I'm not sure why people think programming us the pinnacle of problem solving. Just about any trade involves just as much logical thinking and problem solving.
I'm talking about what are commonly called the skilled trades [0]. Some of the most analytical thinkers I know were trained in a trade. Masons and cabinet makers that have an intuitive understanding of geometry and trigonometry that most people just don't grasp. I learned most of my problem solving skills from my father who was trained as an industrial electrician. Spend a day on a job site and you'll hear the same things you hear programmers bitching about. Most people complain about the engineers and architects not understanding how the real world works just like programmers always bitch about software architects.
It's a real shame that most people seem to look down on the trades as somehow being inferior to white collar work. This is what Mike Rowe has been preaching about for the past 4 or 5 years. Just listen to his TED talk [1].
>Car salesmen are sitting and solving logical problems?
If they aren't then they will be unsuccessful as car salesmen. Apart from "how can I sell more cars?" there is "what is the optimal number of cars I can fit in my showroom?", "how shall I present my most profitable deal to its most likely demographic?", "which aspects of my communication skills can be improved?"...the list is endless. Point being there are logical challenges to be solved everywhere.