The premise is that we're taking the entrance examination for a course of study dedicated to arithmancy: that is, magic based on mathematics. This involves hitting a series of numbers using "spells", each of them a mathematical function that can only be used once per series, so as to write out ten specific sequences. Meanwhile, your examiners seem to have messed up the sound system, so now you can hear every word that passes between them as they observe your progress.
The gameplay itself is, as might be expected, entirely puzzle-based. We're manipulating numbers throughout, and the challenge is to figure out how to apply the different functions/spells so as to achieve the correct sequences. This is livened up considerably by the antics of the examiners and their discussions as to the direction in which a certain vice associate dean -- I think that's the title; it appears the university is tied up in bureaucracy -- is taking it.
It's actually the equivalent of cut-scene rewards for seemingly unrelated casual play, but they were frequent enough and each short enough that it actually felt pretty well integrated. The immersion is further enhanced by replacing the parser's standard messages for both errors and meta commands like "undo" and "save" with commentary from the examiners.
On the whole, a lot of fun for anyone who's into purely cerebral manipulation puzzles. As a breakfast, I think it's a bowl of muesli with fresh fruit and nuts, a newspaper, and a cup of dark-roast coffee: tasty and healthy, relatively "no frills", and with a nice crunch; but we're focused more on the shenanigans of the outside world.