There was a crime, and it was known that either Al, Beth, Dell, or Phil (each a knight or a liar) was guilty. At the trial, the men spoke first, and said:
Phil: Dell did it.
Al: No, Beth is guilty.
Then it was the ladies' turn, who said:
Beth: Al is lying.
Dell: Phil never lies.
Then a lady accused someone, and that let me know she herself was innocent.
And next the other lady accused someone, and that let me know who was guilty.
Who's guilty?
(Answer at bottom)
For Phil, Al, Beth and Dell, the possible combinations of knights and liars are, respectively: (1)KLKK, (2)LKLL and (3)LLKL.
If (1) then Dell is the killer
If (2) then Beth is the killer
If (3) then either Phil or Al is the killer
Beth cannot accuse Dell because it would not allow us to differentiate between (2) and (3) and she could be either innocent or guilty. Beth cannot accuse Paul or Al because we could not differentiate between (2) and (3). She cannot accuse herself it would make her a lying knight in (1) and (3) or a truth telling liar in (2). Thus, Dell must make the first accusation. She cannot accuse herself because she could still be either a guilty knight as in (1) or an innocent liar as in (2) and (3). She can accuse any of the other three, however, and we will know it is not (1), and that she is innocent and that combination (1) is not valid.
Beth makes the next accusation. She cannot accuse herself because that would make her a truth telling liar in (2) or a lying knight in (3). She cannot accuse Phil or Al because she could still either be a gulity liar in (2) or an innocent knight in (3). Instead, she accuses Dell and reveals herself to be the guilty one.
Part One - Dell accuses Beth, Al or Phil
Part Two - Beth accuses Dell
The answer, I think
