Riddles!

[TheGreatErenan]

I suppose Gf!sh's answer would work assuming the gurus all manage to devise the same strategy without speaking to one another.

However, there is another solution:

Suppose there is only one red guru. Then he will see that no other guru has a red mark, and he will deduce that his own mark is red, and therefore he will leave at 4:00 the first day.

Now suppose there are two red gurus. Neither will know if his own mark is red, since they each see one other guru with a red mark. Thus, neither will leave on the first day. However, from the fact that the red guru they can see didn't leave, they will deduce that there must be another red mark. It must be on their own chin. So they would both leave on the second day.

If there are three red gurus, they will not leave on the second day, because they each see two red marks. But from the fact that no one left, they will deduce that there must be a third red mark on their own chin. And they'll leave on the third day.

By induction, if there are n gurus with red marks, they will figure it out and leave on the nth day.