On the west coast of Ireland there are many ancient monasteries. In these places one can go to lead a contemplative life, thinking about God and solving logical problems. This isolated life can also lead some to eccentricity. This problem was set by an abbot, who (one can assume) was more than a little odd.
The order, of which this abbot was leader, was a silent order. The monks never spoke, never wrote to each other. Their faces never gave any indication of what they were thinking. These monks lived for twenty three hours of the day in their cells, copying the bible. For one hour each day they met for group prayers in the great hall. Of course the monks didn't speak at these prayer meetings, but the Abbot leading the ceremony did.
One Monday morning as the monks entered the great hall they noticed that the back of all their heads had been painted, some white and some black. They couldn't see the back of their own head, and all wondered what was happening. The Abbot rose to give his sermon:
Oh monks! There are some amongst us who are unworthy! They must leave this monastery, and they must leave as soon as they know who they are. I have painted the heads of the unworthy monks black, and the heads of the worthy monks white. And monks, remember your vow! Do not speak! Do not tell those you see with black head that they are unworthy, lest you be cast into the pit of hell!
These monks obeyed their leader, and on the the following Sunday, just after group prayers, all the monks with black paint on their heads left the monastery.
How many monks had black paint on their heads?
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solution
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