Stop laughing

While three logicians (they are extreemly talented) were sleeping under a tree, a malicious and mischievous child painted their heads red. Upon wakingup, each logician spies the child's handiwork as it applied to the heads of the other two. Naturally they start laughing. Suddenly one falls silent. Why?


Answer:

The one who fell silent, presumably the quickest of the three, reasoned that his head must be painted also. The argument goes as follows. Let's call the quick one Q, and the other two D and S. Let's assume Q's head is untouched. Then D is laughing because S's head is painted, and vice versa. But eventually, D and S will realize that their head must be painted, because the other is laughing. So they will quit laughing as soon as they realize this. So, Q waits what he thinks is a reasonable amount of time for them to figure this out, and when they don't stop laughing, his worst fears are confirmed. He concludes that his assumption is invalid and he must be crowned in crimson too.