Thank you for these answers! Two half-days of interviews is quite reasonable. I had the impression that things took longer than that, though perhaps I was mistaken because Google takes relatively long to make an offer.
If their interviewing process is anything like the ones I've helped organize, at least 49 out of 50 applicants could be dismissed out-of-hand, either because they didn't read the position description, because they can't write fluently in their native language, or because they can't write simple programs. So taking that as an estimate, Google is accepting perhaps 5–25% of "serious" applicants.
I think the large fraction of non-serious applications is caused by a survivor bias—the qualified candidates get hired quickly, but the unqualified ones keep applying to hundreds of jobs.
And you make a good point about interesting problems—Google certainly works on some neat stuff at an impressive scale.