Drinking with prisoners
You are a prison guard and you are looking after 10 prisoners. There are n-1 bottles of grape juice and 1 bottle of vine. You have to determine which one is the bottle of vine. Here are the rules:
- You can't make it by drinking, smeling or other.
- If anyone drinks even a single drop of vine, he will wake up very drunk.
- You have only one night to discover.
*Prisoners can drink infinite amount of juice/vine, but you (guard) can't drink anything :)
Find the maximum n, so you can be sure which one is the bottle of vine.
The answer is 1024.
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1 solution
First bottle you don't give them and if no one is drunk that was the first one. Second give to first prisoners, third to second... that's trivial. Then next one you give to first pair of them, and you continue giving it to pairs than to 3 of them, 4 of them... And if you have m result is:
∑ i = 0 m ( i 2 ) = 2 m
In this case it's
m = 1 0
n = 1 0 2 4
Consider prisoners as a set of 10 elements. Give one bottle to every subset of this set (if it is an empty set, do not give the bottle). Based on which group of prisoners (subset) is drunk (or not in case you kept the bottle of wine) if it is an empty set.The number of subsets of every set is:
2 m