It's Graduation Day at LKU (Liars and Knights University) where everyone enrolled is either a Liar (who always lies) or a Knight (who always tells the truth). You approach four youths who just received their diplomas, two of whom are Liars and two of whom are Knights. It is known that each of the four majored in a different one of four subjects and minored in a different one of the same four. Each makes three statements:

Roberta:
   1. Friedrich did not minor in botany.
   2. Either Gloria or myself or both took philosophy.
   3. Both girls either majored or minored in botany.

Gloria:
   1. Between them, Melrose and Roberta took all four classes.
   2. I did not minor in botany.
   3. Roberta is a Liar.

Melrose:
   1. I majored or minored in math.
   2. Friedrich is a Liar
   3. Roberta majored in history.

Friedrich:
   1. Melrose did not major or minor in math.
   2. I majored or minored in philosophy
   3. Gloria minored in math.

Which are the Liars and the Knights, and what did they major and minor in?

The posted solutioon to this is wrong. Since Roberta's #2 must be false, neither girl could have philosophy as either major or minor. The posted solution violates this.

Posted by Matt on 2005-06-16 17:52:24