The first level merely needs already defined concepts and constructed formulations. The problem can be solved based on existing theorems without any risk like doing arithmetic.

On the second level, a direct application of theorems in books does not help. The problem must be transformed into a new shape or appended with intermediate steps, which can be considered as a preprocessing stage. Sometimes, smart tricks should be devised and this makes the situation quite difficult. After that, everything becomes crystal clear and the first level craft takes over the work.

Coming to the third level, existing knowledge as well as ingenious transformations cannot solve the problem. Brand new ideas, structures and even a prodigious edifice should be constructed like the whole magic world created by J. K. Rowling. To achieve this level, it requires long time accumulation, observation, continuous hard work with high intensity as well as instincts and insights.