You have three closed boxes with these labels: “Apples”, “Oranges” and “Mixed”. You know all three labels are wrong. You can take a single fruit out of a single box, without looking inside. How do you find out the correct contents of the three boxes?
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The three mislabeled boxes
Here everything depends on taking seriously a very short sentence: all three labels are wrong. From there, a single well-chosen extraction is enough for the rest to fall under its own weight.
Hints
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- Since all three labels are fake, there is one especially informative box.
- The box rotulada “Mixed” no can ser mixed.
- A single fruit taken from that box fixes its contents; the other two are corrected by discard.
Solution
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Answer: Take a fruit out of the box labeled “Mixed”. Explanation: Since all the labels are fake, that box cannot be mixed: it has to contain only one fruit. - If an apple comes out, that box is really the one with apples.
- If an orange comes out, that box is really oranges. From there, the other two are determined by discard, remembering that their labels are also false. A single extraction is enough.
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