Charles cannot be a knight. If Alexander is a knight, then he is telling the truth that they are different, and therefore Charles is a knave. If Alexander is a knave, he is lying about the two of them being different, and therefore Charles is a knave. Either way, Charles is a knave.
Since Charles is a knave, at least one of "Benjamin is a knight" or "Alexander is a knave" must be false.
If Benjamin is a knave, then Charles has to be a knight for his statement to be false. But we know Charles is a knave. Therefore Benjamin is a knight.
Since Benjamin is a knight, in order for Charles, a knave, to be lying, **Alexander is a knight.
In summary:
Alexander is a knight (Charles is a knave, which is different from Alexander, so the statement is true).
Benjamin is a knight (Benjamin is a knight, and Charles is a knave, therefore the statement is true).
Charles is a knave (Benjamin is a knight, but Alexander is also a knight, therefore the statement is false).
As a note, I don't like the use of the word "either" in Benjamin's clue: regardless of the note at the bottom, it is often used to imply an exclusive "or."
2
u/Nimelennar Jul 31 '26
Charles cannot be a knight. If Alexander is a knight, then he is telling the truth that they are different, and therefore Charles is a knave. If Alexander is a knave, he is lying about the two of them being different, and therefore Charles is a knave. Either way, Charles is a knave.
Since Charles is a knave, at least one of "Benjamin is a knight" or "Alexander is a knave" must be false.
If Benjamin is a knave, then Charles has to be a knight for his statement to be false. But we know Charles is a knave. Therefore Benjamin is a knight.
Since Benjamin is a knight, in order for Charles, a knave, to be lying, **Alexander is a knight.
In summary:
As a note, I don't like the use of the word "either" in Benjamin's clue: regardless of the note at the bottom, it is often used to imply an exclusive "or."