poisoned one well then i do not wish to lose sleep over it and plan to blame the caterer anyway
ps i like the idea of the binaries...however i don't speak geek. *no offense, but binary is a forgotten language.....kudos on knowing it
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