Let’s suppose A always lies and B always tells the truth.
You ask A what B would say this being a correct path.
In this case B can’t lie and will tell True, A will then lie about that and will say False, you negate False -> True.
Say you ask B what A would say this being a correct path.
In this case A always lies and if road is correct they will say False, B who can’t lie will tell you A would say False, you negate that -> True.
I’ve always found it easier to just ask the question within the question. To either guard.
“If I were to ask you, ‘which path is safe?’, what would you say?”
If you asked the truth teller he will Indicate the correct path because he would have told you the correct path anyway. If you ask the liar he originally would have indicated the bad path- but now he has to lie about what he would have original told you and will now indicate the safe path. Asking what the other guard would have said just kind of adds another unnecessary logic wrinkle in my mind.
Simple logic twisting really. Ask any guard what other guard would say, negate that answer and you got the right answer.
How though?
A truth B lies
Ask A: answer is No (truth)
Ask B: answers is No (lies)
Let’s suppose A always lies and B always tells the truth.
You ask A what B would say this being a correct path. In this case B can’t lie and will tell True, A will then lie about that and will say False, you negate False -> True.
Say you ask B what A would say this being a correct path. In this case A always lies and if road is correct they will say False, B who can’t lie will tell you A would say False, you negate that -> True.
I’ve always found it easier to just ask the question within the question. To either guard.
“If I were to ask you, ‘which path is safe?’, what would you say?”
If you asked the truth teller he will Indicate the correct path because he would have told you the correct path anyway. If you ask the liar he originally would have indicated the bad path- but now he has to lie about what he would have original told you and will now indicate the safe path. Asking what the other guard would have said just kind of adds another unnecessary logic wrinkle in my mind.
This assumes A can only lie. But I guess that is the riddl.