Christmas my college freshman year was The Christmas of the Rubik's Cube, and being a primarily science and engineering school, everyone came back to the dorms in January having received a half-dozen or so of these time-wasters. Staring down the triple barrels of Phys II, Calc II, and Intro to Programming, there was simply no time to waste, so they languished in piles at the edges of our desks in a multi-colored scramble.
Then one day my roommate walked in, and was surprised to see that all but one in our room had been solved. I'm sure this has been done many times before, but I'd simply used my pocket knife to pop all the face-blocks off each cube, then re-attached them in the correct order. It's not a particularly new or clever solution – Alexander the Great did something similar millennia ago – but hey, it works.
As for that one cube I hadn't solved, the attachments for its blocks were barbed and they wouldn't pop off without breaking. I saved it to challenge budding mathematicians, "Here, let's race. You solve this one, I'll solve that one. Go!" "Wait, you didn't do it right." "Solution's a solution. Look, I've got to get back to my E&M homework. We're doing method of images this week."
Look, life is hard. Sometimes it's OK to take shortcuts. Only be careful not to get cut in the short taking. If it's a triviality to get something working (Rubik's cube, a balky diff pump, etc.) or a matter of safety (flat tire on a lonesome highway at midnight), just get the damn job done already. For more knotty issues such as the method of images, it's good to understand the uniqueness theorem for Poisson's equation. Once you understand the required preliminaries, then (and only then) you can go get the damn job done already, and with confidence in the result.
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