Diagonal Sudoku (X-Sudoku): Complete Rules and Strategies Guide

Diagonal Sudoku — also known as X-Sudoku — is one of the most popular Sudoku variants in the world. It adds a single, elegant constraint to the standard rules: the two main diagonals of the grid must also contain the digits 1 through 9 exactly once. This small change has surprisingly deep consequences for how puzzles are constructed, how they play, and what strategies you need to solve them.

What Is Diagonal Sudoku?

In standard Sudoku, every row, column, and 3×3 box must contain each digit from 1 to 9 exactly once. Diagonal Sudoku keeps all of these rules and adds one more:

The two main diagonals — from the top-left corner to the bottom-right corner, and from the top-right corner to the bottom-left corner — must each contain the digits 1 through 9 exactly once.

These diagonals form an “X” shape across the grid, which is why the variant is also called X-Sudoku. Some sources call it “Sudoku X” or “Cross Sudoku.”

The diagonals are:

• Main diagonal: Cells (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9)
• Anti-diagonal: Cells (1,9), (2,8), (3,7), (4,6), (5,5), (6,4), (7,3), (8,2), (9,1)

Notice that the center cell (5,5) lies on both diagonals. This makes it the most constrained cell in the entire grid — it must satisfy its row, its column, its box, and both diagonals.

Visual Representation

Imagine the standard 9×9 grid with the two diagonals highlighted. Every cell on either diagonal is subject to an additional constraint. Cells at the intersection of a diagonal with a row, column, and box must satisfy all of those constraints simultaneously.

The total number of “units” (groups where each digit appears exactly once) increases from 27 in standard Sudoku (9 rows + 9 columns + 9 boxes) to 29 in Diagonal Sudoku (27 + 2 diagonals).

How Diagonal Sudoku Differs from Classic Sudoku

The addition of two diagonal constraints fundamentally changes the puzzle in several ways.

More Constraints Mean Fewer Solutions

Adding constraints to any combinatorial problem reduces the number of valid solutions. The total number of valid completed 9×9 standard Sudoku grids is approximately 6.67 × 10²¹. The number of valid Diagonal Sudoku grids is significantly smaller — roughly 5% to 10% of that count — because many standard grids violate the diagonal requirement.

This reduced solution space means:

• Puzzles can have fewer givens while still maintaining a unique solution.
• The solving path is often more constrained, with fewer candidates per cell on average.
• Construction is harder because the designer must satisfy more simultaneous requirements.

Diagonal Cells Are More Constrained

In standard Sudoku, each cell belongs to exactly three units: one row, one column, and one box. In Diagonal Sudoku, cells on a diagonal belong to four units (row, column, box, diagonal), and the center cell belongs to five units (row, column, box, and both diagonals).

This means diagonal cells have more peers — other cells that share a unit — and therefore fewer possible candidates on average. The center cell has the most peers of any cell in the grid.

Different Interaction Patterns

In standard Sudoku, rows, columns, and boxes interact in well-studied ways. Adding diagonals creates new interaction patterns:

• A diagonal crosses multiple boxes, creating connections between boxes that do not share a row or column.
• Eliminations along a diagonal can unlock progress in distant parts of the grid.
• Techniques like pointing and box-line reduction gain additional dimensions when diagonals are involved.

Unique Strategies for Diagonal Sudoku

While all standard Sudoku techniques apply to Diagonal Sudoku, the variant introduces several strategies that are either unique or significantly more powerful.

Diagonal Singles

The most basic diagonal-specific technique is simply looking for naked singles and hidden singles along the diagonals. Since each diagonal must contain 1–9, you can treat a diagonal exactly like a row or column for elimination purposes.

Diagonal naked single: A cell on a diagonal has only one candidate remaining after considering its row, column, box, and diagonal constraints.

Diagonal hidden single: A digit can only go in one cell along a diagonal, even though that cell may have other candidates. Assign the digit and eliminate it from the cell’s other units.

