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Skip to content GriP on math, music, and programming Nerdy explanations and thoughts about math, music, and programming. Home About GriP Math Music Programming Back The job system of Octopath Traveler and the symmetric group Octopath Traveler is an RPG where you take control of eight characters, each having a unique job with a unique set of skills. In the course of the game you may give each character a secondary job (but you can’t endow them with the same job twice). Since a party may only consist of four of these characters and it is advantageous to have access to ablities from all eight jobs, I wondered: Given a distribution of secondary jobs, is it always possible to find a party of four characters having access to all eight jobs? It was possible for the distribution of secondary jobs I have used but in general the answer is no. To see why and to find out what kinds of distributions give rise to a favorable party required me to take a deep dive into basic abstract algebra again.

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