There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

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10 months ago

Question :

There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

Answer : 2

Explanatory Answer

We have 3 bottles with 100% P and 1 bottle with 20% impurity
Let’s select 2 bottles at random and mix them completely, we will end up with 2 cases
Case 1 – Both bottles test pure, then we take one of these bottles and test it with one of the two
remaining bottles. It will either come out as pure again or it will show presence of impurity.
We need 2 tests in this case.
Case 2 – We find an impurity presence in one of the bottles, again we take one of the 2 bottles
and test it with 1 of the 2 remaining bottles. It will It will either come out as pure again or it will
show presence of impurity.
We need 2 tests in this case too.
Thus we need a minimum of 2 tests to identify the bottle with the impurity.