Here is one TOUGH logic pro­blem. See if you can solve it. I doubt it. Voice of Rea­son pre­sen­ted this to me and I am wor­king on it.

There are three omnis­cient gods sit­ting in a cham­ber: Gib­berK­night, Gib­berK­nave, and Gib­berK­ne­xus, the gods of the knights, kna­ves, and kne­xu­ses of Gib­ber­land. Knights always ans­wer the truth, kna­ves always lie, and kne­xu­ses always ans­wer the XOR of what the knight and knave would answer.

Unfor­tu­na­tely, the lan­guage spo­ken in Gib­ber­land is so unin­te­lli­gi­ble that not only do you not know which words corres­pond to “yes” and “no”, but you don’t even know what the two words that repre­sent them are! All you know is that there is only one word for each.

With only three ques­tions, deter­mine which god is which.

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XOR is boo­lean for “One or the other, but not both” Which means given two inputs, only one of them can be true for XOR to return true. If they are both the same value (both true or both false) then XOR returns false.

Note 1: What follows are stan­dard rules that are gene­rally assu­med unless other­wise noted. The gods only ans­wer yes/no ques­tions. Each god ans­wers in the sin­gle word of their lan­guage as appro­priate to the ques­tion; i.e. each god always gives one of only two pos­si­ble res­pon­ses, one affir­ma­tive and one nega­tive (e.g. they would always ans­wer “Yes” rather than “That would be true”). Each ques­tion asked must be addres­sed to a sin­gle spe­ci­fic god; asking one ques­tion to all the gods would cons­ti­tute three ques­tions. Asking a sin­gle god mul­ti­ple ques­tions is per­mis­si­ble. The ques­tion you choose to ask and the god you choose to address may be dyna­mi­cally cho­sen based on the ans­wers to pre­vious ques­tions. No self-referential ques­tions (e.g. “is this ques­tion true iff …”).

Note 2: Because of pos­si­ble loop con­flicts, you may not ask any ques­tions regar­ding how a kne­xus would answer.