Each of the three girls Francine, Gertrude and Harriet are either knights who always tell the truth or liars who always tell a lie.

Francine says, "Either I belong or Gertrude belongs to a different type from the other two."

Whose type can you deduce with absolute certainty?

The statement basically says that there is an odd woman out, but it's not Harriet.

FGH
KKK - not possible | Supposedly true statement is false.
KKL - not possible | Supposedly true statement is false.
KLK - possible
KLL - possible
LKK - not possible | Supposedly false statement is true.
LKL - not possible | Supposedly false statement is true.
LLK - possible
LLL - possible

The only constant among the possible situations is that Gertrude is a liar.

 

Posted by Charlie on 2011-12-24 18:14:30