You have 3 jars that are all mislabeled. The jars are labeled as follows:

• One jar is labeled "Apples".
• One jar is labeled "Oranges".
• One jar is labeled "Apples and Oranges".

However, you know that none of the labels are correct. Each jar contains either apples, oranges, or a mix of both, but the labels are incorrect. Your task is to determine the correct contents of each jar by picking just one fruit from only one jar.

Objective:
Correctly label each jar with its actual contents by making the fewest number of picks.

Solution

This puzzle can be solved by using logical deduction based on the information provided. The key is to pick from the jar labeled "Apples and Oranges" because it must contain only one type of fruit.

Step-by-Step Solution for Mislabeled jars Puzzle:

Step 1: Understand the Mislabeling

Since all the jars are mislabeled:

• The jar labeled "Apples" does not contain only apples.
• The jar labeled "Oranges" does not contain only oranges.
• The jar labeled "Apples and Oranges" does not contain a mix; it contains either only apples or only oranges.

Step 2: Pick One Fruit from the "Apples and Oranges" Jar

Pick one fruit from the jar labeled "Apples and Oranges":

• If you pick an apple, you now know that this jar contains only apples.
• If you pick an orange, you now know that this jar contains only oranges.

Step 3: Relabel the Jars

Now that you know the contents of the jar labeled "Apples and Oranges," you can correctly relabel the jars:

• Suppose you picked an apple from the "Apples and Oranges" jar. This jar actually contains only apples.
• The jar labeled "Apples" must be mislabeled, so it can’t contain only apples. Since it’s mislabeled and the "Apples and Oranges" jar now correctly contains only apples, the jar labeled "Apples" must contain only oranges.
• The remaining jar, labeled "Oranges," must then contain the mixed fruits, since the labels are incorrect, and the other two jars have been correctly identified.

Step 4: Final Labeling

Based on the deduction:

• The jar initially labeled "Apples and Oranges" now contains apples.
• The jar initially labeled "Apples" now contains oranges.
• The jar initially labeled "Oranges" now contains a mix of apples and oranges.

Final Answer

To correctly label the jars:

1. Pick one fruit from the jar labeled "Apples and Oranges."
2. Based on what you pick, relabel the jars:
   • The "Apples and Oranges" jar is relabeled based on the picked fruit.
   • The jar labeled "Apples" is relabeled with the other single fruit.
   • The jar labeled "Oranges" is relabeled as the mixed jar.