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“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.”
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.
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