What is this な doing here?

Question

あれ?参加者は20人のはずなのに、21人いる。

I'd translate it as follows: "Huh? I'm sure it should be 20 participants, but 21 are here."

I interpreted "should" because のに to my knowledge indicates a surprise here. Using plain indicative wouldn't reflect that in my opinion.

However, the real "problem" is the bold な. First, I don't know into what category はず falls (formation morpheme like suffix, or anything else like noun, verb etc.). Therefore it is hard for me to try to use other grammatical rules to deduce the meaning of な, like な after nouns in -んです/-のです constructions. And even if I knew that, I still wouldn't know what function it bears here.

Answer 1

筈{はず} is a noun that roughly means that something is expected to hold true, and the な is actually the 連体形/attributive form of the particle だ (断定). It's not making はず into an na-adjective.

Basically, there is an expectation "that there should be twenty participants", and it's being attributed the nominalization particle の, turning it into a noun-phrase. That に that follows then turns that into "despite (noun phrase)..."

Your translation is correct :)