Ne Ni Ni in the quiz question is grammatically incorrect.

Question

Neither is one of two things. Therefore the question in the quiz was grammatically incorrect.` I like neither the guitar, nor the violin, nor the piano` is not phrased correctly.

Answer

Hi James,
I think you are a bit to restrictive. Rudyard Kipling wrote:
"But there is neither East nor West, Border, nor Breed, nor Birth, when two strong men stand face to face, though they come from the ends of the earth!"
The neither..nor..(nor).. construct seems to have been extended to stand for one and only one choice out of several offered, not just two.

Answer

Thanks, I was thinking of the literal meaning of `neither`. I recall that once, as a schoolboy, I got detention for using neither as a negative option for one of three things.