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Three mislabelled fruit bags

Question

Three bags hold, respectively, only apples, only oranges, and a mixture of both. They carry the labels "apple", "orange" and "mix", but you are told every label is wrong. You may take fruit out of bags one at a time and look at it. What is the smallest number of fruits you must draw to be certain of every bag's contents?

Short answer

1. Draw from the bag labelled "mix": since its label is wrong it is pure, so one fruit tells you whether it is the apple or orange bag. Say it is apples. The bag labelled "orange" cannot be oranges and cannot be apples, so it is the mixture, and the bag labelled "apple" holds the oranges.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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