> How many times did you have to solve a brain teaser at work?

There is a fine line between brain teasers and the difficult problems that are our bread and butter. To answer your question: I would categorize many particularly subtle problems I've solved at work as brain teasers, so my number is high.

Relevant problems are a great way to judge someone's problem solving skills, but any problem that gives a glimpse into the way a person thinks is sufficient. I am probably not willing to give a candidate the amount of context to describe, let alone time to solve, the exact problem that I happen to be in the middle of on the day of an interview, but rather one we have already solved and determined to be interview-worthy. This means I certainly don't care about the solution, but rather the path to the solution. If you believe, as I do, that people tend to walk similar paths through every problem they solve, and that the path is important and the solution worthless, then the relevance of the problem is irrelevant.