Programming is very close to logic.
Of course, there are other fields that require logic and problem solving. Engineering, science, for instance.
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].
[0] http://en.wikipedia.org/wiki/Tradesmen
[1] http://www.ted.com/talks/mike_rowe_celebrates_dirty_jobs.htm...
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.