I am somewhat undecided as to the effectiveness of such puzzles as strong indicators of whether someone is a good match for a job. I think it depends on the job. But I have noticed that other companies are starting to use this method to identify people who are likely to be good matches. Poundstone argues in his book that although good candidates might be rejected due to a failure to answer puzzles, they're likely to eliminate poor matches.
I used to work on puzzles when I was younger, but I stopped sometime during high school. Possibly, because I was working during the summertime, I had less time to work on puzzles. (I can remember doing puzzles during the summer partially because there was not much else to do, although I would do other things, such as read or explore the neighborhood. Point of context: from ages 12-18 I spent most if not all of my summers on Cape Cod, Mass.) I may also have had less interest -- I recall getting more interested in running and playing softball with my coworkers.
I have identified this aspect of problem solving as a possible weakness in me, but I'm not sure how it actually helps people, say, to be top students in competitive academic programs. Perhaps it opens up neural pathways that enable the brain to more efficiently identify the solutions to problems without getting stuck or going down dead ends. I don't know much about cognitive science; perhaps there are some studies of sample populations that shed some light on this.
Anyway, the other day I was wondering whether or not the question "is it possible to build any combinational logic circuit out of NAND gates, and if so, how?" is a fair interview question for anyone applying for a software development job. As it turns out, a modified version of this question is on the techinterview site, so I suppose the answer is yes. I know the answer, but it's because of digital design classes where I actually had to build circuits. If I'd never built a circuit in my life, I don't know if I would answer the question correctly in an interview, because I don't know if I would think of all of the cases, especially if I was feeling stressed.