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Recently, I was fiddling with my Rubik's cube and tried scrambling it only using R and U moves. I then tried to solve it using only R and U moves. I didn't use any cube rotations.

It was an interesting puzzle and I'd like to design a twisty puzzle that resembled this. Does this puzzle already exist? Or, does anyone had any ideas on a nice way to design such a puzzle? I'm sure there is a design that would be the same, abstractly, but not look like a bandaged 3x3.

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