Difficulty Scale

Difficulty Scale

I post a lot of things with varying difficulty, so it's become necessary to rate them by a scale of my own construction. (I've also updated the old posts to include these difficulty ratings.) It's a known problem that mathletes (especially those straight out of grade school) sometimes find it hard to determine the correct difficulty to work in, and I hope this scale will help alleviate that somehow. 

These difficulty levels resemble rankings rather than a temperature scale; the numbers only serve an ordinal purpose, i.e. Grade School problems don't have zero difficulty, nor are pre-Olympiad problems harder than High School Intermediate problems by the same degree that High School Intermediate problems are harder than High School Transition.

0 - Grade School: Problems/concepts of this difficulty are strictly grade school material. This means that (i) a competent grade school mathlete should be able to get it without issue, and (ii) the technique is seen only in grade school problems, or it has been largely replaced a more powerful high school method.

1 - High School Transition: Problems/concepts of this difficulty are intermediate between grade school and high school. An exceptional grade school mathlete should have an effortless grasp of these concepts. For most high schoolers, speed and accuracy should be the salient issues at this level.

2 - High School Intermediate: These problems are well outside grade school territory, and form the bulk of the High School Gap. They are usually direct-application exercises of well-known theorems.

3 - Pre-Olympiad: Problems in this level form a bridge between Levels 2 and 4. They often require more 'thinking' compared to High School Intermediate problems, and involve theorems that apply to Olympiad problems.

4 - Olympiad Easy: These problems form the lower bound of Olympiad fare. Most of the time, the proper application of a single theorem or a single astute observation should be enough to solve the problem completely.

4.5 - Olympiad Moderate: There's a level of overlap between 4 and 4.5 depending on one's specialization. Often these require multiple correct steps, or an unorthodox single step.

5 - Olympiad Hard: Problems here are very difficult, and it's no wonder that they make up the hard sections of international Olympiads. They require and they don't show signs of letting up even after many steps in the right direction.

H - Higher mathematics: Concepts labeled H bank on a significant amount of math that's traditionally ascribed to the collegiate level (e.g. calculus, analysis, linear algebra) and is rarely necessary even for Olympiad problems. They may or may not be as complicated as Olympiad-level concepts.



August 2014