KCC's Quizzes AQQ286 about Right Labels on the Right Boxes containing colored balls

Let's define G, R and M the three labels (G=all green, R=all red, M=green and red). There are only two ways to label ALL the box wrongly (see following 2 columns):

Box GREEN --->           R, M

Box RED      --->           M, G

Box RED&GREEN ---> G, R

In the first case, the M label is on the all green box, in the second case the M label is on the all red box. So I'll extract one ball from the box with the M label. If the ball is green, then that box will need to have G as the right label. That means that the M label needs to replace the R one and the R label will replace the G. If the extracted ball is red, then that box is the all red one, the R label is the right one for it; the M label will replace the G and the G will replace the R.

All boxes have the wrong labels, so if we pick a ball out of the Red & Green box, it must be a single colour, so it if is Red, then the box marked Red & Green is Red only.  Likewise, if it is green, then the box must be Green only.  We then have the two remaining two boxes, marked Red only and Green only.  If the ball was Red, then the box marked Red must be Green and the one marked Green must be Red & Green.  Likewise, if the ball was Green, then the box marked Green must be Red and the box marked Red must be Red & Green.

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Since all the labels are false, I extract a ball from the box with the false R&G label and if the ball is G (R ), this box has an exact G (R ) label; the box with the false R&G label has an exact R (G) label and the remaining box has an exact R&G label.

Extract a ball from the "Red&Green" box.  Knowing it is mislabeled, it can't contain both red and green balls, so it will be all the same color as the ball you extracted from it.  Of the two remaining boxes, the one labeled opposite of the color of the ball you extracted cannot be correct either, so it must contain the mix of red and green balls.  That leaves the box whose label is the same as the color of the box you extracted - that one must contain balls the opposite of the color of the ball you extracted.

Excellent reasoning you made gpiarino , you have cracked this enigma, congratulations!

Well reasoned MTF_Walker , you found it, congratulations!

Beautiful steve12 , great reasoning, you have solved the quiz!

Yes, bravo MikeLh , you get it, congratulations!

Well done BrianE , you have found the way to solve this enigma, congratulations!