Sudoku X – Easy

Sudoku X

Sudoku X is a variant of the classic 9x9 Sudoku. In addition to rows, columns, and 3x3 blocks, the two main diagonals must also contain the numbers 1 through 9 exactly once. The diagonals together form an X, hence the name.

The additional rule particularly affects cells on one of the two diagonals. The middle cell lies on both diagonals and is therefore often especially restricted.

Basic Rules

• Each row must contain the numbers 1 to 9 exactly once.
• Each column must contain the numbers 1 to 9 exactly once.
• Each 3x3 block must contain the numbers 1 to 9 exactly once.
• The main diagonal from top left to bottom right must contain the numbers 1 to 9 exactly once.
• The main diagonal from top right to bottom left must also contain the numbers 1 to 9 exactly once.
• A cell on a diagonal is additionally restricted by this diagonal rule.

Solve Strategies

The diagonals function as two additional regions. They can be checked similarly to rows, columns, or blocks.

1. Using the Almost Complete Diagonal

In the following example, we consider the diagonal from the top left to the bottom right.

This diagonal already contains 9, 4, 1, 7, 5, 2, 8, and 3. The only missing number is 6. Therefore, the free cell on this diagonal must be a 6.

This conclusion arises solely from the Sudoku-X rule. In a normal Sudoku, this diagonal wouldn't be considered a separate region.

2. Checking the Center Cell

The middle cell belongs to both diagonals. It can therefore be restricted by two additional regions.

If the middle cell still has multiple candidates based on row, column, and block, both diagonals are additionally checked. Any number already present on either of the diagonals is excluded there.

The center is often a good control point in Sudoku X.

3. Using Diagonal as Exclusion

A diagonal rule doesn't have to immediately assign a number. It can also eliminate candidates.

Any empty cell on this diagonal cannot be a 9, 4, 1, 5, or 3 anymore. These exclusions, together with row, column, and block checks, can later produce a single candidate.

Typical Solution Process

1. Initially solve obvious rows, columns, and blocks as in a normal Sudoku.
2. Then check both diagonals as additional regions.
3. Look for diagonals where only a few numbers are missing.
4. Consistently eliminate diagonal candidates from all diagonal cells.
5. Pay particular attention to the middle cell, as it lies on both diagonals.
6. Finally, verify that both diagonals indeed contain 1 to 9.

Common Mistakes

• Forgetting the diagonal rule and placing a duplicate on a diagonal.
• Checking only one of the two diagonals.
• Treating the middle cell as a normal block cell only.
• Not updating candidates on diagonally placed cells.

Tips for Beginners

• Mental note the two diagonals as additional regions.
• Immediately check the remaining diagonal cells after each entry on a diagonal.
• Start with diagonals where many numbers are already placed.
• Use the diagonal rule primarily for exclusions, even if no direct entry is yet made.

Sudoku X remains close to classic Sudoku but offers two additional strong regions. Those who check the diagonals consistently will find many safe exclusions.