I guess another way to explain that the white-dotted villagers die at time n if there are n white dots in total is the following:Consider one white-dotted person at time n. He sees n-1 dots and also that all those guys with the n-1 dots are alive. He assumes first he has a black dot. He considers what one of those white-dotted guys thinks at time n-1. That guy then sees n-2 guys with white dots and all of them are alive. He assumes that he has a black dot and considers what one of those n-2 white-dotted guys thinks at time n-3. etc. So the second-last white dotted guy in the chain, considered by the third-last guy, sees the only 1 guy with 1 dot; and that guy has not yet killed himself.But then this second last guy must have realized he has the white dot by time n and so killed himself. But he didn;t kill himself, therefore the third last guy's assumption that he has the black dot fails and so he then would have realized before time n that he has the white dot and would have killed himself.In a similar fashion, all of the previous villagers' assumptions about having the black dot actually fail, so we continue in this fashion to get that the first guy's assumption that he has the black dot must be false. Therefore on time n he realizes he has the white dot and kills himself.By the way, if one villager reveals any information about the number of dots he sees, all the other villagers will also kill themselves (i.e. we don't even need anybody to come, just an evil villager )
Last edited by alexrem
on August 12th, 2009, 10:00 pm, edited 1 time in total.