In the mislabelled baskets puzzle, which basket should you sample from to deduce the correct labels?

• A. From the basket labeled Apples
• B. From the basket labeled Oranges
• C. From the basket labeled Apples and Oranges
• D. From the basket labeled Mixed

Answer: (C)

You start with the idea that each label is wrong. The basket labeled Apples and Oranges cannot actually contain both fruits, so it must be pure—either apples or oranges. Sampling from that basket gives a definite clue about its actual contents with just one fruit.

If you draw an apple from the mislabeled mixed basket, that basket is apples-only. That immediately forces the other two baskets: the one labeled Apples cannot be apples (it’s mislabeled), so it must be either oranges-only or mixed. But the basket labeled Oranges also cannot be oranges, so it cannot be oranges-only; it must be the remaining option, which is the mixed basket. The last basket then must be oranges-only. If instead you draw an orange from the mislabeled mixed basket, you swap the roles: that basket is oranges-only, the one labeled Oranges becomes apples-only, and the one labeled Apples becomes mixed. In either case, a single sample from the basket labeled Apples and Oranges unlocks the full correct labeling of all three baskets.

That’s why this starting choice is the best: it uses the mislabeling constraint to identify one basket’s true contents immediately, which then propagates to determine the others.