What's the deal with programming, as a careeer? It seems like the lower levels at least should be readily accessible even to people of thoroughly average intelligence but I've read a lot that leads me to believe the average professional programmer is borderline incompetent.

E.g., Fizzbuzz. Apparently most people who come into an interview won't be able to do it. Now, I can't code or anything but computers do only and exactly what you tell them (assuming you're not dealing with a thicket of code so dense it has emergent properties) but here's what I'd tell the computer to do

# Proceed from 0 to x, in increments of 1, (where x =whatever) If divisible by 3, remainder 0, associate fizz with number If divisible by 5, remainder 0, associate buzz with number, Make ordered list from o to x, of numbers associated with fizz OR buzz For numbers associated with fizz NOT buzz, append fizz For numbers associated with buzz NOT fizz, append fizz For numbers associated with fizz AND buzz, append fizzbuzz #

I ask out of interest in acquiring money, on elance, rentacoder, odesk etc. I'm starting from a position of total ignorance but y'know it doesn't seem like learning C, and understanding Conrete Mathematics and TAOCP in a useful or even deep way would be the work of more than a year, while it would place one well above average in some domains of this activiteity.

Or have I missed something really obvious and important?