[ufxevlwl] Sudoku preserving sliding block puzzle

Create a (kind of) sliding block puzzle based on sudoku-preserving symmetries.  This is more closely a two-dimensional twisty puzzle.

With everything orthogonal, the puzzle might be too easy.  Including the 9! relabeling operation might make things trickier.

Three views: 9 colors of columns, 9 rows, 9 blocks.

Motivated by improving Rubik's cube.  For 2D puzzles depicted virtually, it is easy to see before and after of a move or sequence of moves.