The problem was supposed to be based off of a real world problem. Almost always, when you simplify a problem you have to its core, you end up with a very simple question that appears to have no practical applications.
Normally, this simple question is also easy, in which case simplifing it is the only skill you need. In other cases this question is hard, in which case you need to be able to solve it. Both of these skills are valuable, but should not be tested in the same question.
Also, if you are trying to pick a candidate's brains, their is no reason to make them redo your work of simplification, when you are stuck on the actual problem.
Normally, this simple question is also easy, in which case simplifing it is the only skill you need. In other cases this question is hard, in which case you need to be able to solve it. Both of these skills are valuable, but should not be tested in the same question.
Also, if you are trying to pick a candidate's brains, their is no reason to make them redo your work of simplification, when you are stuck on the actual problem.