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You are packing up after a week-long stay at the Verity Inn. You came here, to Truth Town, to visit your friend but now it's time to go home. You feel in good spirits as you pack your bags. As you are leaving, however, your good mood vanishes when you are approached by the city's guild-master who asks for your help.

"The knight and knave who stand at the crossroads between here and Liar-ville have started causing even more confusion for travellers. It's bad for business! The one has cursed the other one to answer... differently -- and I don't know which -- so I need you to take this curing potion to them and give it to the cursed one. They need to go back to the way they were so that people have a better chance of finding the correct road."

You have to pass by on your way home anyway, so you accept the potion and a leaflet containing further instructions, and leave.

As you approach the fork where the knight and knave are standing, you see that they still look identical. You remember that the one always tells the truth and the other one always lies. You wonder what the curse did that makes this any harder than before? So you read the leaflet of instructions.

Either the knight or knave was cursed by his friend so that whenever someone asks him a question, before he answers, they will both stand behind a tree and flip a special coin together. The coin is labelled "Yes" and "No". If the side of the coin facing up is the same as the answer he normally would have given, his mouth will answer "no" against his will. But if the answer that he normally would have given is different to the side of the coin facing up, his mouth will answer "yes" against his will. The non-cursed one will answer the same way that he used to — regardless of the outcome of the coin-toss (i.e. answer truthfully if they are  the knight or lie if they are the knave). They will only let you ask exactly one question to one of them. — Guildmaster

Oh dear. Things seem to have gotten a bit out of hand.

Clarification 1

They are able to say no more than "yes" or "no".

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  • $\begingroup$ Is 'normally' if not cursed at all or if still cursed, but with a curse that does not affect answering? (e.g. Would a cursed knight answer yes or no on "Are you cursed" if the coin says yes) $\endgroup$ – Retudin Jul 19 at 14:57
  • $\begingroup$ @Retudin good question. A cursed kight would normally have told the truth before being cursed so they would try to say "yes" because they are cursed. But because they are cursed, and because the coin is yes, their answer is magically canged to "no". $\endgroup$ – Lord Ratte Jul 19 at 15:52
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Ask this:

If I asked you "Are both of these statements true? (1) you are cursed (2) the coin landed with 'No' facing up", what answer would you attempt to give?

If you hear "Yes", then the one you asked is the cursed one. If you hear "No", then the one you didn't ask is the cursed one.

Original answer (invalidated by an edit to the question after this was written):

Nothing says you can only ask a yes-no question. So ask "What answer would you normally give if I asked you what 2+2 is?" If you hear "Yes", then the one you asked is the cursed one. If you hear "4", then the one you didn't ask is the cursed one.

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  • $\begingroup$ I have now added something that explicitly limits their responses. $\endgroup$ – Lord Ratte Jul 19 at 15:59
  • $\begingroup$ @LordRatte Okay, updated with a way that works even under your new rule. $\endgroup$ – Joseph Sible-Reinstate Monica Jul 19 at 16:22
  • $\begingroup$ Congratulations. Your answer seems to work. I had to check beckause it wasn't the one I had but they're exactly logically inverse so it's valid. Using a hypothetical is a neat trick. $\endgroup$ – Lord Ratte Jul 19 at 19:50
  • $\begingroup$ Not sure this works, the directions state that first you ask them a question and then they go flip a coin before answering, I don’t think you can ask them a question about their coin flip before they’ve flipped it! “Is it true that tomorrow it rained?” These are nonsensical questions. $\endgroup$ – Amorydai Jul 20 at 5:26
  • $\begingroup$ @Amorydai Your objections would make sense if the coin flip happened after answering, but the coin flip happens before answering. I don't see an issue just because it happens after asking. $\endgroup$ – Joseph Sible-Reinstate Monica Jul 20 at 5:29
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Ask a question that effectively is "are you cursed?" (the reverse could also be chosen)
If you hear yes give the speaker the potion, if no give it to the other.
There are 8 possibilities
* Yes or No on coin (Y/N)
* talking to the liar (L) or not
* talking to the cursed (C) or not
Reasoning backwards:
YCL NCL YC NC YL NL Y N
the answer given y y y y n n n n
the answer intended n y n y n n n n
the truth y n n y y y n n

This is easily asked with 8 OR-connected partial questions.
There is no very simple question appropriate, since all 3 aspects matter.
However there is i.m.o. 1 obvious question to ask, since
* The answer is flipped if asking a liar, which we do not want
* The answer is flipped again if asking the cursed while the coin shows yes, while we always want a switch when cursed.

A working question is thus:
"Is exactly one of the following 2 statements true at the time of your answer? You are a liar. You saw No on the coin while cursed."

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  • $\begingroup$ Good answer. However, can you please clarify the second statement please. What specifically do you mean by "while"? $\endgroup$ – Lord Ratte Jul 21 at 11:43
  • $\begingroup$ With "while cursed" I mean "and you have been cursed" / "and you are under the influence of the curse that may influence your answer" (specifically, when looking at the coin , between question and answer.) It assumes there is no second curse so I guess it is not completely foolproof. It seems to me that a more elaborate formulation does not make it more clear; but if it is ambiguous English, feel free to improve the sentence. $\endgroup$ – Retudin Jul 21 at 15:29
  • $\begingroup$ I think in the other answer Amorydai has a point about time unclarity, I have adapted my answer a bit to cover that. $\endgroup$ – Retudin Jul 21 at 15:53
  • $\begingroup$ that makes sense. Great work. $\endgroup$ – Lord Ratte Jul 21 at 16:13

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