Suppose a mad engineer needs the world destroyed by next Tuesday. For efficiency's sake, he considers "Gray Goo," a hypothetical end-of-the-world scenario in which self-replicating machines devour the entire planet while building more of themselves.
Realistically, what would be required (in terms of technology, resources, schedule, etc) to successfully transform the planet into all-consuming nanomachine?
Ethics aside, what are the fundamental flaws of the Gray Goo scenario?
What are the properties of a nanomachine network engineered to become Gray Goo?
This is not so much a question on how to write a believable Gray Goo disaster as a reality check of the concept itself.
(I may be inspired to resume my mad-science degree this turns out to be feasible, so please do your best to dissuade me today :) )