Here is an interview with Dr. Paul Dear, founder of the N (Nanosatellite)-Prize. The N-Prize will be awarded thus:
"... the N-Prize is a £9,999.99 (sterling) cash prize which can be claimed by any individual, or group, who are able to prove that they have put into orbit a small satellite. The satellite must weigh between 9.99 and 19.99 grams, and must orbit the Earth at least 9 times. This project must be done within a budget of £999.99 (sterling)."
That budget includes launch, and you can't use a donated launch vehicle: someone has to invent a radical nanosat launch system. Conventional rockets, balloon launches, and gun launches are suggested options.
"It’s true that the prize money is ridiculously small for a space competition. Nobody in their right mind is going to enter for the prize money - and people who aren’t in their right mind are my kind of people! If the prize becomes bigger, then we’ll start to see entrants who treat this as a business proposition, and who are willing to invest huge resources to win the prize. I’d rather keep it small, so that we attract enthusiastic nuts who are doing it for the challenge."
Several serious teams have already entered. The N-Prize website is: http://www.n-prize.com/
COMMENT: OK, so it's impossible, or nearly so. Dear doesn't care: he wants to see just how ingenious space enthusiasts can be. I don't think it's going to be done, but I wish "full speed ahead" to everyone trying it: surely, out of their efforts will come some ideas that can be applied to other projects to reduce size and cost. As Shaw said, all progress depends on the unreasonable among us.