It depends on your charter or mission as well as your long term vs. Short term objectives. If your mission involves a larger more expansive view - then you will need to spend a lot more time on unique problem solving that has a strong potential ROI feeding the fulfillment of the mission.
It kind of boils down to ROI (return on investment) vs. risk for me: I look at the ROI and risk (opportunity cost) for almost everything that I choose to do - this helps me compare various choices for what to focus on daily, weekly, monthly and yearly.
Having clear objectives for the month, week and year also help in selecting what percentage of time as per your question. If the solution of this problem feeds the fulfillment of your objectives vs. the solution of this problem prevents a risky situation: that may be the question to answer.
I hope this helps. Feel free to interact so that I can delve into the complexities and nuances that are inevitably there.
Whatever tasks you're doing, whether problem solving or follow-up, I'd start with and devote more time to the ones that have the potential to bring in income. What are the tasks closest to your revenue line? Can that task generate revenue? Can you create a product or deliver a service? Can you save the company money?
If you are problem solving, make sure you are the right person for the issue at hand. Is there someone else that you should consult with or hire that may be better than you at solving that particular problem? Delegation is a powerful productivity tool.
I'm learning that more time needs to be spent on following up and less time on unique problem solving, at least that's true for me. It's easy to spend a lot of time think about problems, but what really matters is implementing solutions, testing, and seeing the results. My advice is to not spend too much time on problem solving which leaves not enough time for getting real work done.
I very much doubt there is a "should be" approach to this: as others have pointed out, it really depends: on the company, sometimes on the industry too, stage of development, the team you're a part of, your personal work style, your manager's expectations and so on.
I've personally experienced both extremes, in companies that - at least from the outside - should be quite similar. One company expected that I work almost exclusively on unique initiatives, to the point of nearly neglecting my core work; the other valued and emphasized core tasks and welcomed what you refer to as "unique problem solving" only after the mundane was fully dealt with.
Needless to say, I didn't think that either one of these extremes was ideal. However, I believe that the extraordinary should remain, well, extraordinary. Most people can't function day after day, quarter after quarter, in a state of continuous awesomeness, one also needs time to decompress, recharge batteries, and fall back onto the familiar.
If I was to mention actual numbers, I'd probably feel that a 60 / 40 split would be ideal (60% core tasks, 40% unique problem solving).
I see this is filed under "CEO Coach" so I'm assuming that you're the CEO or business owner.
In which case you should lean towards unique problem solving as much as possible. And by that I include strategy work, growth work and vision work.
CEOs should not be doing technical work. They should be working out where the company is headed (vision), how it will get there (strategy) and then motivate and inspire their teams to deliver that (growth).
In the startup phase, sure, you have to do a lot of follow-up and technical work yourself. But as time goes on and processes get put in place and your team expands, you want to be doing less and less of this so that you can free up your time for the most valuable thing - thinking and solving problems.
Everyone else on your team can call clients, process orders or deliver product. But only you can think and solve the high-level problems of the business.