How to Play Sudoku X
Master Diagonal Sudoku with this complete guide to rules, techniques, and solving strategies.
The Rules
Standard Sudoku Rules
- 1.
Each row must contain the digits 1-9 exactly once
- 2.
Each column must contain the digits 1-9 exactly once
- 3.
Each 3×3 box must contain the digits 1-9 exactly once
The Diagonal Rule (What Makes It "X")
- 4.
The main diagonal (top-left to bottom-right: R1C1 → R9C9) must contain digits 1-9 exactly once
- 5.
The anti-diagonal (top-right to bottom-left: R1C9 → R9C1) must contain digits 1-9 exactly once
All five constraints must be satisfied simultaneously. Cells on the diagonals have stricter requirements than off-diagonal cells.
Worked Example: Diagonal Elimination
This example demonstrates how the diagonal rule eliminates candidates that standard Sudoku rules alone would allow.
Main diagonal cells
Target cell (R5C5)
Analysis
Given: Four cells on the main diagonal are filled: R1C1 = 6, R2C2 = 2, R3C3 = 8, R8C8 = 9
Target: R5C5 (highlighted), also on the main diagonal. Its row 5, column 5, and 3×3 box are empty in this snapshot.
By row, column, and box alone, all nine digits are still possible at R5C5. But 2, 6, 8, and 9 already appear on the diagonal — so the diagonal rule rules them out.
The remaining candidates are 1, 3, 4, 5, and 7.
This is the rule unique to Sudoku X: the two diagonals eliminate digits that rows, columns, and boxes would otherwise allow.
Note: R5C5 is the single cell lying on both diagonals; in this snapshot only the main diagonal has entries, so only it does the eliminating.
How to Solve
Standard Sudoku Rules Apply
Place digits 1-9 so each row, column, and 3×3 box contains each digit exactly once. These rules are always in effect.
Add the Diagonal Constraint
Both main diagonals must also contain digits 1-9 exactly once. Top-left to bottom-right AND top-right to bottom-left.
Use Diagonal Eliminations
If a digit appears on a diagonal, it cannot appear again anywhere else on that same diagonal. This eliminates candidates that row/column/box rules alone would allow.
Combine All Constraints
Cells on diagonals have four uniqueness rules to satisfy (row + column + box + diagonal). Use all constraints together to solve.
Common Questions
Which cells are on the diagonals?
The main diagonal runs top-left to bottom-right: R1C1, R2C2, R3C3, R4C4, R5C5, R6C6, R7C7, R8C8, R9C9. The anti-diagonal runs top-right to bottom-left: R1C9, R2C8, R3C7, R4C6, R5C5, R6C4, R7C3, R8C2, R9C1. The center cell R5C5 is the only cell on both.
Does diagonal Sudoku need fewer clues than classic Sudoku?
Yes. The two diagonals are extra constraints that keep the solution unique with fewer starting clues. Classic Sudoku typically needs 24-28 givens; Sudoku X can be uniquely solvable with 22-26 givens at similar difficulty levels.
What's the best technique for beginners?
Scan the diagonals first whenever you place a digit. If you place a 7 on the main diagonal, immediately rule out 7 from every other main diagonal cell. Diagonal eliminations happen early and create openings that row/column/box logic alone wouldn't find.
Are all Sudoku X puzzles solvable without guessing?
Yes. Every Sudoku X puzzle on PencilGrid has exactly one solution reachable through pure logic. The generator verifies uniqueness before publishing.
Solving Strategies
Scan Diagonals Early
Whenever you place a digit on a diagonal, immediately eliminate it from every other cell on that diagonal. Diagonal scans reveal openings that row/column/box logic alone would miss, especially in the opening moves when few cells are filled.
Treat the Center as Most Constrained
The center cell R5C5 sits on both diagonals, giving it five uniqueness constraints (row, column, box, main diagonal, anti-diagonal). If you're stuck, check what's still possible at R5C5—it often narrows to one or two candidates before most other cells.
Watch Diagonal-Box Interactions
The three center boxes (top-middle, center, bottom-middle) each intersect both diagonals. When a digit appears on a diagonal within one of these boxes, it eliminates that digit from both the diagonal AND the box. This double-constraint creates quick eliminations.