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The Truth Teller, The Liar, and The Unreliable Man

Logic puzzles require you to think. You will have to be logical in your reasoning.

 

Puzzle ID:#43910
Fun:*** (2.5)
Difficulty:*** (2.81)
Category:Logic
Submitted By:javaguru*us**

 

 

 



There are three men, Alex, Bob and Chuck. One of the men always tells the truth and one always lies. The third man always tells a lie after telling the truth and always tells the truth after telling a lie. The third man can answer the first question truthfully or can lie.

Can you tell who is the truth teller, the liar and the unreliable man by asking just three questions? Each question is directed to a single person.


Answer

First ask Alex, "Does Bob sometimes tell the truth and sometimes lie?"

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

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

If the answer is "yes", you ask Alex "Is Bob the liar?"; if the answer is "no", you ask Alex "Is Bob 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) Alex is the liar and Bob is the truth teller; or
2) Alex is unreliable and lied on the first question and Bob is the liar.

B) If the answer to both questions is "no" then either
1) Alex is the truth teller and Bob is the liar; or
2) Alex is unreliable and Bob is the truth teller.

C) If the answer to the first question was "yes" and the second question was "no" then either
1) Alex is the truth teller and Bob is unreliable; or
2) Alex is unreliable and lied on the first question and Bob is the truth teller.
In either case, Chuck is the liar.

D) If the answer to the first question was "no" and the second question was "yes" then either
1) Alex is the liar and Bob is unreliable; or
2) Alex is unreliable and Bob is the liar.
In either case, Chuck 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 Chuck as either the liar or truth teller. At this point you simply ask Chuck a question to identify either Alex or Bob.

So the final question and results for each case are:

A) You ask Bob "Is Alex the truth teller?"
"yes" means that
Alex is unreliable, Bob is the liar and Chuck is the truth teller;
"no" means that
Alex is the liar, Bob is the truth teller and Chuck is unreliable.

B) You ask Bob "Is Alex the liar?"
"yes" means that
Alex is the truth teller, Bob is the liar and Chuck is unreliable;
"no" means that
Alex is unreliable, Bob is the truth teller and Chuck is the liar.

C) You ask Chuck "Is Alex the truth teller?"
"yes" means that
Alex is unreliable, Bob is the truth teller and Chuck is the liar;
"no" means that
Alex is the truth teller, Bob is unreliable and Chuck is the liar.

D) You ask Chuck "Is Alex the liar?"
"yes" means that
Alex is the liar, Bob is unreliable and Chuck is the truth teller;
"no" means that
Alex is unreliable, Bob is the liar and Chuck is the truth teller.

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