Sujiken – Hard

Sujiken

Sujiken is a triangular Sudoku variant. Instead of a square 9x9 grid, the puzzle consists of a triangle with 45 fields. The rows increase in length from top to bottom: the first row has one field, the second two, up to the ninth row with nine fields.

Like Sudoku, the numbers 1 through 9 are used. The constraints are not only imposed by horizontal rows but also by columns, diagonals, and outlined regions. As a result, Sujiken feels like a mix of Sudoku and triangular logic.

Basic Rules

• The numbers 1 to 9 are used.
• The grid is triangular and consists of 45 fields.
• No number may appear twice in any horizontal row.
• No number may appear twice in any vertical column.
• No number may appear twice on any diagonal.
• Additionally, there are outlined regions. In each 9-field region, the numbers 1 through 9 must appear exactly once.
• A Sujiken is solved when all fields are filled and all row, column, diagonal, and region rules are satisfied.

Strategies for Solving

The most important difference from classic Sudoku is the shape of the grid. One must look not only at rows and regions but also at the inclined lines of the triangle.

1. Completing a 9-Field Region

In the following example, we consider the lower left 3x3 region. It consists of the first three fields of the last three rows.

In this region, the numbers 9, 4, 6, 5, 1, 7, 2, and 8 are present. The only missing number is 3. Therefore, the empty field in row 7, third position, must be a 3.

This step is definite because a complete 9-field region must contain all numbers 1 through 9.

2. Using Diagonals as Exclusions

In Sujiken, a number can be excluded by a diagonal line. In the following grid, we consider an empty field on the same diagonal as a pre-placed 7.

If the empty field is on the same Sujiken diagonal as the 7, no other 7 can be placed there.

The diagonal rule is therefore one of the most important features of Sujiken.

3. Do Not Overestimate Short Rows

The top rows are shorter than nine fields. They do not need to contain all numbers 1 through 9 but must simply not contain duplicate numbers.

In the second row, a 9 is already present. The other field in this row must not be 9. Which number is there also depends on columns, diagonals, and regions.

Typical Solving Process

1. First, check the outlined 9-field regions with many clues.
2. Look for regions where only one number is missing.
3. Use horizontal rows, columns, and diagonals as exclusion lines.
4. Remember that short rows do not automatically contain all numbers 1 through 9.
5. Combine region logic with diagonal exclusions.
6. Verify all lines crossing a field whenever you enter a number.

Common Mistakes

• Treat the triangle as a normal 9x9 Sudoku.
• Assume that every short row contains all numbers 1 through 9.
• Overlook diagonals.
• Do not fully check outlined 9-field regions.
• Judge a field based only on one direction.

Tips for Beginners

• Start with the 9-field regions, as they most resemble classic Sudoku blocks.
• Follow a number along inclined lines.
• Work slowly, as neighboring relations are less familiar than in a square grid.
• Ask yourself with each field: Which row, column, diagonal, and region does it belong to?

Sujiken is especially interesting because well-known Sudoku principles are transferred into a triangular form. Combining regions and diagonals cleanly leads to safe steps without guessing.