Discussion Forum

In a colony, each person is either a truth teller, who always speaks truth or a liar, who always lies or an alternator, who alternates between truth and lie in any order.When a question is asked to three persons P1,P2 and P3 whose names are P, Q, R not necessarily in the same order they replied in the following manner.

P1: I am Q.

      Exactly one of us is liar.

P2: Exactly one of us is truth teller

     P3 is P

P3:Exactly one of us is an alternator

     I am not R

If there is at least one truth teller, then who is R?

Answer:

Explanation:

Suppose, P1 is a truth-teller.As exactly one of them is a liar,  second statement of P2 or P3 must be false. But if the second statement of P2 is false, then P3's second statement must be false.

Therefore, P2's first statement is true.

Therefore, P3's first statement must be false .

Suppose P2 is a truthteller, then P3 is P.

Therefore, P3's second statement is true.

$\Rightarrow$ P3's first statement must be false

Therefore, P1 must be an alternator.

P1's second statement must be false

Therefore P1 is Q.

$\Rightarrow$P2 is R.

If P3's both the statements are true,which is not possible as it violates the conditions given by P2 and P1.