LOCUS Blog An emperor and a party!
You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You’ve got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.
You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.
You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.
What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
~ solution in two weeks
Pls see this link
http://www.goiit.com/posts/list/games-puzzles-and-quizzes-an-emperor-s-party-76604.htm
The least number of prisoners required would be 10 !
Solution :
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1) Label the wine bottles 1-1000 (Let this “number” be called P).
2) Write the corresponding binary number of each P.
3) Now,there would be a max. of 10 bits till the highest number.
4) Now, Let each prisoner correspond to drinking of wine of each bit of the binary numbers (Therefore there will be 10 such prisoners)….
EXAMPLE :
Let there be only 10 Bottles,
Bottle No. | Binary Code |
A|B|C|D
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
10 1 0 1 0
Now Let there be 4 prisoners A,B,C & D respectively.Now each prisoner will drink the wine of bottles which are assigned for him (i.e which are marked as ‘1′ in his column; eg : ‘A’ will drink wine from bottles 8,9 & 10 ; ‘B’ from 5,6,7 etc).
Thus by the combinations of death of prisoners,the bottle can be found out(eg : If A and C are the only prisoners to die,then its the 10th bottle …etc etc.).
Therefore 10 prisoners would be able to test (2^10 = 1024 bottles)…Therefore they can easily test 1000 bottles….
yup! that is the correct solution