It is perhaps worth pointing out that sometimes, a good way to redefine a problem is to "widen" it, that is, to consider another problem of which the original one is merely a special case. That's been called "the power of abstraction," and it's pretty much what accounts for the amazing success of mathematics. And it seems to work in a broader, less scientific sense as well: for the longest time, I couldn't find a todo-list on the web that I didn't hate. Along came the Trello guys and created a collaboration tool with task lists. And bingo, for the special case of a single user, they (perhaps involuntarily, I don't know) created the most awesome todo-list website.
> Great engineers don’t solve problems - they redefine them. In other words, great engineers deftly navigate false premises. This is an invaluable asset and is far more rare than a productive engineer. It changes the playing field entirely. If you’re not constrained by the problem, the solution can be far more valuable.<p>This is actually true of great leaders in general; great engineers just happen to be a specific sort of leader.