Here's a really quick story on how i accidentally worked out this strategy by getting it wrong first. When I started at Amazon and was trying to convince the team that we should do certain things, I did what I'd always been trained to do: I wrote down the problem and then sketched a solution to it. Then I'd start floating the doc around to try to get folks excited about it. And invariably, they'd do what they were trained to do, which was to have a critical response to the proposed solution. They'd argue that I was solving it the wrong way, and I'd be in a spot where we'd have a conversation where I was defending a position. But this was the last thing I wanted — I was trying to get everyone excited about fixing a problem, but I slowly realized that when I approached it this way, I was just getting feedback on my proposed solution.
So I started doing an experiment where I'd write that same doc, including the ideas i had on the shape of the work we should do, but then I'd delete my solution before sharing it. To your question: I'd still totally write my solution ideas down. Partially because I can't help myself and honestly it was a helpful way to think things through. But when I deleted it and shared a doc with just a problem statement, I'd get feedback on the problem statement. It's pretty obvious, but it was also a pretty surprising result: all of a sudden i was in conversations where we were all on the same side of the table. Feedback was either refining the problem (which was awesome) or proposing solutions. And when the person reading your problem statement starts trying to solve it, it's really cool... because they totally start getting invested and the conversations are great.
Like everything, none of this is actually either/or. There are points in between, like including a sketch of the shape of a solution, or properties that a solution would have to have. But the overall thing of separating the problem and the end state of where you want to get to, from the solution and the plan on how to get there is a pretty effective tool from a sharing ownership perspective.