As others have noted in the comments, if the liar has no hats, then "All my hats are green" is, in some formal understanding, true. The liar cannot make true statement so must in fact have at least one hat.
That makes A) a good candidate.
But E) can also be true — and in fact both A) and E) can both be correct.
Thank you for clarifying something that I pointed out in my comment while missing the total point of my comment.
on edit: I don't actually think you made my comment "but all of the questions are potentially true." any clearer than I made it, and evidently you seem to think that only A and E are potentially true, which is obviously wrong.
on second edit: ah I see that you believe the idea that some people are saying that All my hats are green indicates that the liar must have hats https://news.ycombinator.com/item?id=42369002 because evidently the assumption is that the 0 hat has a color green for some reason that is not adequately explained.
If that were true then it also follows that if the liar has no hats then all his hats are every color known to humanity. I don't think that is the way it works however.
instead of going through and making more and more edits, I finally figured out what the problem is here - there are at least two logics being used here - one set theory, in which case for vacuous truth I guess it's true that all the hats are green if you have an empty set, and the other linguistic logic.
In many forms of linguistic logic you need to have an existent hat to have the property green, therefore if you do not have any hats you have no green hats. Which is my preferred method of dealing with this.
Is the column that was linked more likely to be interested in linguistic logic games or formal mathematical logic games? I'm guessing the second, in which case I guess it's true we can conclude A - but I inherently dislike vacuous truths when applied to logic, especially language like this where the normal argument that the second parameter "Green" is never evaluated because we do not have the first "A hat" in the empty set seems suspect to me because we know what Green is separate from a hat, we just need to know if there is a hat we can assign Green to.
That makes A) a good candidate.
But E) can also be true — and in fact both A) and E) can both be correct.