A twist on the old one liar on truth teller riddle

[Carmady]

@Indistinguishable

Just rephrase Hobostew’s answer then; reword the binary relation “x lies more than y” as “either x is the liar or y is the truth-teller”, for example.

True.

@Indistinguishable

I can’t see how this would be possible (see below). But perhaps I misunderstand what you are stating. What’s the answer the xkcd forum gives?

In their statement, the youngest daughter always lied, middle was crazy, and eldest tells the truth. It can easily be converted to this scenario.

The solution is to ask A “Is B younger than C?”

Which of course is the exact same question as yours, but does not rely on the sisters knowing which category each falls into.

@Indistinguishable

Then you can’t do it. You put your one question to one of the daughters (let’s call her A) and she gives you information which is supposed to guarantee you the ability to figure out a non-crazy one. No matter what she says, it would be compatible with the possibility that she herself is crazy and just answering randomly

You don’t need an answer from the crazy daughter at all, if you never choose the daughter that you ask a question to.

You only have to get a meaningful answer from both the liar and truth teller.

But you are right, I’m pretty sure it is impossible without some extra information.

[Indistinguishable]

@Carmady

In their statement, the youngest daughter always lied, middle was crazy, and eldest tells the truth. It can easily be converted to this scenario.

The solution is to ask A “Is B younger than C?”

Which of course is the exact same question as yours, but does not rely on the sisters knowing which category each falls into.

Huh? How does it not require that? A needs to know their relative ages in order to answer that question, and the relative ages are stipulated to correspond to the answering-formats, so A knows that as well.

You don’t need an answer from the crazy daughter at all, if you never choose the daughter that you ask a question to.

You only have to get a meaningful answer from both the liar and truth teller.

The point is, if you only get an answer from one daughter, then you can’t rule out the possibility that that daughter is crazy. So you need to set things up so that, no matter who your question goes to, the two possible responses each indicate one of the other two daughters as non-crazy.

[Carmady]

@Indistinguishable

Huh? How does it not require that? A needs to know their relative ages in order to answer that question, and the relative ages are stipulated to correspond to the answering-formats, so A knows that as well.

I don’t follow. Just because the daughters know their relative ages doesn’t mean they know anything about their relative attitudes with regard to the truth.

The problem stipulates that you know how age corresponds to truth telling, but they might not.

[Indistinguishable]

@Carmady

I don’t follow. Just because the daughters know their relative ages doesn’t mean they know anything about their relative attitudes with regard to the truth.

The problem stipulates that you know how age corresponds to truth telling, but they might not.

Well, alright, but that’s just a trivial relabelling of the problem as it exists. I could further provide a solution where the daughters needn’t know their truth-attitudes nor their relative ages, just what they had for breakfast that morning. The stipulation is provided that the one which ate oatmeal is the youngest and a liar, the one who ate pancakes is the middle child and crazy, and the one who ate waffles is the oldest and honest, though the daughters may not know this. But nothing is actually gained by this solution, and nothing’s really been changed about the problem; I’ve just reworded “liar” into “oatmeal-eater” and so on.

[Indistinguishable]

@Indistinguishable

The point is, if you only get an answer from one daughter, then you can’t rule out the possibility that that daughter is crazy. So you need to set things up so that, no matter who your question goes to, the two possible responses each indicate one of the other two daughters as non-crazy.

Which, as pointed out above, means there’s essentially only one working solution: “You there! If you’re honest, point to which of your two sisters I should marry. If you’re a liar, point to which of your two sisters I shouldn’t marry [of course, you being a liar, you’ll do the opposite of what I say, and point to the one I should marry]. And if you’re crazy, point to any of the two sisters you like [you’ll do whatever the hell you want anyway]”. And then you marry the sister pointed to (the pointing, of course, actually being done via some chosen mapping of “yes” and “no” to the two sisters). Every solution is just this, worded one way or another.