The Bottle Of Wine
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?
The answer is 10.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
If one labels all the different wines with their number in binary, one can then assign a prisoner to each digit in such a number. For example one prisoner would be assigned the 1's digit, one to the 2's digit, one to the 4's, and so on. The prisoners would then drink every wine with a one in their assigned digit place. Which prisoners die would then allow one to reconstruct the number uniquely. One thus only requires as many prisoners as there are digits in the binary representation of 1000, which is 10.