Of course the major goal of parenting is to create a well developed person who can manage his own affairs perfectly well. If you do it right you would want to end up with a kid who could be president or who could run a major company. At the least a guy who can do an important job successfully. Obviously that requires a lot of basic skills and we are trying to teach them responsibility right now. So we are giving each of them a small number of tasks which they need to accomplish and we are trying to make it clear that they have to do what they are expected to do. It is just simple thing for the moment, like picking up after themselves. Obviously that is an important concept. You do not need the child to grow up thinking that someone else is some how responsible for going around behind them and cleaning up whatever mess they might might. You want them to realize that they take responsibility for the things that they do.
Asking them to solve problems is another thing. Some of them are simple enough in theory, but a child does not always look at the same problem you do and see an easy solution. It is important that the child learn to adapt to the world around him and not let things defeat them easily. Any problem can be overcome if you are creative enough in devising a solution. It is an important concept, but it is not an easy thing to teach. For starters it is not always obvious which solution is the best and trial and error often leads to a string of disasters obviously. It is a big deal if you can do it the right way and hard to manage properly.