Logical Puzzles
Medium
3 min
You have three boxes. One contains only apples, one contains only oranges, and one contains both apples and oranges. All three boxes are incorrectly labeled. You may pick exactly one fruit from exactly one box without looking inside. How can you correctly label all three boxes?
Hint
Start with the box labeled "Apples & Oranges".
Answer
Pick one fruit from the box labeled "Apples & Oranges".
Explanation
Because every label is incorrect, the box labeled "Apples & Oranges" cannot contain both types. If you draw an apple, that box must contain only apples. The box labeled "Oranges" cannot contain only oranges because its label is wrong, and it cannot contain apples because the apples box has already been identified, so it must contain both. The remaining box contains only oranges. The same logic works in reverse if the first fruit is an orange.
Step-by-Step Solution
1. Pick one fruit from the box labeled Apples & Oranges.
2. If it is an apple, that box is Apples.
3. The box labeled Oranges must then be Apples & Oranges.
4. The remaining box is Oranges.
5. Reverse the labels if the first fruit is an orange.
2. If it is an apple, that box is Apples.
3. The box labeled Oranges must then be Apples & Oranges.
4. The remaining box is Oranges.
5. Reverse the labels if the first fruit is an orange.