These are the most common solving moves in Diagonal Sudoku and should be your first check whenever you fill a cell on a diagonal.

Diagonal Pointing

In standard Sudoku, pointing pairs occur when a candidate within a box is confined to a single row or column, allowing you to eliminate that candidate from the rest of the row or column. Diagonal Sudoku extends this concept:

Diagonal pointing: If a candidate within a box is confined to cells that all lie on the same diagonal, you can eliminate that candidate from all other cells on that diagonal outside the box.

This is powerful because a diagonal spans the entire grid, so a single diagonal pointing elimination can remove candidates from cells in distant boxes.

Diagonal Pair Elimination

Naked pairs and hidden pairs work along diagonals just as they work in rows, columns, and boxes. If two cells on a diagonal contain only the candidates {3, 7}, then 3 and 7 can be eliminated from all other cells on that diagonal.

Because diagonal cells are distributed across the grid (unlike row cells, which are adjacent), diagonal pair eliminations often have far-reaching consequences.

Cross-Diagonal Interactions

The center cell (5,5) belongs to both diagonals. This creates unique interactions:

• If a candidate is eliminated from cell (5,5) based on one diagonal, it is simultaneously eliminated from the other diagonal.
• Progress on one diagonal near the center often triggers progress on the other diagonal.
• The center cell frequently resolves earlier in Diagonal Sudoku than in standard Sudoku because of its extreme constraint load.

Adapted Fish Patterns

X-Wing, Swordfish, and other fish patterns work in Diagonal Sudoku, but the diagonals add two extra “lines” to consider. An X-Wing pattern might involve a diagonal as one of its two defining lines, creating elimination opportunities that don’t exist in standard Sudoku.

For example, if a candidate appears in exactly two cells in a row, and exactly two cells on a diagonal, and these cells form a rectangle (or the diagonal equivalent), you have a diagonal X-Wing that can eliminate candidates from both the row and the diagonal.

Adapting Standard Techniques

If you already know standard Sudoku techniques, adapting them for Diagonal Sudoku is straightforward. The key principle is: treat each diagonal as an additional “row” for technique purposes.

Singles (Beginner)

Continue scanning for naked singles and hidden singles exactly as you would in standard Sudoku, but include the diagonals in your scan. After filling every naked and hidden single in rows, columns, and boxes, check both diagonals for additional singles.

Pairs and Triples (Intermediate)

Naked pairs, hidden pairs, naked triples, and hidden triples all apply to diagonals. When you scan for subset patterns, include the diagonals as units to check. A {2, 5} naked pair on the main diagonal eliminates 2 and 5 from all other cells on that diagonal.

Pointing and Box-Line (Intermediate)

Pointing pairs and box-line reduction gain extra power in Diagonal Sudoku:

• A candidate confined to diagonal cells within a box can be eliminated from the rest of the diagonal (diagonal pointing).
• A candidate confined to a single box along a diagonal can be eliminated from other cells in that box (diagonal box-line reduction).

Fish (Advanced)

X-Wing and Swordfish patterns can use diagonals as defining lines. When searching for fish patterns, consider the 11 possible line types: 9 rows, 9 columns, and 2 diagonals (for a total of 20 lines). Fish that include a diagonal line are valid and produce useful eliminations.

Wings (Advanced)

XY-Wing and XYZ-Wing patterns work without modification, but the expanded peer lists of diagonal cells mean that wing patterns centered on diagonal cells can produce more eliminations.

Common Patterns in Diagonal Sudoku

With practice, you will notice several recurring patterns that are specific to Diagonal Sudoku.

The Center Cell Resolves Early

Because cell (5,5) belongs to five units, it frequently has a very small candidate list early in the solve. In many Diagonal Sudoku puzzles, the center cell can be determined in the first few moves. Always check the center cell first.

