The abbot has told the monks that there is at least one who has a black mark. Suppose that there is only one monk with a black mark. What does he see on the backs of the heads of the other monks? What do the others see? Can he be sure that there is only one monk with a black head, and that he must be that monk.
Now what would happen if there were two monks with black heads. What would they see? What would the others see? Why won't any monks leave on the first day. Why, when they meet again, will those monks know that they have to leave.
The original problem said the monks left on Sunday, after meeting each other seven times. If it has taken this long for the monks to work out who has black marks and who has white, how many monks have black marks?
Ahh I see, take me back to the Abbot's
problem.
No I give up. Show me the
solution