An adventurer found a locked treasure chest in a dungeon.
He tracked down three brothers (each either a Liar or a Knight) one of whom has the key to open the chest.
Each made a statement:
A: I have the key to the chest.
B: I don't have the key to the chest.
C: B Doesn't have the key.
The adventurer knows that at least one of the three is a Liar, and at least one - a Knight. Who has the key?
(In reply to
Puzzle Answer by K Sengupta)
At the outset, suppose that A is a Knight. This implies that he has the key to the chest. But in that situation, the statements of each of B and C are truthful. Accordingly, all three of A, B, and C are knights. This leads to a contradiction.
Suppose B is a knight. Then he doesn't have the key to the chest, so that C's statement is truthful, and therefore he is a Knight. Since there are 2 Knights, it follows that the remaining individual, that is A, must be the Liar. Then A's false statement implies that he doesn't have the key. Since neither of A and B has the key, it follows that C must possess the key to the chest.
Thus summarizing, we have:
A is a Liar.
B and C are Knights.
C has the key to the chest.
*** It may be evident that my second fully explained solution (present one) has employed a different method compared to the previous one.
Edited on June 9, 2022, 11:03 pm
Explanation to Puzzle Answer
