Scrambled Box Tops - Answer

You can learn the contents of all three boxes by drawing just one marble.

The key to the solution is your knowledge that the labels on all three boxes are incorrect. You must draw a marble from the box labeled "BW" - black-white. If the marble drawn is, say, black, you know then that the other marble in the box must be black also - otherwise the label would be correct. Since you have now identified the box containing two black marbles, you can at once tell the contents of the box marked "WW" - white-white.

You know it cannot contain two white marbles, because its label has to be wrong; it cannot contain two black marbles, for you have identified that box; therefore it must contain one black marble and one white marble. The third box, of course, must then be the one holding two white marbles.