Since we cannot refer to the liar, we can refer to the extended puzzle's author.
The author states that the goal of the extended puzzle is to determine if there is, 'IF ANY' (!!), a correct statement among [A, B, C, D, E]. Thus, there can be zero or at most one statement we can conclude as being true for sure.
The liar didn't said if he has hats. Maybe he has 0. Maybe 1. Maybe n. We just don't know.
'A: The liar has at least one hat.'
> We cannot conclude this statement as sure, since maybe the liar has in fact 0 hats.
'B: The liar has only one green hat.'
> He has maybe 0 hats. Or maybe n | n>1.
'C: The liar has no hats.'
> He has maybe 1 hat. Or maybe n | n>1.
'D: The liar has at least one green hat.'
> He might not have any hats at all.
'E: The liar has no green hats.'
> Since the liar may have 2 hats, one could be green and the proposition could still be false, as it is a lie.
Since we cannot conclude any of the statements as being definitively true, the extended puzzle's answer is none of them are true for certain. It depends on how many hats the liar has.
Since we cannot refer to the liar, we can refer to the extended puzzle's author.
The author states that the goal of the extended puzzle is to determine if there is, 'IF ANY' (!!), a correct statement among [A, B, C, D, E]. Thus, there can be zero or at most one statement we can conclude as being true for sure.
The liar didn't said if he has hats. Maybe he has 0. Maybe 1. Maybe n. We just don't know.
'A: The liar has at least one hat.' > We cannot conclude this statement as sure, since maybe the liar has in fact 0 hats.
'B: The liar has only one green hat.' > He has maybe 0 hats. Or maybe n | n>1.
'C: The liar has no hats.' > He has maybe 1 hat. Or maybe n | n>1.
'D: The liar has at least one green hat.' > He might not have any hats at all.
'E: The liar has no green hats.' > Since the liar may have 2 hats, one could be green and the proposition could still be false, as it is a lie.
Since we cannot conclude any of the statements as being definitively true, the extended puzzle's answer is none of them are true for certain. It depends on how many hats the liar has.