The Problem of Three Hats

From Cyberlaw

Once upon a time in a faraway land, the king wanted his son to marry the smartest young woman in the kingdom. All women were tested. Three tied with the highest possible score. The king seated these three women at a round table. He asked them to close their eyes, which they did. He then announced he was placing a beanie on each of their heads, positioned in such a way that, when they opened their eyes, each would be able to see the beanies on the heads of the other two but would not see the beanie on her own head. The king told the young momen that the beanies might be either red or white. "When you open your eyes, you are to raise your right hand if you see one or more red beanies. When you deduce the color of the benie on your own head,lower your hand, rise and explain. Now, open your eyes."

The king had, in fact, placed red beanies on each of the three women's heads. All three raised their hands. After ten seconds, one of them lowered her hand, rose and explained her deduction that whe was wearing a red beanie. How did she do it?