I'd also assume that there is a den in the sentence that can be omitted. I do not know why, but otherwise the sentence would not make any sense to me. Could somebody explain this?
With ordinals, we don't need an article, and sista works the same way. It's like words like första, andra, tredje, and sista contain enough definiteness in themselves so that you can skip the article. But you can have it too, both ways are fine.
Does "det" alone count as a determiner? One correct answer is given as "Is that the..." but the answer "Is this the.." is counted as wrong.