There is an island where every inhabitant is either of Type X or Type Y. One of the types always tells the truth, and the other type always lies, but you are not sure which is which. You meet two inhabitants of this island, A and B.
A: B is of Type X.
B: We are both 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)
Assume that A and B are of the same type.
Then:
EITHER, both A and B are liars.
OR, both A and B are truthtellers.
If both A and B are liars, then A's false statement implies that B belongs to Type Y. But, B's false statement implies that both of them cannot be Type Y. So, A must correspond to Type X. This is a contradiction since the two of them are NOT of the same type.
If both A and B are truthtellers, then A's true statement implies that B is of Type X. But B's true statement indicates that he must correspond to Type Y. Contradiction. Accordingly, one of A and B must be a liar and the other a truthteller.
Since the two individuals must correspond to different types, this clearly marks out B as a liar. Therefore, A must be a truthteller.
This is in consonance with the given conditions.
Consequently summarizing, we have:
A -> Type Y -> Always speaks truthfully.
B-> Type X -> Always lies.
Edited on March 17, 2022, 2:21 am
Explanation for Puzzle Answer
