Sudoku X – Medium

Solving Sudoku X: Rules and Strategies

Sudoku X is a Sudoku variation. The two long main diagonals form two additional Sudoku units.

Sudoku X is also called Diagonal Sudoku.

Each of the two diagonals contains the numbers 1 to 9 exactly once; the center cell belongs to both.

The goal is a fully and correctly completed puzzle. Each entry must be derived from the visible clues and the already filled numbers.

Rules

• Each cell contains exactly one number from 1 to 9.
• Each row contains the numbers 1 to 9 without repetition.
• Each column contains the numbers 1 to 9 without repetition.
• Each normal 3×3 block contains the numbers 1 to 9 exactly once.
• Each of the two diagonals contains the numbers 1 to 9 exactly once; the center belongs to both.
• Given numbers are not changed.
• Each entry must satisfy all rules.

Orientation in the grid

Rows are counted from top to bottom, columns from left to right. At (4,7), 4 is the row and 7 is the column.

The images show concrete intermediate states. Blue-marked cells are used for the step, red means excluded, and green indicates a certain result. Yellow highlights the currently considered cell. Small numbers in an empty cell are candidates; a circle marks the logically determined value.

Basic idea when solving

Treat each long diagonal as an additional row. Look for missing numbers there and pay special attention to the center cell, which belongs to both diagonals.

After each confirmed entry, recheck the affected row, column, block, and all additional hints. Often, this already leads to the next step.

1. Recognize the two additional diagonals

The lines from corner to corner form two additional groups of nine. The center belongs to both diagonals.

The blue-marked line is the diagonal from top-left to bottom-right. The second long diagonal also contains the numbers 1 to 9 exactly once.

2. Complete an almost full additional group

In main diagonal 1, the numbers 1, 2, 3, 4, 5, 7, 8, 9 are already placed. Only 6 is missing; the cell (6,6) is still empty.

Thus, 6 belongs to (6,6). The image intentionally shows the gap still open; the circled candidate is the resulting entry.

3. Use the extra rule as a candidate exclusion first

Row, column, and normal block initially allow 1, 7, 9 at (1,1). But 7 already appears at (4,4) in main diagonal 1.

Therefore, 7 is eliminated. Only 1 and 9 remain in the open cell. This step does not solve the cell yet but visibly reduces its candidate list.

4. Find the last candidate with the extra group

Without the extra rule, 9 and 7 could still be in (1,1). But 7 is already placed in (4,4) through the same additional area.

So only 9 remains. The target cell is empty and shows the circled candidate 9; only then is the number entered.

5. Find the only place for a number in the extra group

In main diagonal 1, four cells are still open for 9. Three are eliminated by normal Sudoku units: (2,2) by 9 at (2,8); (3,3) by 9 at (3,5); (4,4) by 9 at (4,2).

Only (1,1) remains as the place for 9. The cell itself has candidates 1, 4, 7, 9; the number is thus determined by its only position in the extra group.

6. Enter two missing numbers in correct order

In main diagonal 1, only 9 and 7 are missing; they belong to (1,1) and (4,4). At (1,9), 7 is already in a normal Sudoku unit with (1,1).

Therefore, 7 cannot be after (1,1): 9 is there. For (4,4), 7 remains. This way, a normal unit determines the order of the pair.

7. Determine the center cell with both diagonals

The center cell (5,5) intersects both diagonals. Each diagonal already has eight numbers; both are missing the 5.

Therefore, 5 is placed in the still empty center cell. This step is especially well controllable because both diagonals lead to the same result independently.

8. Prepare a follow-up step with the extra group

In main diagonal 1, only 6 is missing at (6,6). In the same row, (6,6) and (6,5) are still empty.

The extra group places 6 at (6,6). Before this entry, the row cannot yet distinguish the two open cells alone.

9. Execute the prepared row step

After placing 6 at (6,6), only (6,5) remains open in the row. The other eight numbers are fully visible in the image.

Thus, 2 is missing at (6,5). The extra rule provides the first entry; this directly leads to a normal Sudoku step.

Typical solving process

1. Solve confirmed entries in rows, columns, and normal 3×3 blocks.
2. Then, analyze each marked extra group completely.
3. Eliminate numbers already present in the extra group.
4. Search for a missing number with only one possible place in the extra group.
5. Connect pairs and other small candidate groups with the normal Sudoku units.
6. After each entry, recheck all normal and additional groups of the cell.

Common mistakes

• Overlooking the marked extra area: A traditionally allowed candidate might already be there.
• Compare only adjacent marked cells: The entire extra area is one unit.
• Confusing extra group with the normal block: Both groups apply simultaneously and have different boundaries.
• Searching only in complete groups: Even a single exclusion by the extra rule can enable the next step.
• Only check the row after an entry: The affected extra group must also be re-read immediately.
• Rushing too early: If multiple numbers are possible, the cell is not solved yet.
• Not rechecking after an entry: A new number can immediately solve additional cells.

Tips for beginners

• Mark or track an entire extra group instead of just neighboring cells.
• Look first for extra groups with many numbers already placed.
• Check four areas for each cell: row, column, normal block, and extra group.
• A classic possible candidate may still be forbidden by the extra group.
• Use two missing numbers in an extra group together with rows or columns to determine their order.
• Scan the extra group immediately after each entry again.

Solve Sudoku X in small, safe steps. After each entry, recheck the affected row, column, block, and extra hints. This way, you often reach the goal without guessing.