This puzzle was used in more than one place than in Labyrinth. I played video games where they had that puzzle (Ultima 6 had that).

yeah, it could be the liar guard's desire or prime directive to send you down the deadly path. to him that could be interpretated as the correct path. especially if these are automatons working off of some machine logic. like, they don't even need to be out to get you, that's totally something that bad code could do on accident.

What is the quest was to die asap. And everyone the party meets just refused to kill them?