Playing The Blame Game

If the statement 1 is true we end, and if the statement 1 is false then there are 2 possibilities:

1.- The another 2 statements are true, or

2.- One statement is true and the another statement is false among statements 2 and 3.

The first case is impossible,why?... so only the second possibility is possible. Also is impossible all statements are false, because then 1 would be saying that the other statements are false and it would be true. Therefore, there is one only true statement.

$\text{For any 1 statement to be true, the others have to be false.}$

$\text{\Large{So there can only be one true statement}}$

Another badly worded problem (by the same author). The use of the phrase "perfectly logical" here is very ambiguous. One usually thinks of a "logical statement" as being true, which is obviously not the case here.

And by the way, I got it right. I guessed correctly that the question author is actually asking for the number of true statements in a valuation that satisfies the given theory.