From the anthropologist's remark that some villagers had blue eyes and all the rest had brown eyes, the villagers learned that if there had been only one blue-eyed person he would now be able to realize on the first day that he had blue eyes. This knowledge would allow them to begin a series of deductions that would eventually result in their committing suicide. It is interesting to note that the new knowledge is only about what would have happened in a situatuion that is patently contrary to fact, yet it enables valid deductions about the actual state of affairs in the real world.

If the anthropolgist had subsequently kept his mouth shut, the five blue-eyed people would have committed suicide on the fifth day. When the anthropologist then remarked that everyone had already been able to see that the tribe contained both blue-eyed and brown-eyed members anyway, he expedited the process because now if there had been exactly two blue-eyed people they would have realized their eye color on the first day (since the remark insures that there are at least two blue-eyed people, it would allow a person seeing only one blue-eyed person to conclude that he, himself, had blue eyes). Hence, the five blue-eyed people would now commit suicide on the fourth day.