The following image shows two valid Sudokus. The first was copied verbatim off Wikipedia, and the second was obtained by rotating 90 degrees.
Any two distinct valid Sudokus must differ in at least four cells. Given a completed Sudoku a legal "move" consists in changing exactly four cells to form another Sudoku grid.
Is it possible to transform the first grid to the second grid using only legal moves?
(for partial credit: can you succeed if legal moves allowed changing up to 6 cells instead of 4?)