Anti-king Diagonal Hyper Sudoku

Anti-King Diagonal Hyper Sudoku Rule

Anti-King Diagonal Hyper Sudoku is a challenging variant of Sudoku that combines the restrictions of Anti-King Sudoku, Hyper Sudoku, and Diagonal Sudoku. It is played on a 9x9 grid, divided into 3x3 subgrids, with additional 4x4 subgrids within the main grid. The objective is to fill the grid with digits so that each row, column, 3x3 subgrid, 4x4 subgrid, and main diagonal contains all the digits from 1 to 9, while adhering to the Anti-King Sudoku rule.

Basic Sudoku Rules:

1. Each 9x9 grid is divided into 3x3 subgrids.

2. Each row, column, and 3x3 subgrid must contain all the digits from 1 to 9.

3. No digit can be repeated in any row, column, or 3x3 subgrid.

Anti-King Sudoku Rule:

In Anti-King Sudoku, inspired by the King's movement in chess, no two identical digits can be placed in adjacent cells, either horizontally, vertically, or diagonally.

Hyper Sudoku Rule:

Hyper Sudoku introduces additional 4x4 subgrids within the main 9x9 grid. These 4x4 subgrids must also follow the basic Sudoku rules, ensuring that each 4x4 subgrid contains all the digits from 1 to 9 without repetition.

Diagonal Sudoku Rule:

In addition to the basic Sudoku rules, Diagonal Hyper Sudoku introduces the following restriction:

1. No digit can be repeated in either of the main diagonals (top-left to bottom-right and top-right to bottom-left).

Anti-King Diagonal Hyper Sudoku Rule:

Combining all three sets of rules, Anti-King Diagonal Hyper Sudoku dictates that:

1. No two identical digits can be placed in adjacent cells (horizontally, vertically, or diagonally) within the entire 9x9 grid.

2. No two identical digits can be placed in adjacent cells (horizontally, vertically, or diagonally) within each of the 4x4 subgrids.

3. No digit can be repeated in either of the main diagonals (top-left to bottom-right and top-right to bottom-left).

Anti-king Diagonal Hyper Sudoku question

Anti-king Diagonal Hyper Sudoku solution

Solving Techniques:

Solving Anti-King Diagonal Hyper Sudoku requires a combination of standard Sudoku techniques along with the added restrictions imposed by the Anti-King, Hyper Sudoku, and Diagonal Sudoku rules.

1. Scanning for Singles: Look for cells where only one possible digit can be placed based on the given clues and the basic Sudoku rules.

2. Hidden Singles: Identify cells where a particular digit can only be placed in one specific row, column, or 3x3/4x4 subgrid within a block.

3. Naked Pairs, Triples, Quads: Eliminate possibilities for cells based on the presence of pairs, triples, or quads of identical digits in a row, column, or 3x3/4x4 subgrid, ensuring that each of these groups has a unique placement within that block.

4. X-Wing, Swordfish, Jellyfish: Utilize advanced techniques like X-Wing, Swordfish, and Jellyfish patterns to eliminate possibilities for multiple cells based on the placement of specific digits in rows, columns, and 3x3/4x4 subgrids.

5. Process of Elimination: Continue to scan the grid, eliminating possibilities for cells based on the rules and the progress made in previous steps.

6. Unique Rectangles/Quadrilaterals: Identify unique rectangles or quadrilaterals (enclosures formed by combining rows, columns, and 3x3/4x4 subgrids) where specific digits can only be placed in specific cells within that enclosure.

7. Hidden Singles/Pairs/Triples/Quads in Rectangles/Quadrilaterals: Apply the "Hidden" technique within unique rectangles or quadrilaterals to further refine possibilities and identify placements.

8. Diagonal Singles/Hidden Singles: Look for cells where a particular digit can only be placed in one specific diagonal, further restricting the possibilities.

9. Diagonal Pairs/Hidden Pairs: Identify pairs of cells where two specific digits can only be placed in a specific diagonal, eliminating other possibilities.

10. Backtracking: If no further progress can be made, carefully backtrack and reconsider previous placements or assumptions.

Anti-King Diagonal Hyper Sudoku puzzles offer an extreme challenge and rewarding experience for experienced Sudoku enthusiasts, combining the complexities of multiple rule sets into a single, intricate puzzle.