Diagonal Cascades

When you place a digit on a diagonal, it eliminates that digit from many cells simultaneously (up to 8 other diagonal cells, plus the usual row, column, and box peers). This often triggers a cascade of further placements along the diagonal. Diagonal cascades are one of the most satisfying aspects of X-Sudoku solving.

Corner-Diagonal Interactions

The corner cells of the grid each belong to a diagonal. Cell (1,1) is on the main diagonal, cell (1,9) is on the anti-diagonal, and so on. These cells are already highly constrained in standard Sudoku (they have the fewest peers within a box), and the diagonal constraint makes them even more determined.

Box 5 Connectivity

The center box (box 5) is crossed by both diagonals, meaning every cell in box 5 is on at least one diagonal. Three cells are on the main diagonal, three on the anti-diagonal, and three are off both. This makes box 5 the most constrained box in the grid, and progress in box 5 often unlocks progress throughout the puzzle.

Difficulty Comparison: Diagonal vs. Classic

How does Diagonal Sudoku difficulty compare to standard Sudoku?

More Constraints Can Mean Easier

Counterintuitively, adding constraints can make puzzles easier because the solver has more information to work with. A Diagonal Sudoku puzzle with 25 givens may be easier to solve than a standard Sudoku puzzle with 25 givens because the diagonal constraints provide additional elimination opportunities.

This means Diagonal Sudoku constructors often need to use fewer givens to create challenging puzzles. A difficult Diagonal Sudoku might have only 18–22 givens, while a comparably difficult standard Sudoku needs 24–28.

Technique Thresholds Shift

In standard Sudoku, the progression from singles to pairs to fish to chains corresponds to increasing difficulty. In Diagonal Sudoku, the additional constraints mean that diagonal singles and diagonal pointing can substitute for standard pairs in many situations. This shifts the technique thresholds:

Some Techniques Become Rarer

Because the diagonal constraints provide extra elimination power, some intermediate techniques (like standard pointing pairs) become less necessary. The diagonal constraint handles many of the eliminations that pointing and box-line reduction would handle in standard Sudoku. This can make the solving experience feel different even at the same nominal difficulty level.

Tips for Transitioning from Classic to Diagonal

If you are an experienced standard Sudoku solver trying Diagonal Sudoku for the first time, here are practical tips.

1. Start with Easy Diagonal Puzzles

Begin with puzzles that can be solved entirely with singles, including diagonal singles. This lets you build the habit of checking diagonals without the cognitive overload of adapting advanced techniques.

2. Highlight the Diagonals

If you solve on paper or in an app that supports highlighting, visually mark the diagonal cells. This helps your eye include them in scans. Over time, you will automatically include diagonals in your visual scanning pattern.

3. Check the Center Cell First

Always start by examining cell (5,5). It belongs to five units and often resolves immediately or has only 2–3 candidates. Resolving the center cell early provides a cascade of eliminations.

4. Think of Diagonals as Extra Rows

Mentally model each diagonal as a 10th and 11th “row” for the purpose of your scanning routine. When you check rows for hidden singles, also check both diagonals. When you check pairs in rows, also check diagonals.

5. Watch for Diagonal Cascades

After placing any digit on a diagonal cell, immediately scan the affected diagonal for new singles. Diagonal placements often trigger chains of further placements because diagonal peers span the entire grid.

6. Don’t Over-Rely on Diagonals

While diagonals are powerful, most of the grid is still governed by standard constraints. Do not neglect your usual row-column-box techniques. The best approach integrates diagonal checking into your existing solving routine rather than replacing it.

7. Build Up Technique Familiarity

If you are comfortable with standard techniques through X-Wings and XY-Wings, you have all the foundational knowledge needed for Diagonal Sudoku. The unique diagonal strategies are extensions of techniques you already know. For a complete learning roadmap, see our technique progression guide.

