There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?
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Answer: B
To solve this puzzle, we must use the crucial piece of information: all three boxes are incorrectly labeled.
Let the actual contents of the boxes be Apples (A), Oranges (O), and Both (A+O). The labels on the boxes are "Apples", "Oranges", and "Apples and Oranges".
Why we should open the box labeled "Apples and Oranges":
Since this box is incorrectly labeled, it cannot contain both apples and oranges. It must contain either only Apples or only Oranges.
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Scenario 1: We pull out an Apple.
- Since the box cannot contain both, the box labeled "Apples and Oranges" must contain only Apples.
- The remaining contents to assign are Oranges and Both to the boxes labeled "Apples" and "Oranges".
- Since the box labeled "Oranges" cannot contain only oranges, it must contain Both.
- This leaves the box labeled "Apples" to contain only Oranges.
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Scenario 2: We pull out an Orange.
- The box labeled "Apples and Oranges" must contain only Oranges.
- The remaining contents to assign are Apples and Both to the boxes labeled "Apples" and "Oranges".
- Since the box labeled "Apples" cannot contain only apples, it must contain Both.
- This leaves the box labeled "Oranges" to contain only Apples.
In both scenarios, we uniquely determine the contents of all three boxes by inspecting just one fruit from the box labeled "Apples and Oranges".
Why other options fail:
If we open the box labeled "Apples", its actual content is either "Oranges" or "Both". If we pull out an orange, we still cannot determine whether the box contains only oranges or both fruits, leading to ambiguity.
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