Perhaps the tenacity and work ethic needed to study a couple of months for an interview selects for people who would do the job well anyways? Maybe that is what it means to be Googly as a culture fit?
Anyways, practicing solving clever small programming problems at least isn’t boring (though I’m beginning to burn out on it), it reminds me of prepping for a high school or ACM programming contest. As long as it eliminates enough false positives, they’ll keep up with it.
It isn’t just if you can solve these problems, but can you also write straight lines of text on a white board? Also, do it while talking and and standing on one foot at the same time.