Yoak: Labelous

I have in front of me three boxes.  One contains all red balls.  One contains all blue balls.  The third contains a mixture of red and blue balls.  The three boxes are labeled as to their contents, and the three labels correspond to possible contents of a box, but you know that the labels are all misplaced.

You may draw one ball (at random) out of a box of your chosing.  After that, you must rearrange the labels so that they correctly reflect the contents of the boxes.  How do you do this?

1. Mitch Besser said,

May 20, 2009 at 4:36 pm

I think the trick here is that the “labels are all misplaced”.

Start with the box marked as mixture.  You know this box must contain only blue or only red, otherwise the label would be correct.

Pick the ball.  If red, then it the red only box.  If blue, it’s the blue only box.  Place the correct lable on it.

Now one of the boxes has a only label and one box has no label.  You know the one with the missing label can’t be the mixed box because that would mean the one with the only (blue or red) label would be correctly labeled.  So remove the box’s only (blue or red) label on the unmarked box.

Take the remaining mixed lable and place it on the box that now has no label.

You’ve now changed every label and that was required because “ALL WERE MISLABELED”.

Did I get it right?

2. silvioricardoc said,

May 20, 2009 at 5:54 pm

“the labels are all misplaced”.
Therefore, the label mixed must be in either a red or a blue box.
Just pick a ball from the mixed box, then.

If you pick blue:
–>  mixed should be blue
–>  red should be mixed (it was misplaced; can’t be red)
–>  blue should be red

If you pick red:
–>  mixed should be red
–>  blue should be mixed (it was misplaced; can’t be blue)
–>  red should be blue

3. jyoak said,

May 21, 2009 at 3:33 pm

Both of those are right!