Chain Sudoku 6×6 – Medium

Solving Chain Sudoku 6×6: Rules and Strategies

Chain Sudoku 6×6 is a Sudoku variant. Six rows, six columns, and six curved chains form three equivalent types of units.

This chain form is also known under the name Strimko.

In each row, each column, and each chain, the numbers 1 to 6 appear exactly once.

The goal is a fully filled, contradiction-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 6.
• Each row contains the numbers 1 to 6 without repetition.
• Each column contains the numbers 1 to 6 without repetition.
• Each drawn chain contains the numbers 1 to 6 exactly once; standard 3×3 blocks do not apply.
• Given numbers are not changed.
• Every final entry must comply with 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 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 denote used assumptions, red markings exclude options, and green markings indicate confirmed results.

Basic idea for solving

Follow the curved chains completely. After each entry, recheck its row, column, and chain.

After each confirmed entry, it's worth a quick full check of the affected units and additional hints. This creates a chain of small, understandable steps.

1. Complete an almost full row

In unit Row 1, everything is filled except for cell (1,4). Visible are 1, 2, 4, 5, 6; only 3 is missing from the allowable numbers.

Therefore, a 3 goes in (1,4). This move doesn't require guesswork: the other values of the considered unit are fully visible in the image.

2. Complete an almost full column

In column 1, everything is filled except for cell (2,1). Visible are 2, 3, 4, 5, 6; only 1 is missing from the allowable numbers.

Thus, a 1 goes in (2,1). This move doesn't require guessing: the other values of the unit are fully visible in the image.

3. Read the relevant region fully

In chain 1, everything is filled except for cell (2,3). Visible are 1, 2, 3, 4, 6; only 5 is missing from the allowable numbers.

Therefore, a 5 goes in (2,3). This move doesn't require guessing: the other values of the considered unit are fully visible in the image.

4. Fully analyze the drawn region

In chain 4, everything is filled except for cell (1,4). Visible are 1, 2, 4, 5, 6; only 3 is missing from the allowable numbers.

Thus, a 3 goes in (1,4). This move doesn't require guessing: the other values of the considered unit are fully visible in the image.

5. Use the actual region instead of an imagined block

(1,5) and (1,4) both belong to chain 4. Since a 4 is already there, it cannot occur again in the second cell.

The 4 is eliminated from (1,4). In this type of puzzle, the drawn region is decisive; a normal 3×3 block wouldn't be relevant for this deduction.

6. Combine row and drawn region

Cell (1,6) belongs simultaneously to row 1 and chain 4. The open numbers of both units are compared.

Only the number 1 fits both sets, so it is entered in (1,6). Switching between rows, columns, and drawn regions is key to solving.

7. Combine multiple units in one cell

In (1,4), multiple units are still incomplete. After jointly excluding options through all related rows, columns, and regions, only the 3 remains valid.

The candidate set for (1,4) is thus {3}. Such single-cell candidates often only appear after all types of units are checked simultaneously.

Typical solving process

1. First fill immediately complete rows, columns, and relevant regions.
2. Note only candidates allowed by all normal units for open cells.
3. Then apply the additional rule of the puzzle type to these candidates.
4. Enter only values with clear justification.
5. After each entry, recheck all touched units and hints.
6. Repeat until the grid is complete.

Common mistakes

• Using imagined 3×3 blocks: Only rows, columns, and drawn chains count.
• Losing a chain at a bend: Follow all connected circles to the end.
• Guess too early: Multiple remaining candidates are not yet grounds for guessing.
• Not rechecking after an entry: A single value can change multiple units and hints simultaneously.

Tips for beginners

• Start with units or hints that have especially much visible information.
• Write down small candidate sets instead of trying possibilities mentally.
• Always check a candidate against every rule affecting its cell.
• Consider confirmed exclusions as real progress, even if no value is set yet.
• If no move is visible, switch purposefully between rows, columns, regions, and hints.

Chain Sudoku 6×6 becomes clear when normal units and additional hints are consistently reevaluated after each confirmed step. Small, fully justified inferences lead more reliably to the solution than early guessing.