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Let G be the subset of the permutation group of size 48 generated by ring/diameter shifts as shown in the screenshot above. The game applies the composition of one to three randomly to a pattern of enemies in perfect formation for you to attack; you have to pick the inverses.
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Of course, order matters here: ρ°σ≠σ°ρ in general. And there's fun topology: it's an annulus, but opposite points of the outer circle edge are identified, as are those of the inner circle.
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.@paClontz pointed out to me before I started that it's a puzzle game more than an RPG and I'm here for it.