Apologies for the delay in posting the answer…I was on vacation for a week. I got two correct answers to this puzzle – found this puzzle to be just a little tough for younger children, and did not receive any correct answer from the younger lot. Got correct answers from Sirisha and Akash Tayal – go IITD!

Am reproducing the answer from Sirisha, her explanation was simple and short:

Let’s say the sages are A, B, C and A thinks his face is clean. Initially, he thinks B and C are laughing at each other, but then he would expect one or both of them to stop laughing because when B sees that A is clean and C is still laughing, B should realize that his face is dirty and stop laughing. But since neither of them stop, A should realize that his face is dirty and stop laughing.

Only thing is since all 3 should think exactly the same way, they should all stop at the same time in stead of just one by this logic.

Hope you enjoyed the puzzle!