The process of problem solving                          3/1 Hierarchies Let'srecap Problem solving is a natural process. Understanding this process can be developed by considering the definition of a problem. Definition A problem is a request for a result subject to conditions that must be simultaneously satisfied. How tofind out Examining simple problems provides an excellent way of understanding the process of solving problems. The problem below continues you on the journey to learning to solve problems reliably. Thesolutionto allproblems The Mary's Apples problem, shown below, illustrates the logical organization that is common, in varying degrees, to all problems. To start the problem solution you scan the problem, looking for what is asked for. In the process the various conditions and numbers are simply ignored. The phrase how many alerts you to the fact that what is asked for is coming into view. The response to the request happens to be in the same sentence. This process is continued. Each equation requests some information about a particular quantity. This tells you what to look for among the various conditions given in the problem statement. The steps of the solution unravel the problem statement for you. Figure 2.1 Problemsolvingfundamentals The discoveries made by examining the solution of the Mary's Apples problem (Figure 2.1) can be expressed quite simply: Starting a problem solution is the simplest, least time-consuming, part of solving a problem. Problems solve themselves. This can be seen quite strikingly if we suppress the words in the solution shown above. The hierarchical nature of the problem becomes conspicuous (Figure 2.2). Figure 2.2 You will note that each step is a consequence of the previous step and a precursor to the next step. Problems solve themselves. It is valuable to note that at any step the next step does not depend on the previous steps. This is much like your trip-to-the mall discussed in the introduction. You are only concerned with where you are going, not with where you have been. Let's watch this problem solve itself. Figure 2.3 Distinguish between the solution of a problem and the result of solving the problem.
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