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Thanks for the thoughts. How about something like:

Hey Guys:

Thank you very much for the opportunity to interview with <COMPANY>. While I understand that you don't view me as a good fit to work with you guys, I would greatly appreciate knowing what was incorrect about my submission, such that I can continue developing my skills to ultimately attain a point where we are a good fit for each other.

Thank you very much,

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That sounds fine. I'd make a few small adjustments, but it has to be your words. Here I've tried to make it clear that their decision has been accepted, and acknowledge that there's nothing in it for them to provide the feedback:

Hey Guys: Just wanted to say thanks for the opportunity to interview with you. I recognize and understand that for whatever reason you decided I'm not a good fit, and accept that. I was wondering, though, if there'd be any chance of some feedback about my submission. I know that this would take some time and effort on your behalf for no real return, but I'd really appreciate anything you'd care to tell me about my submission. I'm always eager to learn and develop my skills, and perhaps you can help me become a better programmer, and possibly become a good fit for the future.

Yours etc

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