Answer

First ask Man-one, "Does Man-two sometimes tell the truth and sometimes lie?"

A "yes" answer means one of the following must be true:
1) Man-one is the truth teller and Man-two is unreliable;
2) Man-one is the liar and Man-two is the truth teller;
3) Man-one is unreliable and is lying and Man-two is the truth teller; or
4) Man-one is unreliable and is lying and Man-two is the liar.

A "no" answer means one of these must be true:
1) Man-one is the truth teller and Man-two is the liar;
2) Man-one is the liar and Man-two is unreliable;
3) Man-one is unreliable and is telling the truth and Man-two is the truth teller; or
4) Man-one is unreliable and is telling the truth and Man-two is the liar.

If the answer is "yes", you ask Man-one "Is Man-two the liar?";
if the answer is "no", you ask Man-one "Is Man-two the truth teller?"



Depending on the answers to the first two questions, you know one of the following:


A) If the answer to both questions was "yes" then either
1) Man-one is the liar and Man-two is the truth teller; or
2) Man-one is unreliable and lied on the first question and Man-two is the liar.

B) If the answer to both questions is "no" then either
1) Man-one is the truth teller and Man-two is the liar; or
2) Man-one is unreliable and Man-two is the truth teller.

C) If the answer to the first question was "yes" and the second question was "no" then either
1) Man-one is the truth teller and Man-two is unreliable; or
2) Man-one is unreliable and lied on the first question and Man-two is the truth teller.
In either case, Man-three is the liar.

D) If the answer to the first question was "no" and the second question was "yes" then either
1) Man-one is the liar and Man-two is unreliable; or
2) Man-one is unreliable and Man-two is the liar.
In either case, Man-three is the truth teller.



In cases A & B you've identified one person as either the liar or the truth teller and you've identified another person as either not the liar or not the truth teller. In these cases you ask the person who is neither the liar or the truth teller a question you know the answer to. In cases C & D you've identified Man-three as either the liar or truth teller. At this point you simply ask Man-three a question to identify either Man-one or Man-two.

So the final question and results for each case are:

A) You ask Man-two "Is Man-one the truth teller?"
"yes" means that Man-one is unreliable, Man-two is the liar and Man-three is the truth teller;
"no" means that Man-one is the liar, Man-two is the truth teller and Man-three is unreliable.

B) You ask Man-two "Is Man-one the liar?"
"yes" means that Man-one is the truth teller, Man-two is the liar and Man-three is unreliable;
"no" means that Man-one is unreliable, Man-two is the truth teller and Man-three is the liar.

C) You ask Man-three "Is Man-one the truth teller?"
"yes" means that Man-one is unreliable, Man-two is the truth teller and Man-three is the liar;
"no" means that Man-one is the truth teller, Man-two is unreliable and Man-three is the liar.

D) You ask Man-three "Is Man-one the liar?"
"yes" means that Man-one is the liar, Man-two is unreliable and Man-three is the truth teller;
"no" means that Man-one is unreliable, Man-two is the liar and Man-three is the truth teller.