Asterisk Sudoku – Hard

Solving Asterisk Sudoku: Rules and Strategies

Asterisk Sudoku is a Sudoku variant. Nine colored marked cells form a star-shaped additional region within the 9×9 grid.

The scattered Asterisk area is treated as an additional Sudoku unit and contains the numbers 1 to 9 exactly once.

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

Rules

• Each active cell contains exactly one number from 1 to 9.
• Each row contains the numbers 1 to 9 without repetition.
• Each column contains the numbers 1 to 9 without repetition.
• Each normal 3×3 block contains the numbers 1 to 9 exactly once.
• The scattered Asterisk region is treated as an additional Sudoku unit and contains the numbers 1 to 9 exactly once.
• Given numbers are not changed.
• Each final entry must meet 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 refers to the row and the second to the column; (4,7) thus refers to the cell in row 4, column 7.

The examples each show a concrete intermediate state. Blue markings indicate used prerequisites, red markings exclude possibilities, and green markings confirm results.

Basic idea for solving

Start with normal Sudoku units, but always check the marked additional regions afterward. A candidate remains allowed only if it fits in all associated units.

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

1. Close a nearly complete row

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

Therefore, 4 is placed in (1,8). This move requires no guess: the other values in the considered unit are fully visible in the image.

2. Close a nearly complete column

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

Thus, 1 is placed in (3,1). No guess needed: the other values of this unit are fully visible in the image.

3. Read the relevant area completely

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

Therefore, place 1 in (3,1). No guess required: the other values of this unit are fully visible.

4. Use the extra region as a complete unit

In the Asterisk area, everything is filled except for cell (3,7). Visible are 1, 3, 4, 5, 6, 7, 8, 9; the only allowable number missing is 2.

Put 2 in (3,7). No guess needed: the other values in this unit are fully visible in the image.

5. Exclude repetition in the extra region

The number 9 is already at (2,5) in the extra unit. Therefore, the same value cannot appear again in the marked cell (3,7).

9 is eliminated from (3,7). Only this exclusion is shown on purpose; the final value of this cell is also determined by its normal Sudoku units.

6. Locate a number within the extra region

Several cells in the extra unit are open. For 2, other open positions are eliminated by their respective rows, columns, or 3×3 blocks; only (3,7) remains as a possible place.

So, 2 is placed at (3,7). This is a hidden single: the cell itself might initially have multiple possibilities, but the number only fits in one place within the extra region.

7. Combine multiple units in one cell

At (1,8), several units are still incomplete. After elimination through all related rows, columns, and regions, only 4 remains.

The candidate set for (1,8) is therefore {4}. Such single possibilities often arise only when all kinds of units are checked simultaneously.

Typical solving process

1. Start by filling immediately complete rows, columns, and key regions.
2. Note only candidates that are allowed by all normal units for open cells.
3. Then apply the puzzle's additional rules to these candidates.
4. Enter only values that are clearly justified.
5. After each entry, review all touched units and hints again.
6. Repeat the review until the grid is complete.

Common mistakes

• Overlooking the marked extra region: A normally allowed candidate may already be present there.
• Comparing only adjacent marked cells: The whole extra region is a single unit.
• Guess too early: Multiple remaining candidates are not yet a reason for guessing.
• Not rechecking after an entry: A single value can change several units and hints simultaneously.

Tips for beginners

• Start with units or hints that have the most visible information.
• Write down small candidate sets rather than trying to keep possibilities in your head.
• Always check a candidate against every rule affecting its cell.
• Treat confirmed exclusions as real progress, even if no value is yet set.
• If no move is visible, switch deliberately between rows, columns, regions, and additional hints.

Asterisk Sudoku becomes clear once normal units and additional hints are consistently reevaluated after each confirmed step. Small, fully justified conclusions lead more reliably to the goal than early guesswork.