CHALLENGE 1:      HAT PROBLEM

According to the story, four prisioners are arrested for a crime, but the jail is full and the jailer has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can go free but if they fail they are executed.
The jailer seats three of the men into a line. "3" faces the wall, "2" faces "3", and "1" faces "2" and "3". The fourth man, "4", is put behind a wall (or in a separate room).
The jailer gives all four men party hats. He explains that there are two black hats and two white hats, that each prisoner is wearing one of the hats, and that each of the prisoners see only the hats in front of him but neither on himself nor behind him. The fourth man behind the wall can't see or be seen by any other prisoner. No communication among the prisoners is allowed.
If any prisoner can figure out what color hat he has on his own head with 100% certainty (without guessing) and tell the jailer, all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed.
The puzzle is to find how the prisoners can escape.