Take the feedback of everyone who interviewed (your team) into consideration and either offer the position because you feel they are motivated and technically sound or you can fly them in for a 3-4 hour person-to-person after a phone screen or two.
This is what Slide, Facebook, Google, etc. do. None of them mandate puzzles, seems like they use them as a way to "Wow" them.
In the past, I've seen companies give "quizzes" they can do in a limited amount of time. Generally 10-15 question quizzes as a quick way to judge, without wasting your own time, if they are competent enough but hopefully a resume is enough.
Disclaimer: This isn't necessarily my opinion of how it should be done, just how companies that have been around the block do it.