Sometimes the easiest way to solve a specific problem is to solve a harder, general one
Mathematician George Pólya noticed something that seems backwards: a more ambitious plan can succeed more easily than a narrow one aimed straight at your actual problem. Proving one specific case of a pattern can be fiddly, while proving the whole general pattern at once — which covers your case for free — sometimes falls out cleanly. Why would tackling the bigger problem ever be the shortcut?
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A more general problem often has a cleaner, more symmetrical structure to work with, where a specific case is tangled up in irrelevant particular details that obscure the real pattern. Solving the general version strips those distractions away and frequently makes the right method obvious. Pólya named this the 'inventor's paradox' in his classic 1945 book on mathematical problem-solving, and it's since become standard advice in both math and software engineering: generalize first, then specialize.
— George Pólya, How to Solve It — 1945, Princeton University Press
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