Ok... this whole problem started with a 7x7x7 Rubik’s cube. But I’m only telling you that to give some context. Not to ask how to solve the cube.
When solving the cube’s edges you have to math up the colours. Eventually you will get down to the last few edges. I know one algorithm to do this and it works by cycling three pieces around their edges.
(Lower case letter represents the piece colour and upper case represents the edge colour)
Ab Bc Ca can be cycled to Aa Bb Cc and so those three edges are solved. This is a three cycle.
Sometimes though you end up with two edges remaining unsolved, like...
ie a 2-cycle
From what I have been scribbling down I think it is not possible to use my 3-cycle algorithm to solve this.
You can bring in as many other already solved edges to help. So for instance with one additional edge...
Ab Ba Cc I can get to... Ac Bb Ca and so I still have one solved edge and a 2-cycle.
With two additional edges I can do other moves but still can’t get to a 3-cycle that can be solved.
I don’t know how else to express this but I feel like there is something around the number of cycles and the number of edges I can solve and unsolve but I’m not sure.
Is there a more concrete way of approaching this than just trying different combinations of moves? I feel like it can be solved and tell me that I can’t use my algorithm to solve this.
Hope someone can point me in the right direction.