## 147. The Sixth Island

Two inhabitants A and B of this island stated:

A: Either B is a knight, or this island is called Maya.

B: Either A is a liar, or this island is called Maya.

Can we assert that this island is indeed called Maya?
147. If A were a liar, then both alternatives of the disjunction he stated would be false, which would mean that B is a liar. In turn, this would mean that both alternatives of the disjunction stated by B are false, and A must be a knight. The contradiction obtained shows that A is a knight. Therefore, his statement is true, and either B is a knight or the sixth island is called Maya. If the second alternative is true, then the sixth island is, of course, the island of Maya. Suppose the first alternative is true, that is, B is a knight. Then his statement is true: "Either A is a liar or this island is called Maya." But A is not a liar, so the first alternative is false. Therefore, the second alternative is true, and the sixth island is the island of Maya.

In brief, part of our reasoning comes down to the following. We have established that either B is a knight or the sixth island is the island of Maya. But, in addition, we know that if B is a knight, then the sixth island is the island of Maya. Therefore, the sixth island is the island of Maya.

Thus, the island of Maya has been found after a long search! 148. If E were a liar, then it would be true that either E is a liar or C and D are of the same type. This would mean that a liar made a true statement. Since this is impossible, E is a knight. Therefore, his statement is true, so either he is a liar or C and D are of the same type, and since he is not a liar, C and D are of the same type.

Suppose C were a liar. Then A and B would both be liars. The statement made by D would be true, so D would be a knight. Thus, C would be a liar and D a knight, which contradicts their being of the same type. Therefore, C must be a knight. Hence, D is also a knight. Since C is a knight, A and B cannot both be liars, from which we conclude that either X or Y is the correct map. Suppose X is the correct map. Then A is a knight and B is a liar, contrary to the true statement made by D that either A is a liar or B is a knight. Therefore, X cannot be the correct map. Hence, Y is the correct map.