> Well if you solve it, then you've proved that you can solve it, right?
Which gives you more data on how someone works and thinks?
1. Person silently sits for 15 minutes and then codes up a solution that meets the test criteria in another 15 minutes, typing quickly.
2. Person talks about the issues, tradeoffs and experiences while coding. They ask questions and engage in some discussion around the problem set. They end up with a partial solution after 30 minutes.
Of course those are hypothetical extremes, but it is clear to me which scenario gives the interviewer more information.