Difficulties

One of the most popular feature requests on Integrity has been assigning difficulty levels to questions.

After maintaining for a long while that this would do more harm than good, since it is so impossible to accurately assess the ‘difficulty’ of a maths problem, …I have finally decided to introduce them.

Only questions that are speedrunnable have been given difficulty ratings. Currently, this is just differentiation questions (which are only accessible through speedrun anyway).

There are 2 primary reasons for introducing the difficulty levels:

1. This is helpful for customising what kinds of questions you encounter in the Speedrun environment, if you’re looking to practise questions of a particular difficulty level.
2. It can help indicate to less experienced maths fans those questions that are much more challenging than they look, so that they don’t end up pouring excessive time into problems way above their ability level.

The latter should pretty quickly become irrelevant, as once you have sufficient confidence and fluency in a topic you‘ll have no qualms about tackling nasty problems!

These difficulty levels are very weakly correlated with the skill and experience required for a question, and even more weakly correlated with how difficult a solution might be to spot and/or execute. They give little indication as to how long a problem might take – because this will vary astoundingly from person to person.¹

You’ll also notice they’ve been given somewhat cryptic names, instead of some sort of numerical scale. There’s also a pretty small number of them, so each one can cover a fairly wide difficulty range. It’s intentionally fuzzy. This significantly simplifies the process of picking a suitable difficulty while giving me a lot of breathing room.² Also, you’ll build up your own intuition for what each difficulty level feels like as you do questions, and I think that’s part of the fun!

At the end of the day, remember it’s me who’s assigning these difficulties, and while I strive to be as objective and fair as possible, I’m only a purple portal. A lot of this is just based off vibes. You’ll almost certainly find some ratings that you disagree with, and if so, I’m sorry. It honestly doesn’t even matter.

Based

Baseline. These are entry-level questions, probably suitable for an intermediates. Integrity is not intended for absolute beginners (you’d be much better off finding practice questions elsewhere) – the questions I write assume basic proficiency in the topic.

Incline

Standard. The vast majority of questions tend to fall into this category, pretty naturally.

Manifold

Rare. You’ll probably feel pretty satisfied after managing to solve one of these.

Chaos

Exceedingly rare. Reserved for the most ridiculous of questions.