In the two guards riddle, I don't get how the solution makes sensePlease explain
You asked one of the guards which phone does MKBHD has a bias towards, and you should solve it without even needing to ask the other.
>>16973002I'll ask them if I'm good at oral sex. The truth teller cannot in good conscience answer since he does not know. The liar will answer yes. That's how I exit.
>>16973002You're asking this on /sci/, so presumably you are too autistic to parse logic in plain language. Very well.Let [math]D={D1,D2}[/math] be the two Doors (one leads to freedom, the other to death).Let [math]G={GT,GL}[/math] be the two Guards (one always tells the Truth, one always Lies)Let [math]f:D{0,1}[/math] be the freedom function:[eqn]f(D_i) = \begin{cases} 1 & \text{if } D_i \text{ leads to freedom} \\ 0 & \text{if } D_i \text{ leads to death} \end{cases}[/eqn]Define a truth-functional operator for each guard. For any yes/no proposition [math]P[/math]:[math]answer(GT,P)=[[P]][/math][math]answer(GL,P)=¬[[P]][/math]where [math][[P]]∈{0,1}[/math] denotes the actual truth value of [math]P[/math].We want to find a question [math]Q[/math] such that [math]answer(GT,Q)=answer(GL,Q) [/math] We achieve this by composing the two truth functions. We ask a nested question that forces the lie to be applied twice.Consider the question "If I asked the other guard whether [math]D1[/math] leads to freedom, would he say yes?" [math]P≡(f(D1)=1)[/math][math]Q(Gi)=answer(Gj,P)[/math] where [math]j \neq i[/math] the response is:[math]R(Gi)=answer(Gi,Q(Gi))=answer(Gi,answer(Gj,P))[/math] Case 1:[math]R(GT)=answer(GT,answer(GL,P)) [/math] [math]R(GT)=answer(GL,P)=¬[[P]] [/math] Case 2:[math]R(GL)=answer(GL,answer(GT,P)) [/math] [math]R(GL)=¬answer(GT,P)=¬[[P]] [/math] Thus:[eqn]\boxed{R(G_T) = R(G_L) = \lnot [[P]]}[/eqn] The composition answer always involves exactly one truthful evaluation and one inversion, regardless of order: Since the composition [math]id∘¬=¬∘id=¬[/math], the guard you happen to ask is irrelevant.
>>16973002Ask guard A:>if I asked guard B if his door was safe, what would he say?If the answer is "yes:">if guard A were lying, that would mean guard B would tell the truth and say "no." >if guard A were telling the truth, then guard B would lie and say "yes." >either way, that is the danger door. Take the opposite.If the answer is "no:">If guard A is lying, Guard B would tell the truth and say "yes.">If guard A is telling the truth, guard B would lie and say "no.">either way, that is the safe door.The point is that you don't really care which guard is lying. The goal is "don't die."
>>16973092What if the answer is "I don't know."?
>>16973189That being a possible answer defeats the purpose of the riddle so we can discount it as a possibility.
>>16973002imagine there's a million doors and a goat is being raped behind 999,999 of them. Would you still open a door?
>>16973493>so we canno, you cannot. you just cannot assume the guards know which door is safe therefore it cannot defeat the purpose of the riddleyou just didn't write a good riddle, that's all that's all
>>16973539>you just cannot assume the guards know which door is safeThat's explicitly stated in the riddle.
>>16973189>>16973493>>16973539>>16973549The guards both know what's behind the doors, but if they're allowed to say anything other than Yes/No the riddle falls apart.The lying guard only needs to lie, so he could say "I don't know" if asked what's behind the door. Meanwhile, the truthful guard under this premise genuinely wouldn't know if the liar would say the exact opposite of the truth or something like "I don't know", so he must truthfully answer "I don't know" as well.
>>16973683>if they're allowed to say anything other than Yes/NoOr some other binary set of answers that satisfies:>>16973047
>>16973683This. Without a strict limitation on allowable answers they could say any limitless number of truths or falsehooods.
