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    $\begingroup$ Why couldn't they all just point to themselves? Also, this isn't actually a question; it's a directive. That makes it impossible for them to lie or tell the truth, because they aren't answering anything; they're simply being given a directive. There is nothing to indicate whether knights/knaves follow directives or not. $\endgroup$
    – GentlePurpleRain
    Commented Jun 18 at 15:30
  • $\begingroup$ You might be able to say something like, "If any guard other than yourself is a truth teller, which guard is it?", but I still think that if it's valid for the truthteller to give a non-answer, it should be valid for the liars as well. They should be able to imitate any answer that the truthteller gives. $\endgroup$
    – GentlePurpleRain
    Commented Jun 18 at 15:33
  • $\begingroup$ @GentlePurpleRain "among your companions". A clearer way of wording that question could be: "If either of the other two guards is telling the truth, point to him (otherwise don't point to anything)". If the guard you asked is truthful, he won't point to anything (other 2 are liars). If the guard you asked is lying, he'll point to the other liar (1 is truthful and the other is the other liar). $\endgroup$
    – Josh
    Commented Jun 18 at 16:01
  • $\begingroup$ @josh "Yes, I think the question is clearer this way" $\endgroup$
    – Ahmed
    Commented Jun 18 at 16:53
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    $\begingroup$ That gives you which guard is telling the truth. But I guess you have to ask a second question to find the pot of gold, right? $\endgroup$
    – hexomino
    Commented Jun 18 at 17:07