If you have three people standing, all facing the same direction, each person can see the color of the hat of only the person directly in front of them (which can be either black or white). There are two hats of each color (four total). The hats are placed on the persons' heads one at a time, starting with the one in the very front. When someone knows for certain what color hat they have, they need to declare that they have discovered the color of their hat. In this scenario, no matter which hats are distributed, at least one person can be certain of their hat color. What are these scenarios, and what are the probability distributions for each?
