# Math forum

 King and the poisoned wine bottle Options
TomasT
 #1 Posted : Friday, March 18, 2011 2:42:10 PM
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A ruthless king has a cellar of 1,000 bottles of very expensive wine. An
assassin infiltrates the wine cellar to poison the wine. Fortunately the
king’s guards catch the plotter after she has poisoned only one bottle.
Unfortunately, the guards don’t know which one of the bottles is poisoned.

The poison is so strong that no amount of dilution will make it safe to
drink. Furthermore, it takes one month to have an effect. The ruthless
king decides he will get some of the prisoners in his dungeons to test the
wine. But he has only 10 prisoners.

King's advisors tell him that's enough to find the poisoned bottle within a month.

How do they know that?

jainmanali
 #2 Posted : Saturday, March 19, 2011 1:07:41 PM
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may be der would be 100 rows n ten columns n wer he would have been standing dat row would be noted n den dose ten bottles would be given to detect which 1 is poisoned

drachen
 #3 Posted : Saturday, March 19, 2011 4:47:10 PM
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Take 10 Bowls. In each bowl pour a drop from each of 100 bottles. Each bowl will have 100 drops. (The poison is so strong that no amount of dilution will make it safe to drink.) Feed each prisoner a bowl. One prisoner is affected, so you know it's in that batch of bottles.
Give each of the 9 remaining prisoners each a bowl containing a small amount of 11 of those 100 remaining bottles. One bottle will remain unused at this step, If no prisoners are affected, that is the poisoned bottle. If one is, you've narrowed it down to a batch of 11, and have 8 remaining prisoners. Now you can feed a bottle to a prisoner until one dies, and there's your bottle.
I hope that's clear.

jainmanali
 #4 Posted : Sunday, March 20, 2011 10:26:23 AM
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but as u are saying in the 1st case...... but to know which prisoner is affected it takes 1 month n ur work shud be completed in dat 1 month period of tym....

 #5 Posted : Tuesday, March 22, 2011 1:43:23 PM
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each prisoner is given a drop of wine from 100 bottles with a time interval, say 2 mins or so.. and the times r recorded for each botl nd also d person who drinks frm dat bottl.

As it takes a month to get affected by dat wine,
exactly after a month, time wen d person gets affected is re-chekd wid d bottle dat he drank.

Jaspreet
 #6 Posted : Friday, March 25, 2011 11:06:49 AM
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make a matrix of 100 bottles with each row and column having 10 ,10 bottles. then allow the 10 men to drink wine first row wise and then column wise. in this way you can find the exact bottle as max 2 got dead, then by knowing their position you will get to know the exact coordinates of the bottle.

 #7 Posted : Friday, March 25, 2011 2:04:18 PM
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@ jaspreet: but it takes a month to get affected by d wine..!

Jaspreet
 #8 Posted : Friday, March 25, 2011 2:52:26 PM
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@madhuri- yup .. as per the condition " within a month " this one is following that as the final result will come exatly at the end of the month.

i read your's too. in it you took minimum 20 minutes more than a month if you take 2 min of gap.

Elcaco5
 #9 Posted : Monday, March 28, 2011 10:48:32 PM
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I cant believe i did it! lol do it with binary!!   with ten prisoners ( ten bits) how many combinations can you do?

512 256 128 64 32 16 8 4 2 1

now start counting binary feeding the wine to the prisoners until 1000....

0000000001 - first bottle
0000000010 -  second bottle
0000000011 - third bottle and so on...

now depending on the combination of prisoners who die will be the bottle poisoned!! =)

jorgea
 #10 Posted : Monday, November 12, 2012 7:39:32 PM
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Thanks for posting this fun riddle math probem.

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king_cobra1212
 #11 Posted : Saturday, January 12, 2013 1:51:27 PM
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hahaha , a nice and mind blowing maths puzzle.

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