By assigning tasks that have no set answer, you all but eliminate the chance of cheating.

This is another advantage of assigning tasks that require creative thought. Not learning for the sake of learning, learning for the sake of creating.

But then again, simply creating isn't (always) enough. Creating should be done with purpose (that purpose can also be exploring the mind).

So, you need to assign tasks that have no set answer, but that have a positive benefit if and when they are answered.