mixed up marbles

Question

three boxes contain black and white marbles. one box has all blacked marbles,one has all white marbles,and one has a mixture of black and white marbles. All three boxes are mislabeled. By selecting only one marble,determine how you can correctly lable the boxes

Answer 1

Label Mixed   Contains B & W

Label Black   Contains W only

Label White   Contains B only

 

Case 1.  You reach into Black and get white; therefore this is not Mixed..it's really White &

the one labeled Black is really Mixed (i.e. mislabeled) & the one labeled Mixed is really Black (also mislabeled).

 

Case 2.  If instead you reached into the Mixed Bag, you would find either black or white, which identifies this as that particular color. For the sake of argument, say this  produced a black marble--therefore this improperly labeled Mixed is actually White.

 

Case 3. similar to case 1, only you reach into White, get black (because mislabeled)--leaving mislabeled Black which must be mixed and Mixed which must be white.

And that leaves two bags, both mislabeled: White must be mixed & White must be black.

 

So regardless of which mislabeled bag you try, it only takes one draw!