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Anonymous05/09/26, 13:04No.16973002
In the two guards riddle, I don't get how the solution makes sense
Please explain
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Anon05/09/26, 13:32No.16973010
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.
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Anon05/09/26, 15:04No.16973046
I'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.
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Anon05/09/26, 15:10No.16973047
You'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.
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Anon05/09/26, 15:59No.16973092
Ask 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."
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Anon05/10/26, 08:30No.16973519
imagine there's a million doors and a goat is being raped behind 999,999 of them. Would you still open a door?