A group of 25 consists of knights, knaves and liars. Each was asked two questions. 17 answered truthfully to the first question and 6 answered truthfully to the second.

What can be determined about the number of knights and liars in the group?

Since there are only 23 true statements, at least 2 people lied twice.  Therefore there are at a minimum 2 liars.

Arranging the other 23 people:

  All could be knaves. 

  For every knight added to the group of 23, 1 liar must be added.

  Maximum number of knights: 6 (implies 11 knaves 8 liars)

  Maximum number of liars: 8 (same logic)

#liars = #knights + 2

Posted by Leming on 2007-05-31 11:46:43