Logic puzzle: ID the Liar and the Truth-Teller

[Indistinguishable]

Damn you, chrisk! Couldn’t you have at least let some of my post remain original?

[Autolycus]

@chrisk

Okay, let’s see. The first thing is that whoever arranged this could have inscribed whatever he or she wanted in each chest, and put whatever they wanted in it. We don’t really have enough clues to figure out what would be ‘fitting’ to them, and so I wouldn’t open either chest - not without being able to shake them each and listen for something slithering inside, figuring out some way of drilling a tiny hole into both and gassing the inside, or something similar

But we can figure out what the inscriptions might mean either way. If the python is in the silver chest:
The inscription on the silver chest is true.

The inscription on the gold chest is inherently self-referential, since it is talking indirectly about its own truth. However, in this case, if we take as a premise that the inscription on the gold chest is true, then we reach a contradiction, as then both inscriptions are true, which is not what the gold inscription says.
Alternatively, if we take as a premise that the inscription on the gold chest is false, then we reach a contradiction, as only one inscription is true now, which is exactly what the gold chest affirms.

Thus, if the python is in silver, then the inscription on the gold chest is self-referential in an endlessly contradictory way.

On the other hand, if the python is in the gold chest, then the inscription on the silver chest is false. That means that if we assume that the inscription on the gold chest can either be true or false without contradiction. (True - gold chest only is true. False - both inscriptions are false.) Thus, if the python is in gold, then the inscription on the gold chest is self-referential in a meaningless, but non-contradictory way. The pair of inscriptions are consistent either way it could be interpreted.

So, if we assume that the python is placed in such a way that the inscriptions are consistent, then we should open the gold chest. I wouldn’t bet on that - not after reading about Raymond Smullyan’s Portia N.

You owe me an aspirin! Although I’m glad we came to the same answer.

[chrisk]

@Indistinguishable

Damn you, chrisk! Couldn’t you have at least let some of my post remain original?

Well, the spoiler box was something that I didn’t do first. :smack:

[Indistinguishable]

@chrisk

Well, the spoiler box was something that I didn’t do first. :smack:

And, I realize with glee, pedantry about the ambiguity of the word “one” remains all mine.

[chrisk]

@Indistinguishable

It is cute, the way you reason from “Well, if things were any other way, we’d have a ‘truth paradox’ on our hands.” However, the troubling problem (and great talking point) is that I could well build a silver and gold chest with those inscriptions and put treasure in the gold one and a python in the silver one. The world, sadly, doesn’t really give a damn about avoiding ‘truth paradoxes’. How crazy is that?

Yeah - this kind of ‘reductio ad absurdum’ logic only really works when there’s some kind of definitive statement about truth or falsity in the puzzle on which you can hang everything else. “If my reasoning isn’t correct, then the authority lied to me”, in essence, is where you get to with that.

I especially like some of Smullyan’s portia puzzle where he makes up bellini and cellini, the vase makers who insist on inscribing true statements or false statements on their creations. Thus, the inscriptions themselves can refer to who made what, and they get out of being directly self-referential that way.

If there’s an inconsistency, then it invalidates everything the author of the puzzles is telling you about bellini and cellini.

[Harmonious_Discord]

Don’t sweat the chest. Heat both to a roasting temperature for hours, until the python is fully cooked.

[Rigamarole]

@wendigo1974

White guy and and a black guy standing in a room, walk up to either and ask “Are you negro”

Job done in one question.

Yeah. Job done in one question because you just got your nose hammered into your face.

[Mangetout]

Noone Special nailed it in post #2 - the way these puzzles are usually constructed is such that you not only need to determine which is the liar and which the truth-teller, but you also need, based on that knowledge, to decide which of two ways to go, or which of two boxes to open, etc - one will reward you and the other certainly kill you, and you’re only permitted one question.

So it just isn’t enough to ask a straightforward question such as ‘am I clapping my hands right now?’ - because that will at best only identify who is the liar and who the truth-teller - then you have no questions left and you still need to make the crucial decision.

[Malacandra]

@Chronos

There is no such question, unless the thing you want to know is just who’s trustworthy. Assuming you ask a yes-no question, you’ll get (at most) one bit of information in your answer, but to determine both who’s who and the answer to your question, you’d need two bits.

Also, you want to make sure that your question is phrased as a yes-no. For instance, the question “If I were to ask you which path leads to the village, what would you tell me?” is no good. If you happen to ask that question of the liar, he’s free to answer “supercalifragilisticexpialidoceous”, or “banana”, or “mu”, since none of those things is what he would tell you (and hence, all of them are lies, in response to the question “what would you tell me?”). To avoid this problem, you could instead ask “If I were to ask you whether the left road leads to the village, what would you say?”.

Same problem, though: even though the reworded question is yes/no, the liar is still free to say “I don’t know”. So I guess we’re reduced to defining “liar” as “someone who says ‘yes’ when the truthful answer is ‘no’ and vice versa”. Otherwise even the classic ask-one-guard-what-the-other-would-say technique doesn’t work; the liar can say “I don’t know”, and the truth-teller must say “I don’t know”.

[chrisk]

This reminds me of one of Raymond Smullyan’s:

On the island of knights (truth tellers) and knaves (liars), you come upon a small town and find a native on the road just outside of town. You ask him if the Green goose tavern is in this town.

The native fixes you with a frosty stare. “I’m not going to answer that,” he replies, and storms off past you, heading out of town.

What information can you deduce from that?

[Revenant_Threshold]

I’ve never thought the “ask both guys what the other guy would say” solution works. It’s dependent on the the idea that their lies are constrained to being about the two roads. What’s stopping the lie from being “Actually, you need to go back the way you came” rather than just the opposite path?

[wendigo1974]

@Rigamarole

Yeah. Job done in one question because you just got your nose hammered into your face.

Touche … the white guy could well be a redneck.

[Chronos]

Wow, I didn’t know that Knights had such a dislike of taverns.

(we know he’s a Knight, because he said he wouldn’t answer, and in fact he didn’t, so he was telling the truth)

And I should have known that the folks around here wouldn’t be fooled byt the python-puzzle signs.