Fixing three wrongly labelled fruit bags
Question
There are three bags: one holds only apples, one only oranges, and one a mixture of both. Their labels read "apples", "oranges" and "mixed", but every label is on the wrong bag. What is the smallest number of fruits you must draw to relabel all three bags correctly?
Short answer
One. Draw from the bag marked "mixed": its label is wrong, so it holds a single fruit type, and the fruit you see tells you which (say apples). The bag marked "oranges" cannot be oranges and cannot be apples, so it is the mix, and the bag marked "apples" must hold oranges.
Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 2.4 Application of Symmetry, 'Mislabeled bags', p.15; question and answer rewritten by SelfMadeQuant.com.
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