Where to Play Diagonal Sudoku

Diagonal Sudoku is widely available:

• Puzzle books: Many Sudoku publishers include X-Sudoku sections. Look for titles specifically labeled “X-Sudoku” or “Diagonal Sudoku.”
• Apps: Several Sudoku apps include Diagonal Sudoku as a variant mode.
• Websites: Dedicated puzzle sites often offer Diagonal Sudoku alongside other variants.
• Competitions: The World Sudoku Championship regularly includes Diagonal Sudoku and other variants.

For building the foundational skills that translate directly to Diagonal Sudoku (and every other variant), practice standard Sudoku across all difficulty levels at SudokuPulse: Easy, Medium, Hard, Expert, and Evil.

To learn more about other Sudoku variants and how they compare, see our comprehensive guide to Sudoku Variants Explained.

The History of Diagonal Sudoku

Diagonal Sudoku has been part of the Sudoku family since the puzzle’s early days. In Japan, where Sudoku was popularized by Nikoli in the 1980s, variant puzzles including diagonal constraints appeared early on. The variant gained international popularity alongside standard Sudoku in the 2000s.

The World Puzzle Federation has included Diagonal Sudoku in its annual championship since the competition’s early editions. It is considered one of the “classic” variants — similar enough to standard Sudoku to be accessible, but different enough to require adapted strategies.

In competitive solving, Diagonal Sudoku is valued because it tests a solver’s flexibility. Competitors who can seamlessly switch between standard and variant rules demonstrate a deeper understanding of constraint-based logic.

How to Learn Sudoku Fundamentals

If you are new to Sudoku entirely, we recommend mastering standard Sudoku before attempting Diagonal Sudoku. A strong foundation in the basic techniques — naked singles, hidden singles, naked pairs, and pointing pairs — will translate directly when you add diagonal constraints.

Start with our How to Play Sudoku guide for the basics, then work through the technique progression at your own pace. Once you are comfortable solving Medium standard puzzles, you are ready to tackle Easy Diagonal Sudoku.

Frequently Asked Questions

What is Diagonal Sudoku?

Diagonal Sudoku, also called X-Sudoku, adds one constraint to standard Sudoku: the two main diagonals of the grid must each contain the digits 1 through 9 exactly once. The main diagonal runs from the top-left to bottom-right corner, and the anti-diagonal runs from the top-right to bottom-left corner. All standard Sudoku rules (rows, columns, and 3×3 boxes) still apply. The “X” formed by the two diagonals gives the variant its alternate name.

Is Diagonal Sudoku harder than regular Sudoku?

Not necessarily — it depends on the puzzle’s construction. The additional diagonal constraints provide extra information, which can make some puzzles easier to solve than standard Sudoku with the same number of givens. However, puzzle constructors can exploit the interactions between diagonal and standard constraints to create very challenging grids. Overall, the difficulty range is similar to standard Sudoku, but the solving experience feels different because of the diagonal interactions.

What strategies are unique to Diagonal Sudoku?

The most important unique strategies are: diagonal singles (hidden singles along a diagonal), diagonal pointing (candidates confined to a diagonal within a box, allowing elimination from the rest of the diagonal), and diagonal pair elimination (naked or hidden pairs along a diagonal). Additionally, fish patterns like X-Wings can use a diagonal as one of their defining lines, creating elimination opportunities that don’t exist in standard Sudoku.

Can I use standard Sudoku techniques in Diagonal Sudoku?

Absolutely. All standard techniques — naked singles, hidden singles, pairs, triples, pointing, box-line reduction, X-Wings, XY-Wings, and all others — work in Diagonal Sudoku exactly as they do in standard. The diagonals simply add two more units (like two extra rows) where the same elimination logic applies. Most solving consists of standard techniques plus diagonal-specific extensions.

Where can I play Diagonal Sudoku?

Diagonal Sudoku is available in many puzzle books, mobile apps, and websites. Look for titles specifically labeled “X-Sudoku” or “Diagonal Sudoku.” The World Sudoku Championship also features Diagonal Sudoku annually. To build the foundational skills needed for any Sudoku variant, practice standard puzzles at SudokuPulse across difficulty levels from Easy to Evil.