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?

There are 2³ possible combinations.

We know right off that 2 and 3 cannot be the same because of the statement from 3.  If 3 is a Liar, then statement 2 is true meaning 2 is a Knight.  But if 3 is a Knight, then his statement is true, making 2 a Liar.  This eliminates half of the possible combinations.  The four that remain are {KKL, KLK, LKL, & LLK}.

Consider now if the second person is a knight.  This means that indeed 'Grok' = 'One'.  However, if the first person is also a Knight, his answer of 'One' would be false.  Yet if the first person is a liar, then his answer of 'One' would be true.  Thus, two more combinations are eliminated.  The two that now remain are {KLK, & LLK}.

Of the two remaining choices, both are valid if 'Grok' = 'Two'.  For anything else, only the latter remains valid.

Knight, Liar, Knight

or

Liar, Liar, Knight 

Posted by hoodat on 2007-07-02 09:45:53