Keeping a problem solver happy requires a reasonable stream of interesting problems to solve.
The child's toy of different shaped pegs needing to be placed through different shaped holes seems to me to be even beyond the aptitude of some business/project managers. If they struggle with that what hope is there for keeping an average techie from getting bored.
..... but the effort may hold almost no value for the business. It’s often difficult to understand why the business doesn’t want those solved too – can’t they see the current solution is sub-optimal?
Depends what emphasis is placed on the problem. If the problem is not a business requirement then it can be used as a coffee break / back burner puzzle as a way of expanding and enhancing skill. It is important that it *is* a puzzle then it helps prioritise the work that is needed to be done. I have found what a manager thinks is a problem that needs to be solved isn't always what the Director sees as an issue. And no doubt there will be cases where a Directors problem is a non-issue for the Board.