3
$\begingroup$

The knights and knaves puzzle is old, well known and thoroughly solved.

https://en.m.wikipedia.org/wiki/Knights_and_Knaves

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"?

$\endgroup$

1 Answer 1

2
$\begingroup$

"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."

EDIT: There's actually a really neat solution to this: The guard who does not speak is lying. This is obvious if the first guard is telling the truth, and if not then the statement that one guard tells the truth must be false, forcing guard 2 to lie. So ask them which door leads to death and then waltz out of it.

ORIGINAL: If we take each sentence to be a separate statement, and assume each guard to be either a knight or a knave, then:
- "You can only ask one of us" is a lie. Therefore, after asking your question to the first guard, you can try asking the second - if it works, we are in this scenario. If they refuse to answer, it's the standard problem.
- "one of us always tells the truth and one of us always lies" is also a lie, so both guards are the same, and given that this is a lie that means they're both knaves. So if you are in this scenario, you just need to invert whatever you're told.

Of course, "If I asked you X, what would you say?" gets you a truth-y result from either a knight or a knave, so that would also solve this variant.

*"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"."*

This is a paradox.

- If G1 is telling the truth, then G2's statement is true if and only if G2 speaks only lies, which is clearly nonsense.
- if G1 is lying, then no-one speaks truth, so G2 is also lying, and so there are no liars. Again, nonsense.

The only conclusion to draw is that these guards are not knights nor knaves. This makes information from them effectively a coin flip, and so there is no solution.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.