There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

Since all three boxes are incorrectly labelled:

1. Choose the box labelled 'Apples and Oranges'.

2. Since it is mislabelled, it cannot contain both fruits; it must contain exclusively apples or exclusively oranges.

3. If you draw an apple, then this box contains only Apples.

   • Now, the box labelled 'Oranges' cannot contain oranges (since it's mislabelled) and cannot contain apples (since they are in the first box). Thus, it must contain Apples and Oranges.

   • The remaining box labelled 'Apples' must contain Oranges.

4. A completely symmetric logic works if an orange is drawn.

Therefore, opening the box labelled 'Apples and Oranges' uniquely determines the contents of all three boxes.

Hence, option (B) is correct.