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 20111224 18:14:30 