SOLUTION: There are three baskets sitting next to each other on a high shelf so that you cannot see the contents of any basket. Under the first basket is a sign that says APPLES. Under the s

Question 178983: There are three baskets sitting next to each other on a high shelf so that you cannot see the contents of any basket. Under the first basket is a sign that says APPLES. Under the second basket is a sign that says ORANGES, and under the thrid basket is a sign that says APPLES AND ORANGES. Each basket is incorrectly labeled. One basket contains all apples, one all oranges, and one a combination of apples and oranges. Is it possible to reach up on the shelf and without looking into any of the baskets select one piece of fruit and on the basis of knowing what that piece of fruit is correctly label all three baskets? Explain your reasoning.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Since ALL of the baskets are incorrectly labeled, you know without testing anything that:

The basket labeled APPLES actually contains all oranges or a mixture.

The basket labeled ORANGES actually contains all apples or a mixture.

The basket labeled APPLES AND ORANGES contains either all apples or all oranges.

If you select one piece of fruit from the basket labeled APPLES AND ORANGES and:

If it is an apple, you know that the basket labeled APPLES AND ORANGES must contain all apples, and therefore the basket labeled ORANGES can only contain the mixture, and the basket labeled APPLES must contain all oranges.

But if it is an orange, you know that the basket labeled APPLES AND ORANGES must contain all oranges, and therefore the basket labeled APPLES can only contain the mixture, and the basket labeled ORANGES must contain all apples.

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