Logic: Fork in the road with three men

Originally Posted by Benny

For those reading this who like a little irony... in replying to all the posts in this topic. I earnt more tokens than I had to cough up for the prize!

If your posts had not been relative I would have deleted them, and, deducted double the tokens.

However this has been one of the longest and enlightening posts yet. Siliconhell whole heartedly agrees that statements and answers should be challenged. ;-)


Well Done

Siliconhell

[Midders]

ask man 1

"What would man 2 say if I asked him if this road leads to city A?"

if the answer is yes then it's the other road.

If you're askin the liar about the truthfull person he'd change the no the truthfull person would answer to a lie.
If you're asking the truthfull person about the liar he'd keep the liars yes answer.

As for how to work the random one into the equation, I haven't figured that out just yet.

[Mike]

I could not suss this on at all :-?

Mike ...

[Midders]

All the men know which of them tells the truth, which one lies, and which one is the random response person.

If you asked a liar what man 2 (whom the liar knows to be a truthfull person, for sayings sake) would say when asked "Does this road leads to City A?", they'd lie and tell you the opposite. Changing the truth to a lie.

If you asked the Truthfull person what man 2 (whom the truth teller knows to be a liar, yet again just for sayings sake) would say when asked the same question then the truthfull person would tell you the liars answer, which of course is a lie.

Either way you find out a lie so you know it's the opposite road to take.

Hope that clears it up a bit more.

How about asking one man the same question twice! Ask man 1 what would man 2 say blah blah blah and then ask him what would man 3 say, etc etc, etc. Technically if you asked the truthfull or lying person then they could only really answer one of the 2 questions! They know which of the other men is random but they can't actually say yes or no to the question because they don't KNOW how he'd answer so couldn't lie or tell the truth. So you know he's not the random person and as such take the other road, as per earlier explanation.
OR
If you end up asking the random person, then you'd get an answer to both questions which identifies him as the random person, so you then ask the question again to one of the other 2 men about the 3rd man.

:?: I think :?:

[Mike]

](*,) :-k My head hurts



Mike ...

[Midders]

[Nemisis]

If i were to ask the three men about whethet or not is left fork (for instance) is the right way to City A........The truthteller will say "yes" if the left fork leads to City A,and "no" otherwise. The liar will answer the same, since he will lie about where the left fork leads. The randomizer may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly report the road to City A.

If however the third person randomly answers yes or no it is clear that you must ask at least two questions, since you might be asking the first one of the randomizer and there is nothing you can tell from his answers.

Start by asking A "Is B more likely to tell the truth than C?"

If he answers "yes", then:
If A is truthteller, B is randomizer, C is liar.
If A is liar, B is randomizer, C is truthteller.
If A is randomizer, C is truthteller or liar.

If he answers "no", then:
If A is truthteller, B is liar, C is randomizer.
If A is liar, B is truthteller, C is randomizer.
If A is randomizer, B is truthteller or liar.

In either case, we now know somebody (C or B, respectively) who is either a truthteller or liar. Now, use the technique for finding information from a truthteller/liar, viz., you ask him the following question: "If I were to ask you if the left fork leads to City A, would you say 'yes'?"

If the answer is "yes", take the left fork, if "no" take the right fork.

[Midders]

Pardon :-?

[Benny]

Hi everyone,

I'm glad you're still interested in this puzzle, but unfortunately I don't have much free time in which to go through it with you (hence why I haven't replied straight away)! I only check this site about once a month at the moment l

I can tell you that the answer has been explained earlier in this thread, so you should look up the previous posts

Best wishes,

Benny.