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

Explanation:

all bags are mislabeled. that means, whatever is written on either of the 3 bags, is wrong.

so, the bag labeled "green" is NOT the one with 2 green apples. the one labeled "red" is NOT the one with 2 red apples.

and - my favorite - the one labeled "red/green" is NOT the one with the mixture.

so, we pick one apple from the bag that is currently (mis-)labeled as "red/green".

as it cannot be the mixed bag, it must be one of the pure color bags.

whatever color shows up, we know this is the bag with 2 apples of that color.

then the bag that was labeled with that color must be the other pure color (if it were the mixed bag, it would mean that the third bag was labeled correctly, which is not the case). and then the third bag is the mixed one.

for example :

we get a red apple in our first pick.

so, the bag, that was originally (but wrongly) labeled as "red/green" gets the label "red".

then the bag with the original (but again wrong) label "green" gets now the label "red".

and the third bag with the original (but wrong) label "red" gets the "red/green" label.

if the first apple is green, then the same principle just with reversed colors applies.