## Puzzle : Solution of “Way to the heaven?”

Well,

Finally I am sitting down to write the solution to the puzzle I posed in my earlier post. Please read the problem statement in the earlier post.

Solution : The question that you should ask should go like this

“If I were to ask you that the left path goes to heaven, would you nod your head?”

Let’s analyze the responses to this question case by case.

Case 1 : Left path goes to heaven

Case 1a : conventions are nod = yes and shake=no.

Suppose you asked this question to the angel ( who always speaks the truth ). As the left path really goes to heaven angel would say “yes”. And because nodding indicates “yes” he would want to say “yes, I would nod my head”. He has to convey this merely be his head movement so ultimately he will nod his head.

What if this question was asked to the demon ( who always lies ). The left path goes to heaven. So when asked the above mentioned question the demon would want to say “No, the left path does not go to the heaven”. He can say this by shaking his head. However, the question is whether he would nod his head. As he was originally going to shake his head he would again try to lie by saying “yes, I would nod my head” resulting in his nodding.

Case 1b : Conventions are  shake=yes and nod=no.

How would angel respond in this scenario? Well, he would want to say “yes, the left path goes to the heaven” which he can indicate by shaking his head. So to indicate that “no, I would not nod my head” he will nod his head as nodding indicates “No”.

What about the demon? He would want to say, “No, the left path does not go to the heaven” which he can indicate by nodding his head. As he is a liar, he would say that he would not nod his head which he originally would. So to indicate that “No, I would not nod my head” he would have to nod his head according to the conventions.

Case 2 : Right path goes to the heaven.

By the similar argument given in case 1, you can easily see that in all scenario, they would end up shaking there head. So we can deduce that nodding would indicate that left path goes to the heaven and shaking would indicate that right path goes to the heaven irrespective of what the conventions are and irrespective of who was asked the question.

Nice trick isn’t it??

–Saurabh Joshi