Argyle Sudoku – Medium

Solving Argyle Sudoku: Rules and Strategies

Argyle Sudoku is a Sudoku variant. Marked lines running diagonally through the grid complement the classic Sudoku units.

Each individual Argyle line must not contain repeating numbers. The lines are shorter than nine cells and do not need to contain all numbers from 1 to 9.

The goal is a completely filled, conflict-free puzzle. Each move must follow from the visible clues and already confirmed entries.

Rules

• Each active cell contains exactly one number from 1 to 9.
• Each row contains the numbers 1 to 9 with no repeats.
• Each column contains the numbers 1 to 9 with no repeats.
• Each normal 3×3 block contains the numbers 1 to 9 exactly once.
• On each individual Argyle line, no number can repeat. The lines are shorter than nine cells and do not need to include all numbers from 1 to 9.
• Given numbers are not changed.
• Every final entry must satisfy all rules simultaneously.

Orientation in the Grid

Rows are counted from top to bottom, columns from left to right. For a pair of numbers, the first number indicates the row and the second the column; (4,7) thus refers to the cell in row 4, column 7.

The examples each show a specific intermediate state. Blue markings indicate the assumptions used, red markings indicate exclusions, and green markings indicate confirmed results.

Basic Idea for Solving

Start with secure Sudoku steps and then follow each entered value along all touched Argyle lines.

After each secure entry, it is worthwhile to do a quick full walkthrough of the affected units and additional hints. This creates a chain of small, understandable steps.

1. Close an Almost Complete Row

In the row unit of Row 1, everything is filled except for cell (1,4). Visible are 1, 2, 3, 4, 5, 6, 8, 9; only 7 is missing from the permissible numbers.

Therefore, 7 goes into (1,4). This move does not require guesswork: the other values in the considered unit are fully visible in the picture.

2. Close an Almost Complete Column

In the column unit of Column 1, everything is filled except for cell (3,1). Visible are 1, 2, 3, 4, 5, 6, 7, 9; only 8 is missing from the permissible numbers.

Hence, 8 goes into (3,1). This move does not require guesswork: the other values are fully visible in the image.

3. Read the Relevant Region Fully

In the 3×3 block 1, everything is filled except for cell (2,2). Visible are 1, 3, 4, 5, 6, 7, 8, 9; only 2 is missing from the permissible numbers.

Therefore, 2 goes into (2,2). This move does not require guesswork: the other values are fully visible in the image.

4. Exclude a Number Along an Argyle Line

The marked line connects (1,5) with (2,4). Since 4 is already at (1,5), it is excluded from (2,4).

The Argyle rule here provides a safe candidate exclusion. It does not require every number on the line; the critical point is that no number repeats.

5. Check Two Intersecting Lines Simultaneously

Cell (4,5) is on two marked lines. One already has 8, the other 6.

Both values are excluded from (4,5). An intersection thus gains two additional exclusion sources beyond row, column, and 3×3 block.

6. Combine Line and Block Exclusions

For (2,4), after exclusions from row, column, and block, multiple possible numbers remain. The marked diagonal removes the values already on it.

Leaving only 6; it is entered into (2,4). It then acts again as an exclusion across the entire Argyle line.

7. Merge Multiple Units in One Cell

In (1,4), multiple units are still incomplete. Through the combined exclusion by all associated rows, columns, and regions, only 7 remains.

The candidate set for (1,4) is thus {7}. Such singleton cells often arise only after all types of units are checked simultaneously.

Typical Solving Process

1. Fill in immediately complete rows, columns, and key regions.
2. Note only candidates compatible with all normal units for open cells.
3. Then apply the puzzle-specific additional rule to these candidates.
4. Enter only values with clear justification.
5. After each entry, check all touched units and hints again.
6. Repeat the walkthrough until the grid is complete.

Common Mistakes

• Interpreting an Argyle line as a complete nine-unit: Lines only require different values.
• Checking an intersection in only one direction: An intersection cell belongs to both marked lines.
• Guess too early: Multiple remaining candidates are not yet a reason to guess.
• Not rechecking after an entry: A single value can change multiple units and hints at once.

Tips for Beginners

• Start with units or hints with especially much visible information.
• Note small candidate sets instead of mixing possibilities mentally.
• Always check a candidate against each rule affecting its cell.
• Treat secure exclusions as actual progress, even if no value is set yet.
• If no move is visible, shift purposefully from rows to columns, regions, and hints.

Argyle Sudoku becomes clear once normal units and additional hints are consistently reevaluated after each secure step. Small, fully justified deductions are more reliable than early guessing.