How did Brian solve his problems?
Brian solved his problems through a combination of skills, ability, knowledge, determination, and luck. In different points in the narrative, he was able to either use his resources to help him survive or was the benefactor of situational good fortune to assist his cause. For example, it was his knowledge that enabled him to become a good fisherman, refining the spear so that he could catch more fish or build the food shelf to keep his food away from the animals. It was luck that he was able to land the plane in a clear portion of the forest away from dense foliage. It was fortunate that the tornado ended up tilting the plane, but through his ability to swim was he able to fish out the survival pack.
Yet, I think that the one underrated element in his entire narrative was Brian's use of mental toughness in helping him survive. I think that the reflection that Brian underwent about Mr. Perpich's words helps to set the stage for his survival throughout the work. Brian was able to control the situation and better understand his own condition as he reflected about Perpich and the lessons he taught, which suddenly enter Brian's frame of reference at the moment they are most needed: "...a guy named Perpich, who was always talking about...thinking positive, staying on top of things." Brian is able to solve many of his problems from this point by "thinking positive" and "staying on top of things." In this incremental and positivist approach, Brian is able to endure the challenging trials of the wilderness and eventually triumph over them.