The Poisoned Party Havoc
You have arranged an important party, where you invited the most important people, celebrities, and famous people. Just an hour before the commencement of party you come to know that exactly one of 1000 wines you have in stock is poisoned .
You cannot run the event without wines, at the same time you cannot dare to kill anyone with a poisoned bottle of wine.
Luckily, you are given a bunch of 500 rats to determine the poisoned wine bottle.But here's the catch, it will take exactly 1 hour for the poison to work , and you cannot test it on anything else than rats . Assuming that each rat has the ability to drink all bottles of wine, you have a very good count and placement of rats in a separate chamber to differentiate. What is the least number of rats you require to get the accurate wine of bottle ?
Hint : Try to generalize this for number of bottles, and one poisoned.
Tip : Try finding the same for 2 bottles, 1 poisoned. 3 bottles, 1 poisoned, and so on.
The answer is 10.
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1 solution
You got n rats. You want them to drink different bottles in such a way that you can find which bottle is poisoned by seeing which combination of rats is poisoned. The number of combinations of n rats = ( 1 n ) + ( 2 n ) + . . . . . . + ( n n ) = 2 n − 1 . ( 2 n − 1 ) is first greater than 1 0 0 0 when n = 1 0 .
We have ( 1 n ) + ( 2 n ) + . . . . . . + ( n n ) because you can have 1 rat for a drink, 2 rats, and so on.