There are seven monks with black marks
Suppose only one monk has a black mark, then he will see that all the others have white marks. Since he knows that there is at least one monk with a black mark, he will know that it must be him, and he will leave immediately (on Monday). This didn't happen, so there can't be only one monk with a black mark.
Now suppose there are two monks with black marks. These two monks will see the other having a black mark, but at first they will not know whether they also have a black mark, and so neither will leave on Monday. When, on Tuesday they see the other again they will know that there can't be only one black mark (otherwise the other would have left on Monday) therefore they know that they must have a black mark, and so leave, on Tuesday.
Similarly if there are three monks with black marks, they will leave on Wednesday. Continuing this argument you can see that if the monks leave on Sunday (after prayers) that there must be seven with black marks.