The phrase "none the wiser" is an idiom that means not having gained any additional knowledge or understanding despite an explanation or situation. In this context, the person is stating that even after receiving explanations, they did not become more knowledgeable or wiser.

Option A, "wiser," is the correct choice to complete the sentence and maintain the idiomatic expression. The other options ("wise," "wisest," and "worse") do not fit the intended meaning of the phrase "none the wiser."