The Math behind Sudoku Ripeto

Mathematically, solving a Sudoku Ripeto or Custom Sudoku puzzle can be formulated as a problem of hypergraph coloring. As with classical Sudoku, finding puzzles and solutions can be performed with techniques like constraint programming or dancing links.
Of interest are questions of existence, enumeration and minimality. For example: what is the minimum number of clues that a Sudoku Ripeto puzzle played with numbers 111222333 may have? The answer for classical Sudoku is 17.
Many interesting decision questions about Sudoku Ripeto may well be NP-complete. In this case there could be no worst-case polynomial time algorithm able to answer them. One of these questions is: given a partially filled board, does it have a solution? For partially filled Latin squares the problem is known to be NP-complete indeed.