Liar’s paradox modification in Labyrinth

Posted by on November 30, 2007 at 11:05 pm.

labyrinth_guards1.jpg

Top Red Guard: “You can’t ask us. You can only ask one of us.”
Top Blue Guard: “It’s in the rules, and I should warn you that one of us always tells the truth, and one of us always lies. That’s a rule too.” Gesturing to the TRG, “He always lies!”
TRG: “I do not! I tell the truth!”
TBG: “Oh, what a lie!”
Sarah:
“Alright,” to the TRG, “answer yes or no: would he [TBG] tell me that this door leads to the castle?”
TRG: “Uhhh…yyyes?”
Sarah: “Then, the other door leads to the castle, and this door leads to certain death.”
Both Guards: “oooOOoooh.”
TRG: “How do you know? He could be telling the truth!”
Sarah: “But then he wouldn’t be. So if you told me that he said ‘yes’, I know the answer is ‘no.'”
TRG: “But I could be telling the truth!”
Sarah: “But then he would be lying. So if you told me that he said ‘yes,’ then I know the answer would still be ‘no.'”
TRG: “Wait a minute,” to the TBG, “is that right?”
TBG: “I don’t know –I’ve never understood it!”