### Question:

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. You are allowed to open just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?

### Answer:

**Let’s find out together below**

### Explanation

Imagine three mysterious boxes—Box A, Box B, and Box C. One box contains only apples, another holds oranges, and the third has a mix of both apples and oranges. However, all the labels have been mistakenly switched, leaving you to wonder which fruit is in which box.

But here’s the catch—you are allowed to open just one box and take out a single piece of fruit. Without peeking, without any clues other than the fruit you hold in your hand, you must decipher the contents of all three boxes. Sounds like quite the challenge, doesn’t it?

Now, let’s dive into the clever solution. All you need to do is reach for the box labeled “Apples + Oranges.” Grab a fruit from inside, and take a close look. What do you see? Is it an apple or an orange?

Here’s where the magic happens. Depending on the fruit you’re holding, you can immediately label all three boxes correctly. Let’s break it down step by step:

##### If you picked an Apple:

- Change the label on the box you opened (“Apples + Oranges”) to “Apple.”
- There are two boxes left, labeled “Apples” and “Oranges”. But since you already labeled another box as “Apples”, we are now left with labeling these two boxes correctly as “Oranges” and “Apples and Oranges”. Since the initial labels were wrong, the one previously labeled as Oranges has only the option of going with “Apples and Oranges” as its correct label.
- The box previously labeled “Oranges” should now be relabeled as “Apples and Oranges.”
- Lastly, the remaining box is the one that was initially labeled as “Apples”, so label it as “Oranges.”

**If you picked an Orange:**

- Change the label on the box you opened (“Apples + Oranges”) to “Oranges”.
- There are two boxes left, labeled “Apples” and “Oranges”. But since you already labeled another box as “Oranges”, we are now left with labeling these two boxes correctly as “Apples” and “Apples and Oranges”. Since the initial labels were wrong, the one previously labeled as “Apples” has only the option of going with “Apples and Oranges” as its correct label.
- The box previously labeled “Apples” should now be relabeled as “Apples + Oranges.”
- Lastly, the remaining box is the one that was initially labeled as “Oranges”, so label it as “Apples.”

By analyzing just one fruit, you can successfully unveil the true identity of each box. It’s like being a fruit detective, putting your deduction skills to the test and coming out victorious! So, the next time you encounter a tricky labeling situation, remember this clever solution and solve it like a pro. Happy puzzling, my fellow detectives!