In front of you are three boxes. One contains only apples, one contains only oranges and one contains a mix of apples and oranges. Each box is labeled, like this:
- Box 1: “apples”
- Box 2: “oranges”
- Box 3: “apples & oranges”
Unfortunately, all three boxes are mislabeled. That’s where you come in – you’re going to help me fix those labels.
Here’s the challenge: You get to choose one, and only one, box. I will remove a randomly selected piece of fruit from your chosen box and show it to you (so you can tell if it’s an apple or an orange). After that, you will be able to accurately and definitively relabel all three boxes.
Choose wisely, grasshopper. If you manage to solve this puzzle, leave me a comment with your solution. Good luck and don’t forget to eat your fruit!
Solution: If you choose box 1 or 2, you may be in trouble. For example, suppose you choose box 1 (the box labeled “apples”) and you see an orange – then you won’t know if that box contains only oranges or a mix of apples and oranges. You face a similar dilemma if you choose box 2 (the box labeled “oranges”) and you see an apple.
Let’s see what happens if you choose box 3 (the box labeled “apples & oranges”). Let’s assume you see an apple drawn from box 3. You therefore know box 3 contains only apples. Why? It can’t contain a mix (because you already know it’s mislabeled) and it can’t contain only oranges (because you now know it contains at least one apple). There’s only one possibility left: box 3 contains only apples.
Now think about box 2, which is labeled “oranges”. Since we know it’s mislabeled, it can’t contain only oranges and we just discovered that box 3 contains only apples so box 2 must contain a mix of apples and oranges. By process of elimination, we then know that box 1 contains only oranges.
So, if the fruit removed from box 3 is an apple, then the correct labeling is as follows:
- Box 1: “oranges”
- Box 2: “apples & oranges”
- Box 3: “apples”
By a very similar process, the details of which I’ll leave as an exercise to the reader :), if the fruit removed from box 3 is an orange, then the correct labeling is as follows:
- Box 1: “apples & oranges”
- Box 2: “apples”
- Box 3: “oranges”
There you have it – if you wisely choose the box with the mix of apples and oranges for your free sample, everything falls into place. And if you worked that out for yourself, orange you glad I didn’t tell you the answer? Sorry, I couldn’t resist.
Hats off to Muzaffer, Maurice, Al, Simon and Kimberly for finding the answer!