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?
Explanation:
Let the bottles be A, B, C and D.
We first mix equal quantities of A and B and test the mixture.
Case 1: If any one of A or B contains 20% impurities, test will detect the impurity. Then we check A for impurity. If impurity is detected then A contains I else B contains I. ∴ 2 tests are required to detect I.
Case 2: If none of A or B contains impurities, test will not detect the impurity. This means one of C or D contains I. Then we check C for impurity. If impurity is detected then C contains I else D contains I. ∴ 2 tests are required to detect I.
In both cases 2 tests are required to detect I.
Hence, 2.
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