Argyle Sudoku – Medium

Argyle Sudoku

Argyle Sudoku is a variant of the classic 9x9 Sudoku. The grid initially looks like a normal Sudoku: there are 9 rows, 9 columns, and nine 3x3 blocks. Additionally, diagonal lines are overlaid on the grid. These lines form the typical Argyle pattern.

The task is to fill in the numbers 1 to 9 so that all standard Sudoku rules are met, and additionally, no number repeats on any drawn Argyle line. The lines are not individual Sudoku regions containing all numbers from 1 to 9; instead, they serve mainly as additional exclusion rules.

Basic Rules

• The playing field consists of 9 rows and 9 columns.
• Standard Sudoku rules apply: each row contains the numbers 1 to 9 exactly once.
• Each column contains the numbers 1 to 9 exactly once.
• Every 3x3 block contains the numbers 1 to 9 exactly once.
• Additionally, no number may repeat on any drawn Argyle line.
• An Argyle line is not necessarily required to contain all numbers from 1 to 9, as many lines are shorter than 9 cells.
• The given numbers must not be altered.
• The puzzle is solved when all cells are filled without violating any Sudoku or Argyle line rule.

Strategies for Solving

1. Continue using normal Sudoku deductions

At its core, Argyle Sudoku remains a Sudoku. Nearly complete rows, columns, and 3x3 blocks remain a good starting point.

In the first row, only the number 2 is missing. This cell can therefore be safely filled with 2. The Argyle lines do not affect this simple deduction.

2. Use an Argyle line as an exclusion rule

The most important new way of thinking is: a number that already appears on an Argyle line cannot appear again on the same line. This can rule out candidates, even if the row, column, and block initially would allow the number.

In row 4, the two open spots are missing the numbers 6 and 7. The cell in row 4, column 5 lies on an Argyle line. The number 6 already appears on this line in row 1, column 2. Therefore, 6 cannot be in row 4, column 5.

Thus, only the 7 remains for row 4, column 5.

The conclusion is clear: the row allows only 6 or 7, and the Argyle line excludes 6.

3. Do not treat Argyle lines as complete regions

A common mistake is to treat an Argyle line like an additional 9-region. This is incorrect. Many Argyle lines are shorter than 9 cells. If, on such a line, the numbers 1, 3, 5, and 8 are present, it does not automatically mean that all other numbers are also on this line.

The correct principle is: a number cannot appear twice on the same line.

Typical solving process

1. First check normal Sudoku deductions in rows, columns, and 3x3 blocks.
2. Mark candidates for open cells if no direct number is visible.
3. Next, check the Argyle lines: which candidates already appear on the same line?
4. Eliminate these candidates accordingly.
5. If only one candidate remains after elimination, fill in the number.
6. After each entry, recheck the row, column, block, and the affected Argyle line.

Common Mistakes

• Guess too early instead of using the additional rule as a reliable exclusion.
• Only check rows and columns, overlooking the special marking of the puzzle.
• Enter a number that is locally correct but violates the special rule.
• Fail to update candidates after each new entry.
• Misread a marking or apply it to the wrong cells.

Tips for Beginners

• Start like a normal Sudoku with well-filled rows, columns, and regions.
• Then, specifically check the special rule. Often, early safe exclusions arise there.
• Always work with the question: Which numbers are really allowed, and which are excluded by a rule?
• Only enter a number when it can be unambiguously derived.
• If you get stuck, change your perspective: from rows to columns, regions to the special rule, or from individual cells to candidates.

Argyle Sudoku rewards careful elimination. The diagonal lines usually do not provide immediate complete numbers but remove candidates at exactly the points where a standard Sudoku remains open.