Diagonal Sudoku (Sudoku X) - Play Free Online

Diagonal Sudoku — also called Sudoku X — is a popular variant that adds two extra constraints to the classic 9×9 puzzle: both main diagonals must also contain the digits 1 through 9 exactly once. The top-left-to-bottom-right diagonal and the top-right-to-bottom-left diagonal each become an additional "region" alongside rows, columns, and 3×3 boxes.

This extra constraint makes the puzzle both harder and easier at the same time — harder because every diagonal cell must satisfy an additional uniqueness rule, but easier because diagonal cells have more peers, giving you more information to work with. The result is a deeply satisfying logic challenge that rewards careful observation.

All standard Sudoku rules apply: fill the 9×9 grid so that every row, every column, and every 3×3 box contains the digits 1 through 9 exactly once.

In addition, the main diagonal (top-left to bottom-right: cells r1c1, r2c2, … r9c9) must contain each digit 1–9 exactly once.

The anti-diagonal (top-right to bottom-left: cells r1c9, r2c8, … r9c1) must also contain each digit 1–9 exactly once. The center cell (r5c5) lies on both diagonals and is therefore the most constrained cell on the board.

Start by focusing on the center cell (r5c5) — it belongs to a row, column, 3×3 box, and both diagonals, giving it the most constraints. If you can narrow it down early, it unlocks progress across the entire board.

Next, scan the diagonal cells. Each diagonal cell has peers in its row, column, box, and the entire diagonal — up to 32 unique peers instead of the usual 20. This means more eliminations per placement, so diagonal cells are often the fastest to solve.

Use pencil notes aggressively on diagonal cells. When you place a digit on any diagonal cell, eliminate that digit from all other cells on the same diagonal. Combine this with standard Sudoku techniques — naked singles, hidden singles, pointing pairs — for maximum progress.

Prioritize the diagonals: Cells on the main or anti-diagonal have extra constraints, so they're often easier to resolve. Start each scan by checking diagonal cells before moving to the rest of the grid.

Exploit the center cell: r5c5 is the only cell on both diagonals. It belongs to 5 constraint groups (row, column, box, main diagonal, anti-diagonal). Resolving it early dramatically reduces candidates across the board.

Watch for diagonal-only eliminations: Sometimes a digit is eliminated from a diagonal cell purely by the diagonal constraint, even when the row/column/box still allow it. These are easy to miss but very powerful — always check both diagonals when placing a digit.

Regular Sudoku has three constraint types: rows, columns, and 3×3 boxes. Diagonal Sudoku adds two more — the main diagonal and anti-diagonal — for a total of five constraint groups. This means 18 of the 81 cells (those on either diagonal) have significantly more peers than in a standard puzzle.

Many solvers find Diagonal Sudoku slightly easier for a given number of givens because the extra constraints provide more information. However, puzzle designers compensate by providing fewer givens, keeping the overall difficulty comparable. The diagonal constraint also introduces unique solving patterns not found in regular Sudoku.