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You are visiting an island and need some information. The island has liars, truth-tellers, and togglers. Critically, togglers alternate truths and lies in their answers. When you meet someone, how can you tell if they are a liar, a truth-teller, or a toggler with just one question?

It seems to me that the question needs to be met with yes, no, or no answer respectively. However, I haven't been able to find a question that satisfies this condition.

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    $\begingroup$ Just one question asked total, or just one question to ask as many times as you like? $\endgroup$
    – Ian MacDonald
    Mar 5 at 2:08
  • $\begingroup$ Are the questions restricted to being ones that are yes/no answerable (per title) or can they be any random question? $\endgroup$
    – bobble
    Mar 5 at 4:11
  • $\begingroup$ Does also a single question exist which, moreover, also tells apart which kind of toggler? One that lies on odd or one that lies on even numbered questions? $\endgroup$
    – FirstName LastName
    Mar 5 at 14:09
  • $\begingroup$ @FirstNameLastName: Such a question would need (at least) four possible answers. $\endgroup$
    – Beta
    Mar 5 at 14:31
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    $\begingroup$ @FirstNameLastName: Right, I was making an observation, not a rebuttal. Your question must be broader than yes/no. And I agree about the title; it is usually not spelled out in these questions what will happen if you ask a yes/no question which the person cannot legally answer, but if frustrated silence is allowed, then I guess we'd call that a question with two possible answers, but three possible responses. $\endgroup$
    – Beta
    Mar 5 at 14:58

1 Answer 1

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"If I ask you in the future whether you are a truth-teller, will you answer 'yes'?" (yes: truth, no: liar, silent: alternator)
It's the standard method for getting the answer to an a question for knights and knaves. With an alternator, he won't know whether the future question will be when he's scheduled to lie or not, so will be unable to answer.

(For those unfamiliar with this rule, if I ask in the future, the liar will answer "yes" to that future question. He will therefore lie and say "no" to this question.

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    $\begingroup$ I posted the question.And the answer seems correct. The problem comes from Krantz´s Techniques of problem solving book. It's problem 1.5.3 at pg. 31 (google it). Thank you for your help, ralphmerridew. $\endgroup$
    – Emerson
    Mar 7 at 1:13

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