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I'm looking for a simple way of solving the MoYu Puppet cube (version 2 to be precise). It's a shapemod of a 3x3 Rubik's cube on which 7 of 8 corners have additional parts which form a bigger 2x2 cube around the 3x3 cube. These parts effectively act as bandages, preventing certain moves on the inner 3x3 cube.

I've found this tutorial where the Puppet cube is solved by first making it into a square shape, and then using formulas which preserve the shape during the entire process. Obviously, these formulas are much larger than those for a classic cube.

Is there a known way of solving the Puppet cube using formulas closer to those for the original Rubik's cube, that doesn't necessarily preserve the shape throughout the solution?

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