Sudoku X (Diagonal Sudoku)

Sudoku X, also known as Diagonal Sudoku, adds one extra constraint to the classic Sudoku puzzle: in addition to the standard rules, both main diagonals of the grid must also contain the digits 1-9 without repetition. This seemingly simple addition significantly increases the puzzle's complexity and requires the solver to think in a new dimension.

Rules

1. Fill the 9x9 grid with digits 1-9.
2. Each row must contain digits 1-9 without repetition.
3. Each column must contain digits 1-9 without repetition.
4. Each 3x3 box must contain digits 1-9 without repetition.
5. The main diagonal (top-left to bottom-right) must contain digits 1-9 without repetition.
6. The anti-diagonal (top-right to bottom-left) must contain digits 1-9 without repetition.

Strategies

• Diagonal Elimination: Cells on the diagonals have an additional constraint, which means they often have fewer candidates than non-diagonal cells.
• Center Cell: The center cell (row 5, column 5) belongs to a row, a column, a box, and both diagonals — five different groups. This makes it the most constrained cell on the board.
• Diagonal Intersection with Boxes: Where diagonals pass through 3x3 boxes, the combined constraints can quickly narrow down candidates.
• All Standard Techniques: Naked singles, hidden singles, pairs, X-Wings, and all other standard Sudoku strategies still apply.

Diagonal Sudoku is one of the earliest and simplest Sudoku variants. It appeared in Japanese puzzle magazines shortly after the standard Sudoku format was established by Nikoli in the 1980s, though the exact date and creator are unknown.

The concept of adding diagonal constraints to Latin square puzzles predates modern Sudoku. Diagonal Latin squares have been studied in mathematics since at least the 19th century, and diagonal magic squares have an even longer history.

The variant gained wider recognition during the global Sudoku boom of 2005-2006, when newspapers and publishers sought to offer new challenges to readers who had become proficient at standard Sudoku. It appeared in The Daily Telegraph and other newspapers, and became a staple of puzzle competitions.

Sudoku X is now a standard category in the World Puzzle Championship and appears regularly in puzzle magazines from Nikoli and other publishers. Its elegant simplicity — adding just one rule to the original — has made it one of the most enduring Sudoku variants.