Grammar question about [sentence]のに

Question

I was asked by my teacher to read a kid friendly manga, something easy to start with.

I am not having issue with the vocabulary and I understand the general gist of a sentence but I am having issue with "why" is the sentence constructed that way.

そういえばほかのボールがどこにあるかもわからないのにどうやって探すんだ？

So what I get from this is :

Come to think of it how are we going to find the place, that I don't know, where the ball is.

But I am a bit confused grammar-wise with two things :

あるかも

and

わからないのに

These are my best guesses :

あるかも -> か　is to show that the character is asking where is the place of the ball

も is used here to say the character doesn't know anything about it

わからないのに -> に say that the previous part of the sentence is where they need to look

の I really have no idea why a no would be here

Thank you for your help !

Answer 1

The sentence can be roughly divided into three parts:

そういえば、｛ほかのボールがどこにあるか｝もわからないのに、どうやって探すんだ？

• そういえば is a common set phrase, "come to think of it", "as I recall."
• ほかのボールがどこにあるか forms an embedded question. "where the other balls are".
• ～が分かる is "to know/understand ～".
• The following も replaces が, and adds the nuance of "(not) even". See: The meaning of 「尋ねられもしないこと」 and How to say "even" in Japanese?
• のに is a common conjunction that means "although", "despite the fact that ～". See examples here.

Come to think of it, how can we find (it) when we don't even know where the other balls are?

I don't know what exactly they are searching for from this context. Maybe they are searching for something which is related to 'the other balls'.