This is why we at Google don't (or shouldn't, at least - it's widely discouraged) ask brainteaser questions in interviews.
I disagree on whiteboard coding though. I don't find it that easy, but I think it's reasonable to expect a demonstration of relevant skills before you hire a candidate. Any sensible interviewer won't expect syntax-perfect code on a whiteboard, but it's at least a way of seeing if the candidate can walk the walk rather than just talking for an hour.
> I guess I do not see how you can lose if you take the contract-to-hire approach ..
For the first month, the vast majority of people are relatively unproductive. After the next month, good candidates are generally still going through a significant learning curve. Contracting several candidates for a few months to pick one who seems good enough is expensive for relatively little output - apart from salaries, they need desks and computers etc, and you have to do some interviewing to pick them in the first place. It's not a worthless approach, but I don't see it as a panacea.