The knights and knaves puzzle is old, well known and thoroughly solved.
In Labyrinth there's a variation, where one of the participants tell us the rules:
"You can only ask one of us. It’s in the rules. And I should warn you that one of us always tells the truth and one of us always lies."
What if that person is the liar? Is it still possible to solve this?
Another variation going around says:
"Two guards are standing before two doors. One leads to your goal the other to a painful death.
Guard one says "one of us speaks only truth".
Guard two says "one of us speaks only lies"."
Is this even possible? Is it necessary to assume, that the lying won't start until after these statements? Is it necessary to assume, that lying about "always truthful" can mean "occasional liar"?