I’m having trouble understanding this part sentence since I can’t really make our the use of the final の.
The use of の here is similar to this sentence.
What pen can I use?
どんなぺんを使ってもいいですか
The blue one.
青いの.
In the example sentence you provided, you could probably translate it to, “My son’s room is the brightest one”
I believe this is covered in Genki 1, chapter 10 if you need further reading 
Hope that helps
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thank you, somehow this went totally over my head for some reason. 