Question

Each of these labelled bags contains two apples.

One bag contains two green apples, another two red apples and the third one green and one red apple.


All three bags are mislabelled. You may look at only one apple from any one of the bags.


Which bag should you select from to be sure you can determine the content of all three bags?


- Bag 1 ?


-Bag 2 ?


-Bag 3 ?

Answer 1

bag 3

Explanation:

Let's call the labels "green", "red", and "mix".

Pick mix for two reasons :

1. First, it's not mixed so whatever color you pick is the color of the pair.
2. Also, if you pick from either of the other two, you can't know if it's a mixed bag or not.

So, let's pretend you pick a red out. Move the label red to the bag. This must be true - cannot be a mix.

Now, you have the mix label in your hand, one bag with a label (green), and one bag without a label (previously red).

Since all bags mislabeled to begin, move the green label to the blank bag - since this label must be wrong.

Put the mix label on the remaining bag.