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The three mislabeled boxes

Timeless ingenuityLevel 1 · Starter · ●○○○○

You have three closed boxes with labels: "Apples", "Oranges" and "Mixed". You know all three labels are wrong. You can take only one fruit from a single box (without looking inside first). How do you reliably correct all three tags?

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Hints

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  1. Take a fruit out of the box labeled “Mixed.”
  2. Since the “Mixed” label is also false, that fruit tells you exactly what that box contains.
  3. With this data fixed, correct the other two labels by discarding so that they all look good.

Solution

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Answer: Take a fruit out of the box labeled “Mixed”.
Three mislabeled boxes: deduction from a single draw
Explanation:
Since all the labels are incorrect, the “Mixed” box cannot be mixed: it must contain only one fruit.

  1. You take a fruit from that box.
  2. If apple comes out, that box is “Apples”; If it comes out orange, that box is “Oranges”.
  3. With that, the other two are deduced by discarding, respecting that their labels were also false.

Example: if in “Mixed” there is an apple, we already know that that box is “Apples”.
The box labeled “Oranges” cannot be “Oranges” nor can it be “Apples” (already assigned), so it is “Mixed”.
The rest remains as “Oranges”.

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