What is your process for evaluating "how someone solves a problem" and how does that inform your hiring decision? Does it simply come down to "does this person

What is your process for evaluating "how someone solves a problem" and how does that inform your hiring decision? Does it simply come down to "does this person solve the problem the way I would"? How do you address confounding issues like performance anxiety induced by constraints not present in a normal work scenario? My observation is that many companies don't address those problems well.