There are three bins: one with 30 apples, one with 30 oranges, and one with 15 of each. Each is labeled "apples," "oranges," or "mixed." Given that all three labels are wrong, how many pieces of fruit must you look at to determine the correct labels?
1. **Identify the problem constraints:**
   - There are three bins, each labeled incorrectly.
   - One bin contains only apples, one contains only oranges, and one contains a mix of both.
   - The labels are "apples," "oranges," and "mixed."

2. **Pick a fruit from the bin labeled "mixed":**
   - Since the labels are all wrong, the bin labeled "mixed" cannot actually contain a mix of apples and oranges. It must contain either only apples or only oranges.

3. **Determine the content of the bin labeled "mixed":**
   - Suppose you pick a fruit from the bin labeled "mixed" and it is an apple. This means the bin labeled "mixed" actually contains only apples.

4. **Relabel the bins based on the first observation:**
   - Since the bin labeled "mixed" is actually the apple bin, the bin labeled "oranges" cannot contain only oranges (because all labels are wrong). Therefore, it must be the mixed bin.
   - The remaining bin, which is labeled "apples," must then be the orange bin.

5. **Verify the logic:**
   - If the fruit picked from the bin labeled "mixed" is an apple:
     - The bin labeled "mixed" is actually the apple bin.
     - The bin labeled "oranges" is the mixed bin.
     - The bin labeled "apples" is the orange bin.
   - If the fruit picked from the bin labeled "mixed" is an orange:
     - The bin labeled "mixed" is actually the orange bin.
     - The bin labeled "apples" is the mixed bin.
     - The bin labeled "oranges" is the apple bin.

6. **Conclusion:**
   - By picking just one fruit from the bin labeled "mixed," you can determine the correct labels for all three bins.

The final answer is $\boxed{1}$.