Sudoku DG – Hard

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Sudoku-DG, also known as "Offset Sudoku," is a variant of the classic Sudoku, a number placement puzzle. The traditional Sudoku grid consists of a 9x9 matrix, subdivided into 3x3 subgrids, referred to as "regions." Some cells are pre-filled with numbers, termed "givens." The objective is to populate the empty cells in such a way that each row, column, and region contains the numbers 1 through 9, with each number appearing exactly once. The name "Sudoku" implies "single numbers" as each number should appear only once in each of the three "directions" (row, column, and region).

Basic Rules

1. Grid Structure: The puzzle features a 9x9 grid, divided into 3x3 regions.
2. Givens: Some cells are pre-populated with numbers, known as "givens."
3. Number Placement: Each row, column, and region must contain the numbers 1 through 9 without repetition.

Additional Rules for Sudoku-DG

1. Disjoint Groups: In addition to the basic Sudoku rules, Sudoku-DG introduces 9 disjoint groups, each corresponding to a relative box position within the regions and highlighted with a distinct color.
2. Group Numbering: Each colored group of 9 cells must also contain the digits 1 through 9 without repetition.

Basic Solving Tips

• Single Possibility: If a cell is the only one in its row, column, or region that can contain a particular number, then it must contain that number.
• Single Candidate: If a number is a candidate in only one cell of a row, column, or region, then that cell must contain that number.
• Elimination: Exclude numbers from cells based on the numbers already present in a particular row, column, or region.
• Disjoint Group Consideration: Pay attention to the colored groups and ensure that the numbers 1 through 9 appear in each disjoint group without repetition.