There is a land where every inhabitant is either of Type X or Type Y. One type always tells the truth, and one type always lies. You meet two inhabitants, A and B.
A:B is of Type X.
B:At least one of us is of Type Y.
Which type tells the truth, which type lies, and what are A and B?
(In reply to
Puzzle Answer by K Sengupta)
Asuume that both A and B are liars. Then, by A's false statement B belongs to type Y. Acoirdingly, B's statement is true. This is a contradiction. Therefore, it follows that:
Either: Both of them tells the truth
Or: One of them lies and the other tells the truth.
Assume that each of the statements A and B is true. Then A's true statement implies that B is of type X and B's true statement implies that A must belong to type Y. This is a contradiction, since no two truthtellers can belong to diffrent types.
Therefore one of them is a liar and the other is a truthteller.
Assume, A tells the truth and B always lies. By A's true statement, it follows that B is of type X. Then, B's false statement implies that both A and B belong to type X. This is a contradiction since by assumption, A and B must belong to different types.
Assume that A lies and B tells the truth. Then by A's false statement, it follows that B belongs to type Y, which is in conformity with B's true statement implying, inter-alia that, A belongs to type X. This confirms the validity of this case.
Consequently summarizing the foregoing, we have:
A-> Type X -> Always lies.
B-> Type Y-> Always twlls the trurh.
Edited on March 16, 2022, 2:41 am
Edited on March 16, 2022, 2:51 am
Explanation for Puzzle Answer
