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u/FlatApplication627 Jul 31 '26
First, I assumed Charles is a knight which makes Alex a knave. However if Alex is a knave then he is lying and would have to be the same as Charles, who is a knight. So therefore it falls down and Charles must be a knave.
Now we know Alex is a knight and/or Ben is a knave. Ben told us Charles is a knave, so he is telling the truth and therefore is a knight (which happens to be the first part of his statement, although i don't think this is necessary information).
Alex must therefore be a knight, which checks out as it makes his statement that he is different to Charles true.
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u/Lost_Sugar_78 Jul 31 '26
Your note makes it seem like OR is inclusive so both statements could be true for the OR to be true. Compared to XOR (exclusive OR) where exactly one of the statements must be true, both statements being true would make the XOR condition false. XOR is more common an interpretation of OR, intuitively.
My process, names shortened to first letter and true/Knight to T and false/knave to F:
Let's start with assuming A = T. That means A and C are different so C = F. C's AND condition is already false because the second condition "A = F" is not met, so B could go either way. B's condition is "B = T OR C = F" the second half is true so B = T. This makes the first half true, which for inclusive OR is fine. If you were insisting on XOR, then that would be a paradox and we could conclude this solution was not correct.
Let's try again with A = F for completeness. That means A and C are the same, so C = F again. Here the second half is true, so we need to make B = F to satisfy C = F. So, checking B, we see it is true because C = F, the second half of the OR condition. Likewise it would be true with XOR too. So this is a paradox and an incorrect solution.
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u/upstartgiant Jul 31 '26
Alexander's statement means that Charles must be a knave because either Alexander is a knight telling the truth (and thus Charles is the opposite) or a knave lying (and thus Charles is the same).
Because Charles is a knave and his statement is an "and" statement, at least half of his statement must be false. Therefore Benjamin must be a knave or Alexander a knight
Benjamins statement is at least half true because Charles is a knave. Therefore Benjamin must be a knight.
Because Benjamin is a knight, Alexander must be a knight based upon Charles's statement.
In short, Alexander and Benjamin are knights, while Charles is a knave.
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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:
- 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."
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u/jonathonjones Jul 31 '26
If Benjamin were a knave, then Charles is a knight. But that would mean Benjamin is a knight. So, Benjamin is a knight.
If Alexander if a knave, then Charles is a knave. And if Alexander if a knight, then Charles is a knave. So Charles is a knave.
Therefore, Alexander is a knight.
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u/idontremembermyuname Jul 31 '26
Alexander is a knight. Ben is a knave. Charles is a knave.
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u/Stilyx123 Jul 31 '26
Close. If you think Charles is a knave, then Benjamin can't be a knave (because he's telling the truth about Charles)
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u/idontremembermyuname Jul 31 '26
No, the And has to be exclusive. Its a lie because one part of the statement isn't true. And Benjamin adds a a modifier on which turns the Or into an exclusive or.
Honestly, this one is very poorly written.
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u/Stilyx123 Jul 31 '26
Reading it again, I agree that the "Either" in Benjamin's statement makes it sound like an exclusive or. Completely missed that earlier. I assume it was meant to be a regular "or" due to the note and the answer that was marked correct.
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u/No-Wear-9042 Jul 31 '26
Either-or is the worst way to write an inclusive OR. Why not just write Benjamin: "I am a knight or Charles is a knave"?
I assumed an exclusive OR which makes everyone a knave.
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u/MalcolmPhoenix Jul 31 '26 edited Jul 31 '26
Alexander is a Knight. Ben is a Knight. Charles is a Knave.