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 is definitely not mix, and not labeled “apple” either (since label is wrong).
  • So it must be the apple-only bag.

Step 2: Deduce the Others

Now you know:

  • The bag labeled “mix” actually contains only apples.
  • The bag labeled “apple” can’t be apples or mix → must be orange-only
  • The bag labeled “orange” must then be the mix.

Same logic holds if you’d pulled out an orange first.

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