An intern's productivity sort of lies in "how fast they learn". Can they pick up things by just being pointed into the right directions or do they need everything spoon-fed, in small doses, with repetition, to then still get it wrong?
At least in our place, we do not really expect them to be productive in the usual sense, but they definitely have ample opportunity to give us a feeling of their place on the bell curve.
(as an anecdote: We currently have some 17 year old apprentice which puts some of our seniors to absolute shame, myself included. The amount of motivation, learning hunger, quick thinking and ability to ask the right questions is really astounding, especially given that he essentially just started and has next-to-no education in our area to speak of as of yet)
To be cynical, there are no dumb questions, only dumb people. Some people ask the same question over and over, and others have different questions, rather rapidly getting to very interesting questions.
There are many dumb questions. Asking me about ancient Chinese history for example. (this is a particularly dumb question to ask in the context of this thread where it is an off topic question asked to someone who knows very little about the topic)
We had some awesome interns, very interested in learning and working! I'm talking about those who weren't and surprised Google (and Facebook) hired them soon after.
So how is your interview process better than theirs, since you keep getting these lousy people? I saw many worthless people in the places I worked at before Google, then at Google I didn't see anyone close to that bad, so to me their process seems to work. They were very open about their data around hiring and scoring hires as well, and that data was very clear that the interview they arrived at was the best interview, they tried and experimented a lot and arrived at it.
Alternatively maybe those people were just unmotivated to work for you and spent their internship preparing for Google.
