1 Draw. The key is each box must be labeled *incorrectly*. It gets a bit harder if the labels are just randomized. First, you draw from the BW Box. Since it can't be BW, it has to be either BB or WW, so whatever color you get, put that label on the box. The box you just identified is correctly labeled, so set it aside. So you now have 1 Colored box, one Blank box, and the BW label. Well, the Colored box doesn't match its label, so move that to the blank box, set it aside, and put the BW label on the remaining box.
The key is each box must be labeled *incorrectly*. It gets a bit harder if the labels are just randomized.
First, you draw from the BW Box. Since it can't be BW, it has to be either BB or WW, so whatever color you get, put that label on the box.
The box you just identified is correctly labeled, so set it aside. So you now have 1 Colored box, one Blank box, and the BW label. Well, the Colored box doesn't match its label, so move that to the blank box, set it aside, and put the BW label on the remaining box.