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At the heart of most problems is a contradiction between two requirements or factors. These contradictions can either by technical; where alternative solutions improve one aspect of the design at the expense of another: or physical; where the physical state of the object must be in two states at once. If these contradiction can be understood, and innovative solutions found, significant advances can be made.
In many systems the majority of the contradictions can be easily found. For example, in the case of the car, the requirement to go as far as possible can be thought of as the need to carry the maximum fuel load. This is contradicted by the need to weigh as little as possible extend endurance, and thus reduce fuel load. With the conventional internal combustion engine this is not a significant problem. However the electric car shows the contradiction in sharp focus.
An innovative solution might be to reduce the weight of the fuel by increasing its energy density (i.e. better batteries). However, by identifying the contradiction it becomes possible to think past this. The best solution is one where the contradiction is removed: where there is no link between the amount of fuel and the weight. This could be achieved by obtaining the fuel from outside the moving car. This brings the solutions of solar power, but also highlights the possibility of tram like systems, with the car tapping the fuel source from non moving sources.
In addition it is important to identify those contradiction which are not obvious. Often the design of the existing object was based upon an understanding of the obvious factors and contradictions, but ignorance of the minor ones. This can lead to factors which hindsight can identify and improve.
Keep a list of the contradiction inherent in those problems you attack on a day to day basis. Add to the list as you find new ones and try and identify the interrelation between these contradictions. If you can find a way of removing or reducing multiple contradiction at once, you have a greater probability of identifying a workable solution.