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A Fork in the Road

This puzzle can be posed in many ways. Friend Timm Wheeler showed it to me in about this form:

You come to a fork in the road. One path leads to Nirvana; the other, to Hell, but you do not know which leads where. A being stands at each path of the fork. One always tells lies; the other always tells the truth, but you do not know who tells what. You must ask one question of one of the beings to determine which path leads to Nirvana.

Being me, I set about brute-forcing the logic of the thing, and ended up with this written down, which I recently rediscovered on a flash card I had lying around:

Given recent realisation that I did it wrong (see somewhere below), I'm going to go through and, in italics, try to recall in more detail how I arrived at the conclusion I did.

Two forks

One to Nirvana

One to Hell

Two beings

One always lies

One is always truthful

You do not know which is which.

-----

GIVEN FOR THE SAKE OF FIGURING THAT LEFT IS NIRVANA:

-----

Which road leads to Nirvana?

T: The left

L: The right

But who is who?

This one is a no-brainer. You don't know which road goes where, and which guy might be lying to you. If you just pick one of them and ask, you have no way of knowing whether it's true.

-----

Does the left fork lead to Nirvana?

T: Yes

L: No

But which is which?

Different question, same problem. But we're doing better, drilling down a bit.

-----

Were I to ask the other, "Which fork leads to Nirvana?", which would he say?

T: Left

L: Right

Same problem.

LOL DISREGARD THAT I FAIL AT LOGIC

I'm still not sure how I arrived at this little gem of failure, but as best as I can figure, I did something like this: Okay, left is Nirvana. We're asking Truthful first. Truthful, were I to ask the other [Liar], "Which fork leads to Nirvana?", which would he say? Now, if Nirvana is left, and I asked Liar which way Nirvana is, obviously he will lie and say Right. Now, what I must have done (for lack of any better ideas at the moment), is not think the last bit through, and assume a reversal of the answer as we focused back on Truthful. In Truth, Truthful would simply Truthfully relay what Liar's answer would be, but I overlooked how the exchange would work out and blindly swapped the answer around on an assumption. Oops.

-----

Were I to ask the other, "Does the left fork lead to Nirvana?", what would he say?

T: No.

L: No.

-----

Confirm:

Were I to ask the other, "Does the right fork lead to Nirvana?", what would he say?

T: Yes.

L: Yes.

-----

If I had done the previous one correctly, it would have stopped there, but I got here instead. I'm not sure I had any good procedural reason for trying this one. It may have been an idea that popped into my head, so I tested it. Being essentially the same as the previous one, except focusing on a specific path, of course it worked fine.

Ask of either:

"Were I to ask the other, 'Does the [left/right] fork lead to Nirvana?', what would he say?"

No from either indicates that the given fork leads to Nirvana.

Yes from either indicates that it leads to Hell.

QED.

Oops

Valerie e-mailed me today, 1 July, to point out that "Were I to ask the other, 'Which fork leads to Nirvana?', which would he say?" actually works just fine. I'm not sure what I was thinking when I ruled that one out, but in any case I certainly screwed up there. Here:

I think the question 'Were I to ask the other, "Which fork leads to Nirvana?", which
would he say?' might actually work. (I hope I didn't fuck this up somewhere.)

---

Nirvana is the left path:

Were I to ask the other, "Which path leads to Nirvana?", which would he say?

T: right (L would say "right", and T answers accurately.)

L: right (T would say "left", and L tells you the opposite.) 

---

Nirvana is the right path:

Were I to ask the other, "Which path leads to Nirvana?", which would he say?

T: left (L would say "left", and T answers accurately.)

L: left (T would say "right", and L tells you the opposite.)

--

The answer either being will give is the path that leads to Hell. 

It's not much different from the question you ended up with, but I figured it's
still worth mentioning because it's a little more similar to "Which way would the
other being tell me to go?"

The Popular but Incorrect Answer

There is a popular answer to this puzzle that I see many people use, usually the ones who are too lazy or dull to figure this out for themselves, so they Google it. It is:

Which way would the other being tell me to go?

This is widely considered to be the correct answer, and understandably so. After all, if you ask the truthful one which way the lying one would tell you to go, he will point to the path to Hell, and if you ask that of the lying one, he will also indicate the path to Hell. Right? Maybe not.

That answer presupposes that either of the beings have your best interest at heart, or that they are partial in any way to your fate. A logic puzzle such as this must not be compromised by such assumptions which have not been explicitly stated. The solution that I have reached above is the only way I have found to certainly and logically determine which path leads to Nirvana, and which leads to Hell. Amazingly, I have been accused (by aforementioned friend Timm Wheeler) of adding unstated information to the puzzle in pointing out this logical flaw!

Contact me with any comments on this. The passion still simmers. ;)

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