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February 21, 2018, 05:12:11 PM
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: Find the poisoned bottle!  ( 4761 )
« : July 09, 2007, 06:19:39 PM From Ria»

Find the poisoned bottle!

You are the owner of a renowned Wine catering services. You have a big offer of catering service to a party for the King of your place. So they have ordered a thousand bottles of wine.
You are obviously so happy about it and worked hard to arrange the complete order. But suddenly tragedy occurred, one of your employee accidentally mixes a poisoned bottle with the wine bottles in the container. Being the same type of bottle you are not able to distinguish it without drinking and the death occurs in 24 hours after drinking.
The ceremony being tomorrow, the King will order for your execution, if the order is not completed. Now you have to find a solution to it. You cannot have another 1000 bottles and you have to figure out that bottle. The King takes care of this situation and tells you that you have 1000 prisoners to let them drink the bottles and find out the poisoned bottle.

Find the minimum number of prisoners required to find the poisoned bottle among 1000.

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« #1 : August 08, 2007, 06:17:15 PM From piyush»

its 64...isnt it??
« #2 : August 08, 2007, 07:51:18 PM From Ria»

64 is not right. But explain the reasoning which led you to that answer. It will help others who don't have a clue on how to go about it.
« #3 : August 14, 2007, 07:31:22 PM From Sudarshan»

Is it 9...?

Its by making the wine bottles into two lots (say 500, 500 initially) and mixing a small dosage of wine from each bottle in a lot and taste it to one prisioner.

thus 500 further becomes 250, 125, 62, 31, 16, 8,4 and 2
« #4 : August 14, 2007, 08:12:42 PM From atul»

The signal I get by giving person poison is either he lives or dies so get a binary result. I can assign each of 1000 drinks a unique binary number using 10 digits. so I need 10 persons.
assign drinks the number from
0000000001 to 1111101000.
I will give all drinks who has 1 as first digit, to person 1
and all drinks who has 1 as 2nd digit, to person 2

As all the drinks are uniquely identified hence each drink will kill a unique combination of people and I have 1 to 1 mapping back to the sets of drink.

Though a easy way can be put 1 for the digit when person died and zero when he survives and you have a 10 digit number identifying the poisoned drink
« #5 : August 14, 2007, 10:23:55 PM From Sudarshan»

even my previous answer is wrong...i forgot the case that it takes 24hrs to die...
« #6 : August 15, 2007, 11:29:24 PM From spazinvader»

Isn't this strategy similar to the "hamming code error detection" method?
« #7 : August 17, 2007, 08:52:07 PM From Shrinidhi»

Great answer Atul.  8)
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