Finding a good formulation for a problem is often most of the work of solving it.
I agree with this intuitively, and I feel like I have seen this principle at work in my own work and in the problems I have tried to solve. However, when I try to convince others of this idea, I struggle to find examples that they can connect with or that they find compelling.
I suspect that programmers find this idea appealing because we routinely work with formal systems, and all of us know the experience of making a minor change in perspective and seeing an impossible problem turn into an easy one. So I'm most interested in examples that have nothing to do with code, examples that a lay audience would be able to grasp.
I would be particularly interested in examples from the history of science or medicine, if anyone can think of some. Scott and Scurvy is the only example I currently know of, and while interesting, does not seem like a perfect fit.