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I would say both experience and technical knowledge plays an importance role in molding you as a successful problem solver in any field, but not necessarily limited to that.There are other skills and important qualities one must possess that help him to be a successful problem solver, such as creative thinking, multi-tasking, emotional quotients, effective communication etc..
One of the first of many hurdles I have faced when I started my career was making people (or my team) believe in me and my capabilities as a supervisor. People (or team) follows the one who they trust and respect, once you gain that things will get easier.
Thank you for the invitation.
I will rely on my experience