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At your bathhouse job, you encounter a pair of rainbow serpents, each having two heads, hiding behind a wide pillar. They seem to be bent around the pillar with a head from each serpent visible on each side

You know that for each rainbow serpent, one head will tell the truth and the other will lie. You also know that they are rather ill-tempered, and they'll only allow at most 4 questions between the 2 of them, and that's if you only ask about them. Unfortunately, you have to go ask if they have any problems, and will be expected to fix them if there are any. So you must determine which head is a liar and which is honest, within only 3 questions.

How can you guarantee this, regardless of the answers you get?

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** Edited after clarification note, that we have two serpents each with two heads (so 4 heads in total), under assumption that all heads are visible . This solution will work regardless or arrangement of heads around pillar.

Q1 - ask first head: "If I would ask YOUR other head if you are a liar, what will it answer?" : answer YES mean asked head is truth teller, otherwise asked head is liar
Q2 - ask second head same question, with same logic
Q3 - ask third head same question, with same logic
=> fourth head is whatever didn't appear twice ( so if Q1-2 resulted in two liars and one truth teller, 4th head is obviously truth teller )

Reason why Q1 works:

  • if we are asking truth-teller head, then answer to "if you are a liar" should be NO, but its OTHER head is then liar and it would answer YES. And since asked head is truth teller, it will report that YES => so if asked head answer YES it is truth teller
  • if we are asking liar head, then answer to "if you are a liar" should be YES, and since OTHER head is then truth teller it would answer that YES. But since asked head is liar, it will therefore reply NO => so if asked head answer NO it is liar
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  • $\begingroup$ There are 4 heads, split between the 2 sides of the pillar $\endgroup$
    – Ichthys King
    Aug 1, 2021 at 21:10
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Ask three of the heads "Are you a snake?" The ones that say yes are truthful heads and the ones that say no are lying heads. Identify the fourth head by elimination.

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