One day you meet three persons, each either a Knight or a Liar. You ask "How many of you are knights?", and the first person answers "Grok!".

Not understanding, you ask the second one "What does 'Grok' mean?", and he answers "One", but then the third one cries out "That's false!".

What can you tell about each person, if anything?

If "grok" means "one", then the second is a Knight and the third is a Liar. But then the first speaker can't be a Knight as that would make his statement false, and he can't be a Liar as that would make his statement true.  So "grok" can't mean "one".

"Grok" could mean "zero", in which case the three would be Liar, Liar, Knight.

If "grok" means "two", then the first and third are Knights, and the second speaker is a Liar: that is, the three would be Knight, Liar, Knight.

Since you do know, as you did at the beginning, that the second and third are opposite types, and that "grok" can't be "one", that number two is a Liar and number three is a Knight. Number one could be either.  "Grok" could even mean "whatever" indicating indifference on the first person's part.

Posted by Charlie on 2007-06-29 10:22:36