The three wise men

(not for kids)
Once upon a time, there lived two wise men: one always told the truth and one always lied. You must’ve been reading this for the nth time. But these men lived when you were a child. When you were nine. Now they don’t live. Now they’ve died.

Now there live three wise men. Wise they are, for they know it all. They know where’s Satan, they know where’s God, whence the Sun rises, where does it fall. But they don’t know how to speak English, they don’t know it at all. And even if they know, they choose not to show. But they can understand English, can’t speak it though. They speak a strange language, of a time long ago. ‘Da’ and ‘Ja’ are two of the words they would speak. One of them means ‘Yes’, and the other means ‘No’. Which one means what, trust me, I still don’t know. One of them always speaks the truth, and another would always lie and the third one would speak randomly, and don’t ask me why. (he may speak the truth, and may lie. It depends on his mood. If he’s in a good mood, he’ll lie :). And the mood fluctuates randomly.).

You’ve got to determine which of the three men speaks the truth and which one always lies. ( And I will tell you which one speaks randomly, for I am also wise!! ). You can ask three questions (each addressed to exactly one of them); only three, I’m afraid. To one man, however, more than one question may be made. You can ask all the three questions to the same man, or may ask one question to each; it is up to you to choose (Great liberty!!). But remember ‘Da’ and ‘Ja’ are the only words they would ever use.

Solution:

Well, there can be many varied solutions to this problem. It also depends upon some of the assumptions that we make. Following is the solution that I have derived:
Did you notice that the problem could be solved in just two questions if the wise men replied in ‘Yes’ and ‘No’ instead of ja and da? Now what da and ja means is the only extra variable that we have to derive. So, what we have an extra question for? The third question should be able to resolve the extra variable that we have. Now, in order to attack this question logically, we should first do away with the da and ja jargon. Let us see how the response would be if the wise men speak ‘Yes’ and ‘No’ instead of ja and da.

1. To A: What would B say if asked whether A always speaks the truth?

(i) If B is random, A is either True or Liar: no answer

(ii) If B is True, A is Liar : Yes

(iii) If B is Liar, A is True: No

(iv) If B is True or Liar, A is random: Yes or No.

In case of Yes in 1:

2. To B: What would C say if asked whether B always speaks the truth?

(i) If C is random (=> A is liar, B is True) : no answer

(ii) If C is True, B is liar (=> A is random): Yes

(iii) If C is Liar, B is True(=> A is random) : No

In case of No in 1:

2. To B: What would C say if asked whether B always speaks the truth?

(i) If C is random (=> A is True, B is Liar): no answer

(ii) If C is True, B is liar (=> A is random): Yes

(iii) If C is Liar, B is True(=> A is random) : No

In case of Yes Yes, No No, Yes No or No Yes:

(A is random)

3. To C: Is B True?

(i) If C is True, B is Liar : No

(ii) If C is Liar, B is True : No

In case A doesn’t answer in step 1: B is random

In case B doesn’t answer in step 2: C is random

Hence, we can always identify the random man in the first two questions, and then we can ask such a question to any of the non-random player that the answer is always ‘No’.

That’s the trick. You got it? No, I won’t elaborate further. The problem stands solved here. If you still cannot get till the solution, well, I’ve already said the problem is not for you.

Anyways, the rhyme was made by me. Did you like it?

Disclaimer: I don't make puzzles. So, obviously, this one has been taken from some place on the planet, and first thought of by some beautiful mind of our species. But the words are mine.