Imagine that you have three boxes, one containing two black balls, one containing two white balls, and the third containing one black ball and one white ball.

The boxes were originally labelled for their contents (BB - WW - BW) but someone has inadvertently switched the labels so that now every box is incorrectly labelled.

Without looking inside, you are allowed to take one ball at a time out of any box that you wish, and by this process of sampling, you are to determine the contents of all three boxes.

What is the smallest number of drawings needed to do this?

I've seen this one before. You first have to take one from the box labelled "BW." Let's assume that the ball is black (it works either way). Since no box has the correct sign, this must be the "BB" box. Now, since no box has the correct label, you simply put the "BW" sign on the box labeled "WW" (since you can't leave the "WW" sign on the other box), and putthe "WW" sign on the remaining box.