Nodoka first shows up in chapter 48 as one of the Deathival competitors, representing Brute Sloth. She comes across as pretty isolated—not the type who gets excited about fighting. There's definitely something sad about her.
A flashback reveals she had a rough start: homeless as a kid until Shidou and his crew found her and took her in for experiments. It's the same situation Hitomi went through, which is why they share a last name. Both of them got caught up in whatever Shidou was doing.
During the Deathival, Nodoka ends up saving an unconscious Pure, and the two click immediately. They become friends pretty quickly after that.
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