Answer to POW #3:

You only need to look at ONE marble to correctly label the boxes. Choose one marble from the box (incorrectly) labeled BW. There are two cases:

Case 1: If the marble is white, then the BW-labeled box is really the WW box. This means that the BB-labeled box must really be the BW box (it can't be WW since that is now the first box, and it can't be BB since it is *incorrectly* labeled). Therefore the WW-labeled box must really be the BB box (the only remaining choice).

Case 2: Similar to Case 1; if the marble is black, the BW-labeled box must really be BB. Therefore the WW-labeled box must be BW, so the BB-labeled box must be WW.

Source: This problem appeared on the 2003 JMU High School Math Contest.