In the didactics course I took last year, a "problem" was defined as something to which you didn't know the answer/solution immediately.
Eg. to me, computing an integral is not a problem, because I know how to do it. It's a routine. To others, computing an integral would be a problem indeed. On the other hand, finding my way when driving is a hard problem for me and would be not a problem for someone else.
If the question is not a problem, I will solve it the traditional way. The integral will be computed right away. If I'm doing dishes, you wouldn't be able to discern me from an SJ. (I will have to correct this picture and will do this soon.)
But when I'm solving problems... I'll get a million ideas first and test them out before some reason (Te?) kicks in and tells me to look it up, to ask,... and then I ignore it because my way was just so much more fun.
If there aren't any problems in my life, I create them, because life without problems is boring. I'll ask for problems. Eg. starting the "ask an ENTP" thread is one of these. Your question is not easy and I'm solving it now in the ENTP way, writing down all sorts of ideas. Afterwards, I will edit the post and check consistency. And I'm really happy with such questions as I'm doing the thing I do the best while at the same time helping others. (So not only Ne and Ti are happily at work, but Fe too...) I will start all sorts of crazy projects to keep myself happy.
Now correcting the dishwashing Tamske picture - you WILL be able to discern me from an SJ. The SJ will wash dishes, and when they are ready, he will start something new. I will wash dishes on automatic pilot, while three quarters of my attention is solving problems or devising stories or imagine what ESTJ hubby will say when the dishes are done ... Suddenly, I will jump away from the sink and jot something down.
The only way for me to do routine work is putting a problem into my head first and start doing the routine. The nicest thing is if there is a problem I NEED to solve - like, composing exam questions. It's hard for an ENTP with current MBTI interest to create non-MBTI related ideas. I've done this already a few times with success: first read the handbook or the learning goals and then start doing dishes (cleaning the house, work in the garden, ...)
Uh... I'm not making a point of doing things differently. If there is a problem, I just rush ahead before checking if it wasn't already solved.Because one of my very good friends, who is an ENTP, makes a point of doing everything the opposite way of what you'd expect. (Plus, being an ESTJ, I can't relate to that sort of behavior very well... )
I can get the ESTJs (and ISTJs) doing their work in the accustomed manner. I wish I would be able to do that too, and get the boring work out of the way and be totally free to work on all those projects. But... when the work is done, they don't start creating things!! I can't get how they fill in their leisure time - why would you lose your time watching television or playing Railroad Tycoon when you could use it better?
Sigh. You can't get both sides, it seems. Either you can get the work done first like a good SJ and you have a lot of leisure time but no ideas, or you have all sorts of creative ideas like the NPs but no real leisure time because there is always work that still needs to be done.
Edit. I still need to do this: Thanks for the compliment, EJCC!