This is a variation of the above problem, but very hard for some people to solve. Everyone can see that each woman could be thinking that her own forehead might be red or white because the other two women could be raising their hands because of each other. Again, this is the point where most people stop, and indeed, where the women stopped while all three hands were up. The trick to solving this problem is to REALLY put yourself into the smart woman's shoes. If you REALLY were she, you'd say, either I have a white spot or a red. Suppose you had a white spot. Then the other two women would be looking at one white spot and one red. They would each quickly figure out that that only reason the others hand was up was because of their own red spot. The fact that neither of them figured it out was the tip off to the first that she must also have a red spot. Most people put themselves in the place of the first person, but to solve this one, you must then also put yourself in the place of a second woman.