So far this blog has been only about cake-cutting. Not that I am going to stop writing about that, but this blogs needs a little change. I remember a very old puzzle which involves logic.
Problem : One fine day, you find yourself dead ( not a very good opening line..eh? ). You start your journey in search of eternal peace and happiness or in other words, you start your journey to search heaven. After traveling for a long long time, you come across a huge gate. You also notice that there is a fork after the gate. One of the path leads to heaven and the other one leads to hell. Two guardians are guarding the gate. One of them is an angel and another is a demon ( or a knight and a knave etc etc ). Angel always speaks the truth and the demon always lies. You are supposed to ask only one question to only one of the guardian. Clearly, you want to go to heaven, so you would try to ask which path would go to heaven. However, given the constraint that you can ask only one question , how would you frame the question??
Solution : The question you would ask is : “If I ask the other guard about which side leads to heaven, what would he answer?”. It should be fairly easy to see that irrespective of whom do you ask this question, you will always get an answer which leads to hell. So you can chose the other path to continue your journey to heaven.
If you do not see how this works. Here is an explanation.
Without loss of generality, let us assume that the left path leads to heaven.
If you ask an angel about which path leads to heaven, as he speaks always the truth, he
would say “left”. Now that the demon always lies, when he is asked what “the other guard (angel) ” would answer, he would definitely say “right”.
Similarly, if you ask the demon about which path leads to heaven, he would say “right”. As the angel speaks nothing but the truth, he would say “right” when he is asked what “the other guard( demon ) ” would answer. So in any case, you would end up having the path to hell as an answer. So you can chose the other path as a way to heaven.
A very trivial puzzle eh? I know, many of us has come across this puzzle sometime. Ok, now try this one :
Problem : Similar to the puzzle above, one guard ( the angel ) always speaks the truth and the other guard ( the demon) always lies. The trouble is that none of them can speak, so they can only nod ( up-down movement of the head ) their head or shake ( left-right movement of the head ) the head. You do not know who is the angel and who is the demon. In addition to that, you even do not know whether a nod means a “yes” or a “no”. And again, you are allowed to ask only one question that would decide your fate for eternity. What would be your question?
I will post the solution to this problem in my next post. Till then, readers ( if any 🙂 ) can scratch their head.