Harry Potter is curious

The $2$ nd man cannot be Cadmus, the truthful man, since he claims the $3$ rd man is Cadmus. Therefore either the $1$ st or $3$ rd man is Cadmus. $\text{Case 1: 1st man is Cadmus}$ Since he is the truthful man, his statement that the $2$ nd man is Antioch must be true. Antioch's statement is false, so the $3$ rd man is Ignotus, and he happens to be telling a lie. In this case, the $2$ nd man is $\boxed{\text{Antioch.}}$ $\text{Case 2: 3rd man is Cadmus}$ His statement must be true that the $1$ st man is Ignotus, leaving the $2$ nd man to be $\boxed{\text{Antioch.}}$ Although it doesn't matter in this case, this is a contradiction since he would be telling the truth about Cadmus, making case $1$ the only correct case. Even so, there is no possible answer other than $\boxed{\text{Antioch.}}$

If you liked this riddle, try the riddle of the three gods, also known as the Hardest Logic Puzzle Ever.

Because I happen to be confused when the names aren't "standard", let me rephrase the problem.

Knights always tell the truth. Knaves always lie. Normals can tell the truth or lie. There are three men; you know one is a knight, one is a knave, and one is a normal, but not which is which. The first man says that the second man is a knave. The second man says that the third man is a knight. The third man says that the first man is a normal.

One of the three statements must be true (since it's spoken by a knight), and one must be false (since it's spoken by a knave). The third one must also be false as well, since it's impossible for two of the statements to be true; if two are true, by elimination the remaining man will take the remaining role which makes the third statement true. Thus the normal lies now. We can then rephrase the sentences:

• The first man says the second man lies.
• The second man says the third man tells the truth.
• The third man says the first man lies.

We know that "A says B tells the truth" means A and B both tell the truth or both lie. Similarly, "A says B lies" means exactly one of A and B tells the truth; the other lies. Thus there are only two possibilities, either the first man tells the truth or both the second and the third mans tell the truth. Since there is only one true sentence, the first case is the actual case; the first man is a knight, which means the second man is a knave. The second man is Antioch .

As Cadmus always tells the truth he cannot be the 2nd person cause the 2nd person says that 3rd person is Cadmus.

Then if we take that third person is Cadmus then the second person has to be Ignotus but 3rd person says 1st person is Ignotus so it does not match.

Now we have only one option left that is Cadmus is 1st person then Antioch has to be 2nd person and then he lies about the 3rd peson claiming him to be Cadmus rather than Ignotus and then Ignotus also lies telling that 1st person is Ignotus. (Note-: In the first case Ignotus tells the truth but in the second case he lies.)

So our answer has to be {Antioch}

Since no name are repeted it's obvious 2 of them lied.

So the 2nd one can't be Cadmus (because he will tell the truth and the 3rd one will be Cadmus to).

The 3rd one can't be Cadmus for the same reason, to because in this case the 2nd one will tell the truth and only Cadmus will.

So the 1st one is Cadmus and tell the truth, which means the second one is Antioch.

The way to figure this out is to create each scenario and play it out. Immediately we know the 2nd man is not Camdus (C) because if he was, it would be a lie. So there are 4 possible remaining scenarios. 1.) 1=A 2=I 3=C 2.) 1=I 2=A 3=C 3.) 1=C 2=I 3=A 4.) 1=C 2=A 3=I The fourth scenario is the only one that is plausible. The first man is C telling the truth that the second man is A. The second man is A lying about the third man being C. The Third Man is I, deciding to lie in saying that the first man is I. The other three scenarios will not work.

Statements:

• 1st says 2nd is Antioch.
• 2nd says 3rd is Cadmus.
• 3rd says 1st is Ignotus.

Right from that, we know 2nd man can not be Cadmus. So, 2nd can be Ignotus or Antioch. If he was Ignotus telling the truth (3rd is Cadmus), that would lead to a contradiction because 3rd says Ignotus is the 1st. If 2nd was Ignotus lying, that would mean 3rd man would be Antioch, which would make the 1st Cadmus, which also leads to a contradiction since 1st claims the 2nd is Antioch. Therefore, the only possible answer is:

1st man is Cadmus; 2nd man is Antioch; and 3rd man is Ignotus.

Remember that the third man says that the first man is Ignotus. Assume that man is Cadmus. Then the first man has to be Ignotus. Assume that Ignotus is telling the truth. Finally, the second man is obviously Antioch.