A psychological theory that explains why people remember only the outcome?
I'm not sure about the problem-solution context, but there is the fairly well-studied "peak-end" phenomenon in which people appear most sensitive to the strongest and/or the final levels of positive or negative experiences in an episode. Daniel Kahneman has done a lot of work on this phenomenon, you can find a list of his papers on his website. A fairly simple demonstration is in this article:

Kahneman, D., Fredrickson, D.L., Schreiber , C.A. , &amp; Redelemeier, D.A. (1993). When more pain is preferred to less: Adding a better end. Psychological Science, 4(6), 401-405.