"I want to see how you approach solving problems"- Is almost always bullshit.

One person I knew at work had a question he used to always ask in interviews. One day while discussing this I asked him to show me some working code for his question. He struggles for a while then gives up(Note, this is his own question). Then he repeats the same trite - "We are just testing their approach".

And I was like "Oh sure, Their approach towards something whose answer you don't even know, to evaluate against."