Why is it that the phrase “solving the Rubik’s cube” has such a different meaning to me than it does to others? For a long time I was quite puzzled by people who made the implausible claim that they had “solved” the Rubik’s cube. And then I had a sudden insight: they were using the word in a way that was very different from the way I use it.
To me, you can’t claim to have solved the Rubik’s cube unless you have invented (on your own) an algorithm that will turn any randomly arranged Rubik’s cube into the correct configuration. But apparently many people have a far lower bar. They interpret “solving” to be the process of using a known algorithm in order to turn a cube into the correct configuration.
I think of this as the difference between genuine problem-solving and going through an exercise. For example, using the quadratic formula is not problem-solving. Independently deriving the quadratic formula, or manipulating a non-obvious equation or word problem into a form in which the quadratic formula can be used, would be examples of problem-solving.