Diagonal Sudoku (X Sudoku)

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What Is Diagonal Sudoku (X Sudoku)?

Diagonal Sudoku, also commonly called X Sudoku, is a Sudoku variant that adds two diagonal constraints to the classic Sudoku rules.

In addition to the standard row, column, and box rules:

Both main diagonals must also contain each digit exactly once.

The diagonals form an "X" shape across the grid — which is why this variant is widely known as X Sudoku.

Diagonal Sudoku does not introduce extra symbols or numbers. All difficulty comes from how diagonal constraints interact with standard Sudoku logic.

Tips for Solving Diagonal Sudoku (X Sudoku)

Diagonal Sudoku follows the same logic as classic Sudoku, but the two diagonal constraints fundamentally change how candidates interact.

The tips below focus on how standard techniques behave differently once diagonals are active, based on real solving patterns rather than theory.

1. Diagonal Naked Single

This is often the first diagonal-specific placement you will make.

While scanning the grid, you may find a cell on a diagonal where every number except one is eliminated by:

• its row
• its column
• its box
• and the diagonal itself

For example:

If a diagonal already contains 1, 2, 3, 4, 5, 6, 7, 8

then the remaining diagonal cell must be 9, even if the row and box still look flexible.

What makes this easy to miss is habit: many solvers finish checking rows and boxes before looking at diagonals.

In Diagonal Sudoku, diagonals deserve equal priority.

2. Diagonal Hidden Single

Diagonal Hidden Singles are more subtle — and more important.

This happens when a digit appears as a candidate in multiple cells of a row, column, or box, but only one of those cells lies on the diagonal.

Example:

In a center 3×3 box, the number 9 appears possible in two cells.

However:

• one cell is on the main diagonal
• the other is not

If the diagonal already contains every digit except 9, then 9 must go in the diagonal cell, even though the box itself does not look constrained.

Experienced solvers regularly re-check diagonals specifically for this pattern.

3. Diagonal Locked Candidate (Box–Diagonal Interaction)

This is where Diagonal Sudoku starts to feel different from standard Sudoku.

Sometimes, all possible placements of a number on a diagonal are confined to:

• a single row, or
• a single column, or
• a single box

When that happens, the diagonal behaves like a locking unit.

Example:

If all possible positions for 5 on the main diagonal lie inside one box, then 5 cannot appear elsewhere in that box, even in cells not touching the diagonal.

This interaction often unlocks progress far away from the diagonal itself — a classic Diagonal Sudoku moment.

4. Diagonal Naked Pair

A Diagonal Naked Pair occurs when two diagonal cells contain the same two candidates, and nothing else.

Example:

Two cells on the diagonal can only be {7, 8}.

No other diagonal cell can contain 7 or 8.

What makes this powerful is that:

• diagonals are long units (9 cells in 9×9)
• eliminating two candidates from seven other diagonal cells often triggers new singles

If you already know Naked Pairs in rows and boxes, this will feel familiar — just remember to actively scan diagonals for them.

5. Diagonal Hidden Pair

This is one of the most commonly overlooked techniques in Diagonal Sudoku.

A Diagonal Hidden Pair appears when:

• two digits only appear in the same two diagonal cells
• even though those cells may contain extra candidates

Example:

On the diagonal, only cells A and B can contain {4, 6}.

Even if A currently allows {1,4,6} and B allows {2,4,6}, you can safely reduce both cells to {4, 6}.

This cleanup often prepares the grid for a diagonal Naked Single shortly after.

6. Diagonal vs Row / Column Tension

Not every diagonal deduction comes from "clean" patterns.

Sometimes you notice tension instead:

• a diagonal wants a number in one area
• but rows or columns nearby block most options

In practice, this shows up as:

"If this digit goes here on the diagonal, the row collapses."

When you encounter that feeling, pause and test the diagonal assumption logically:

• Does it force repetition?
• Does it eliminate all candidates in a neighboring unit?

This kind of reasoning feels less mechanical and more exploratory — and it's a sign you're solving Diagonal Sudoku the right way.

Common Beginner Mistakes

• Forgetting to enforce diagonal uniqueness
• Missing diagonal Hidden Singles
• Treating diagonal digits as optional constraints
• Ignoring diagonal pairs and groups

Most errors happen because players mentally "downgrade" diagonals compared to rows and boxes.