Mislabeled Jars | Puzzles for Interview - Interview Preparation PDF Download

Problem Statement

There are 3 jars, namely, A, B, C. All of them are mislabeled. The labels on each of the jars are as follows:

• Jar A: Candies
• Jar B: Sweets
• Jar C: Candies and Sweets (mixed in a random proportion)

You can put your hand in a jar and pick only one eatable at a time. The shape of the candies and sweets are identical, and there is no way to differentiate them by touching alone. Your task is to determine the minimum number of eatables that must be picked in order to label the jars correctly.

Solution

• Start by picking one eatable from Jar A. Since Jar A is mislabeled, you know that it cannot contain only candies. It must contain either only sweets or a mix of candies and sweets.
• If you pick a candy from Jar A, you can deduce that Jar A must contain the mix of candies and sweets. This is because Jar A cannot contain only candies (as it is mislabeled) and it also cannot contain only sweets (since you picked a candy from it).
• If you pick a sweet from Jar A, you can deduce that Jar A must contain only sweets. This is because Jar A cannot contain only candies (as it is mislabeled) and it also cannot contain a mix of candies and sweets (since you picked a sweet from it and Jar C is mislabeled).
• Now that you know the contents of Jar A, you can easily determine the contents of Jar B and Jar C by process of elimination. For example, if Jar A contains the mix of candies and sweets, then Jar B must contain only candies and Jar C must contain only sweets (since all jars are mislabeled).

Conclusion

By picking only one eatable from Jar A, you can correctly label all three jars. This is the minimum number of eatables that need to be picked to solve the puzzle.