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Logic puzzle 001.sol

This is a logic problem using the power of deduction.

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Step 1: Identify that all the labels are wrong

Since the puzzle states that every basket is labeled incorrectly, the contents of each basket will not match its label.

  • The basket labeled "Apples" does not contain only apples.
  • The basket labeled "Oranges" does not contain only oranges.
  • The basket labeled "Apples and Oranges" does not contain a mixture of both apples and oranges.

Step 2: Choose the "Apples and Oranges" basket

Since all the labels are wrong, this basket cannot contain both apples and oranges. It must contain only apples or only oranges.

Step 3: Pull out one fruit from the "Apples and Oranges" basket

Reach into the basket labeled "Apples and Oranges" and pull out a single fruit. There are two possible outcomes: - If you pull out an apple, this means the basket contains only apples. - If you pull out an orange, this means the basket contains only oranges.

Let’s assume you pull out an apple for the sake of this explanation.

Step 4: Relabel the baskets based on the fruit you pulled

  • Since you pulled out an apple, the basket labeled "Apples and Oranges" must contain only apples.
  • This means the basket labeled "Apples" cannot contain only apples (since its label is wrong), and it also cannot contain only oranges (because no two baskets can have the same type of fruit). Therefore, the basket labeled "Apples" must contain only oranges.
  • The basket labeled "Oranges" must be the one with the mixture of apples and oranges (because it’s the only option left).

Solution

Here’s the correct labeling of the baskets:

  • The basket labeled "Apples and Oranges" contains only apples.
  • The basket labeled "Apples" contains only oranges.
  • The basket labeled "Oranges" contains both apples and oranges.

This method works because you’re guaranteed that all labels are incorrect, and pulling one fruit reveals enough information to correctly deduce the contents of each basket.