Math  /  Discrete

QuestionExample 1: The Boxes There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose. How can you label the boxes correctly?

Studdy Solution

STEP 1

1. Each box is labeled incorrectly.
2. You can pick one fruit from one box to determine the correct labeling.

STEP 2

1. Choose a box to pick a fruit from.
2. Use the information from the fruit to determine the correct labels.
3. Relabel the boxes correctly.

STEP 3

Choose the box labeled "APPLES AND ORANGES" to pick a fruit from. Since all boxes are labeled incorrectly, this box cannot contain both apples and oranges.

STEP 4

If you pick a fruit from the "APPLES AND ORANGES" box and it is an apple, then this box must contain only apples. If you pick an orange, then this box must contain only oranges.

STEP 5

Assume you picked an apple from the "APPLES AND ORANGES" box: - The "APPLES AND ORANGES" box is actually the "APPLES" box. - The box labeled "ORANGES" cannot contain only oranges, so it must be the "APPLES AND ORANGES" box. - The remaining box labeled "APPLES" must be the "ORANGES" box.
If you picked an orange: - The "APPLES AND ORANGES" box is actually the "ORANGES" box. - The box labeled "APPLES" cannot contain only apples, so it must be the "APPLES AND ORANGES" box. - The remaining box labeled "ORANGES" must be the "APPLES" box.
The correct labeling is determined by the fruit picked from the "APPLES AND ORANGES" box.

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