I would walk out of a job interview that asked brain teasers. It's not revealing of anything and tells the interviewers that either you've heard that piece of trivia before, or you got lucky and reasoned it out. And "we just want to see how you think" is evidence that the interviewers hadn't thought about how to actually determine what kind of an engineer you were.
The best interview I ever had was basically a small amount of spec work accompanied by a writeup of why I did what I did.
It's been a long time (if ever) since I've heard anybody suggest that abstract algorithm questions are great interview questions or should be used exclusively, but I seem to constantly hear that they are totally useless and if you ever ask such a question you're an idiot and I'm leaving. It seems to me that both perspectives are much too extreme.
I didn't walk out, the company said they wanted somebody who did TDD so I wrote an algorithm that created a function that passed all the tests they defined and sent them the function.
The best interview I ever had was basically a small amount of spec work accompanied by a writeup of why I did what I did.