First, working in Google, Facebook, Amazon, or Twitter is overrated more likely than not. Remember that. You don't really need to work in a big company to have fulfilling job that allows you to grow professionally and pays decently. (Don't be greedy.)

Second, remember that interviewing is both way lane. It's not only a way for employer to assess candidate, it's a way for a candidate to assess the potential employer. Treat it as such.

This may be a cliché, but if all I got asked in the interview was some random puzzles and nobody was interested in the work I had done in the past, I would probably avoid such company. They don't seem to hire based on competency, so I'm likely the first one with the ability to develop and deploy a well-designed system (completely different thing from algorithms). I don't like to struggle with making each and every step. The same stands if they require specific education.

And the last thing, in current landscape there's plenty of jobs in IT and only so many competent programmers, sysadmins, netadmins, or DB operators. It's the employers who struggle with finding good candidates, not the other way around.