I'm not sure exactly what you're asking here, but depending on their role, a data scientist solves all kinds of problems! They also can give other people critical information for them to be able to solve their problems.
For example, a data scientist might be given a question like "Try and look at the behavior of people who cancel our product after 3 months vs those who keep using it. Are there any key differences in what they do in the first 2 weeks?"
The answers they come up with might be used to help a product manager or user experience team improve the product -- they give them the information they'll need to solve their problem. But along the way they'll have plenty of problems of their own to solve. Depending on the company, that might include things like "how do I get that data", "how do I query that data to actually answer that question", and "how do I visualize the results in a way that can help people really understand what's happening?"
All of those sorts of problems can be really fun and rewarding to solve!