There is a way to find all the unanswered but there isn't a way to get to a list of all the posts that have NOT been solved yet. Can you make this available on the community?
You can use search facets to achieve this. Here's a good place to start - all of the unsolved posts in the community. You can filter further from there down to say the Designer Discussions if that's the area you want to focus on. You could also try filtering by label if there is a topic you feel you can help answer effectively.
