Best Answer Writersblock , 30 July 2007 - 01:31 AM

Martini,

Spoiler for ...

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Originally I thought this was impossible, but I think I have solved it. Nice one.

I saw that:

There are 6 possible states for the order of the men: TRL, TLR, LTR, LRT, RTL, RLT

There are 8 possible combinations of anwers for questions: TTT, TTL, TLT, TLL, LTT, LTL, LLT, LLL.

Theoretically it's possbile if you could figure out a way to get any of the 8 combinations of answers assigned to the states, but with the unreliability of Random's answers, I thought it was impossible. There is always a possiblity in any solution where Random will exactly mirror T or L for answers. He could always lie or always tell the truth and you can never tell when he is lying or telling the truth. This being given, I thought you can NEVER separate 6 distinct answers to apply to the 6 states, and therefore can never be sure who is who.

After a minute though, I saw through my own error in logic. I was always dealing with questions where T and L would give the same answer regardless of the order of the men. I saw that if you can get T and L to give a Yes/NO answer, then you can figure out where R's worthless answers are. The only way I saw to do this is to ask about the order of the men themselves.

So:

Ask #1 if L is standing on R's right arm (our left if they are facing us).

The answer gives you a split in the order they are standing:

If YES, then it has to be T telling the truth, L telling a lie, or one of R's worthless answers, so: TLR, LTR, or RTL, RLT.

If NO, then it has to be T telling the truth, L telling a lie, or R and his worthless answers, so: TRL, LRT, or RTL, RLT.

Now we know, based on the answer to #1 where to avoid R's worthless answers. We now ask T or L "Is T in the lineup?" If answer 1 was Yes, we ask person 2, if it was no we ask person 3.

The answer now will give us some more info. If it's Yes, it's T answering the truth, if it's no, it's L answering a lie. So based on who we asked, we now know:

Yes, Yes: Has to be LTR, or RTL

Yes, No: TLR, RLT

No, Yes: LRT, RLT

No, No: TRL, RTL

Now any question separating the two possiblities works - just make sure you are avoiding R's worthless answers.

For example:

Yes, Yes - ask #2 if #1 is L. (We know #2 is T and will tell the truth) - Yes = LTR, No = RTL

Yes, No, - ask #2 if #1 is T. ( We know #2 is L and will tell a lie) - Yes = RLT, No = TLR

No, Yes - ask # 3 if #1 is L. (We know #3 is T and will tell the truth) - Yes = LRT, No = RLT

No, No, - ask #3 if #1 is T. (We know #3 is L and will tell a lie) - Yes = RTL, No = TRL

So we have the order and know who is who.

I saw that:

There are 6 possible states for the order of the men: TRL, TLR, LTR, LRT, RTL, RLT

There are 8 possible combinations of anwers for questions: TTT, TTL, TLT, TLL, LTT, LTL, LLT, LLL.

Theoretically it's possbile if you could figure out a way to get any of the 8 combinations of answers assigned to the states, but with the unreliability of Random's answers, I thought it was impossible. There is always a possiblity in any solution where Random will exactly mirror T or L for answers. He could always lie or always tell the truth and you can never tell when he is lying or telling the truth. This being given, I thought you can NEVER separate 6 distinct answers to apply to the 6 states, and therefore can never be sure who is who.

After a minute though, I saw through my own error in logic. I was always dealing with questions where T and L would give the same answer regardless of the order of the men. I saw that if you can get T and L to give a Yes/NO answer, then you can figure out where R's worthless answers are. The only way I saw to do this is to ask about the order of the men themselves.

So:

Ask #1 if L is standing on R's right arm (our left if they are facing us).

The answer gives you a split in the order they are standing:

If YES, then it has to be T telling the truth, L telling a lie, or one of R's worthless answers, so: TLR, LTR, or RTL, RLT.

If NO, then it has to be T telling the truth, L telling a lie, or R and his worthless answers, so: TRL, LRT, or RTL, RLT.

Now we know, based on the answer to #1 where to avoid R's worthless answers. We now ask T or L "Is T in the lineup?" If answer 1 was Yes, we ask person 2, if it was no we ask person 3.

The answer now will give us some more info. If it's Yes, it's T answering the truth, if it's no, it's L answering a lie. So based on who we asked, we now know:

Yes, Yes: Has to be LTR, or RTL

Yes, No: TLR, RLT

No, Yes: LRT, RLT

No, No: TRL, RTL

Now any question separating the two possiblities works - just make sure you are avoiding R's worthless answers.

For example:

Yes, Yes - ask #2 if #1 is L. (We know #2 is T and will tell the truth) - Yes = LTR, No = RTL

Yes, No, - ask #2 if #1 is T. ( We know #2 is L and will tell a lie) - Yes = RLT, No = TLR

No, Yes - ask # 3 if #1 is L. (We know #3 is T and will tell the truth) - Yes = LRT, No = RLT

No, No, - ask #3 if #1 is T. (We know #3 is L and will tell a lie) - Yes = RTL, No = TRL

So we have the order and know who is who.