Crates Puzzle

You can also solve this with a chart showing what each crate can contain.

The crates' content cannot match their labels, so there are two possibilities for each crate?

AO	A	O
A	O	A
O	AO	AO

If you pick an apple from the crate labelled "Apples and Oranges", you can eliminate oranges under it. You know this crate has apples.

AO	A	O
A	O	A
	AO	AO

This tells you that the crate labelled "Oranges" must not have apples.

AO	A	O
A	O
	AO	AO

Now you know the crate labelled "Oranges" must have apples and oranges. Therefore, the crate labelled "Apples" must not.

AO	A	O
A	O
		AO

The crate labelled "Apples" must have oranges.