An anthropologist arrived to the shaman's den where there were two persons, one with a green hat and one with a blue hat. One of the shaman's students had said that there was a Star Predictor with the Shaman. However, they were look-a-likes and the anthropologist couldn't tell who was who. So he asked from the man with the blue hat 'Is the shaman an honest person?' The blue hatted person answered either yes or no from which the Anthropologist could tell which one was the Shaman. How could he tell?

I have struggled with this problem a while. All I could come up with has been that if he answered no, it must be the other person since of the liar's paradox. I haven't come up an answer how he could tell which one is which if he would have answered yes.

I tried to research this problem but I couldn't find this problem anywhere. This was asked from 10th graders in philosophy as an example of logic problems.


This puzzle is very difficult, or indeed impossible, until you work in the :

As OP says, if the answer was yes, no information was gained.

But the puzzle explicitly says that the Anthropologist did gain information, which means that

the answer must have been no.

In that case, the person that answered must surely be

the Star Predictor, because the Shaman would always have answered "yes", regardless of his being honest or not.

  • $\begingroup$ Thank you so much. Usually I pay attention to these kinds of details but now it slipped my mind. $\endgroup$ – ENTL Mar 6 '20 at 8:05
  • $\begingroup$ Do we implicitly assume that a dishonest person cannot tell the truth about their dishonesty? $\endgroup$ – trolley813 Mar 6 '20 at 16:49
  • $\begingroup$ @trolley813 that's the usual premise in liars puzzles. It's usually explicitly stated, but here it's pretty much ok to omit it; we can deduce the existence of such a rule from the fact that the single yes/no answer gave the Anthropologist all the necessary information to identify the Shaman; that wouldn't be the case if such a stipulation didn't exist. $\endgroup$ – Bass Mar 6 '20 at 17:14
  • $\begingroup$ @Bass Thanks! I know about liars puzzles and got used to that thing stated explicitly. So, it turns out that it's not always the case $\endgroup$ – trolley813 Mar 6 '20 at 18:37

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