This classic logic puzzle tests your deductive reasoning with minimal information:

You have three bags:

  1. One has only apples
  2. One has only oranges
  3. One has a mix of both

Each is labeled (“apple,” “orange,” or “mix”) — but all labels are wrong.
You may reach into any bag and pull out one fruit at a time (without looking).

Goal: Determine the correct contents of all three bags with the fewest possible pulls.

Step-by-Step Strategy

Step 1: Pick the Bag Labeled “Mix”

Since all labels are wrong, the bag labeled “mix” must contain only apples or only oranges.

Reach into the bag labeled “mix” and pull out one fruit.

Let’s say you pull out an apple.

Then you know:

  • This bag cannot be the mix (because its label is wrong).
  • Since it must be a single-fruit bag and you pulled an apple, it is the apple-only bag.

Step 2: Deduce the Others

Now you know the bag labeled “mix” actually contains only apples.

What about the bag labeled “apple”?

  • It cannot contain apples (since all labels are wrong, and we already found the apple bag anyway).
  • Could it contain the mix? If it did, the third bag (labeled “orange”) would have to contain only oranges. But we know all labels are wrong, so that’s impossible!
  • Therefore, the bag labeled “apple” must contain only oranges.

By elimination, the third bag (labeled “orange”) must contain the mix.

Final Answer

Pull one fruit from the bag labeled “mix.”
If it’s an apple → that bag is apples.
Use the “all labels wrong” rule to deduce the other two.

Reference