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There is the up-up-down-down method that basically uses only one algo over and over but you still have to rotate the cube after each up-up-down-down before applying the next up-up-down-down.

I am sure that is not quite what you meant, but this is what is referred to as the 'using only one algo to solve the rubiks cube' this also only works (AFAIR) for 3x3x3

https://www.youtube.com/watch?v=n7irFvVkLpk

Twistypuzzling produces great Youtube videos for all types of twisty puzzles.



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