Three puzzle competitors are blindfolded. A white piece of paper is glued to each competitor's forehead and they are told that not all of the pieces of paper are black. The blindfolds are removed and the competitors are told that the prize will go to the first to deduce whether the paper on his forehead is black or white.
The three competitors are silent for a short time, then all three announce white at the same time. Why?
Answers in the comments please. Note that there are two possible answers to this one - one relatively easy and intuitive, one harder and more 'logical'.