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The mapping step in analogical problem solving primarily involves establishing connections between the source problem and the target problem. In this context, the analogy makes it necessary to relate the components of one problem to those of another. For example, in the well-known analogy involving a fortress and a tumor, the fortress represents a problem that requires a strategic approach to overcome defenses, while the tumor signifies a medical issue that needs to be addressed. By connecting the fortress to the tumor, one can utilize insights gained from solving the fortress problem to inform potential solutions for the tumor problem.

In this way, the mapping step is crucial because it enables the problem solver to apply knowledge from a familiar situation (the fortress) to a less familiar one (the tumor), facilitating a deeper understanding and more effective problem-solving strategy. This step distinguishes itself from simply identifying the problem, choosing a solution strategy, or deciding on the analogy to use, as it specifically focuses on the connections drawn between the two scenarios.