#### whauk

##### Member

(nearly) all methods with steps work by reducing the cube group to smaller and smaller subgroups until only identity (=solved cube) is left. (between the steps the subgroup may be left again. however that is not of our interest in this topic.)

i found one exception though: when solving the inverse scramble with a "normal" method (and therefore finding a solution for the actual scramble by inverting the solution) you actually do some fancy stuff with cosets. but i am too lazy to think about it in detail right now. however it clearly doesn't work by reduction to subgroups on the normal scramble and still has steps.

are there other exceptions that i missed? or can somebody construct a method that doesn't work by reducing to subgroups

**and**can be understood "directly". (my example doesn't fulfill this since, when watching a solution of the inverse scramble being executed on the normal scramble it most likely looks like random moves to you; apart from the last ~6 turns that just happen to solve everything)

maybe we didn't think about many other solving methods yet because we were too fixated on the approach using subgroups. however i do not really believe in this.

inb4 pseudoblocks is essentially the same concept as with the inverse-scramble-stuff.