The alternative, of course, is to re-address what it means to be a productive individual, and to perhaps concentrate on a social safety net.
However, crucially, there are thousands of important and hard problems out there available to anyone with a roof over his head, food and internet access.
Anyone who doesn't find a hard problem to work on, and this includes those in employment with excellent safety nets, is going to go bad sooner or later (drugs, sociopathy, crime, mental illness, suicide, etc).
Most people don't need hard problems to work on to find purpose or self-actualization. Most are happy to grind away on tedious takes that take time but are not mentally challenging, or care for children or an elderly parent(s). This should be fine under a basic income model.
Provide for everyone, let people who want to work on hard problems work on them.
Note also that one cannot merely look after children, because they need to see a greater purpose in what you do.