Asterisk Sudoku – Hard

Asterisk Sudoku

Asterisk Sudoku is a classic 9x9 Sudoku with an additional group of nine marked cells. These cells form a star-shaped pattern, hence the name Asterisk. Besides rows, columns, and 3x3 blocks, this marked Asterisk group must also contain the numbers 1 through 9 exactly once.

This creates an extra region that does not have to be contiguous. These scattered cells make the puzzle interesting: a digit placed in a marked cell affects not only its row, column, and block but also the entire Asterisk group.

Basic Rules

• The normal Sudoku rules for a 9x9 grid apply.
• Each row contains the numbers 1 to 9 exactly once.
• Each column contains the numbers 1 to 9 exactly once.
• Each 3x3 block contains the numbers 1 to 9 exactly once.
• The nine marked Asterisk cells form their own region.
• In this Asterisk region, each number from 1 to 9 must also appear exactly once.
• The given numbers must not be changed.

Strategies for Solving

1. Read the Asterisk cells as an additional region

The marked cells function similarly to an extra 3x3 block, but they are scattered across the grid. If eight of these nine cells already contain numbers, the last Asterisk cell can be determined directly.

In the marked Asterisk cells, the numbers 1, 2, 3, 4, 5, 7, 8, and 9 are already present. The only missing number in the Asterisk region is 6. Therefore, the still empty marked cell in row 5, column 8 must be a 6.

2. Cross out Asterisk candidates

Even if a number in an Asterisk cell cannot be immediately placed, it creates safe exclusions. If a 4 is already in an Asterisk cell, no other Asterisk cell can also be a 4.

This exclusion applies in addition to row, column, and block constraints. A candidate must pass four tests: row, column, 3x3 block, and Asterisk region.

3. Combine normal Sudoku logic with Asterisk logic

The puzzle becomes especially strong when a cell has two possibilities according to normal Sudoku rules, but the Asterisk region eliminates one of them.

The empty Asterisk cell in row 5, column 8 is not guessed. It is clear because the Asterisk region already contains eight different numbers and is missing only a 6. Then, the 6 can also be eliminated from row 5, column 8, and the right middle 3x3 block.

Typical solving process

1. First, solve obvious normal Sudoku steps.
2. Then, check the Asterisk cells as their own nine-part region.
3. Note which numbers are already present in the Asterisk region.
4. Cross out these numbers from all other Asterisk cells.
5. If only one spot remains for a number in the Asterisk region, enter it.
6. Use each entry again for row, column, and 3x3 block.

Common mistakes

• Guess too early instead of using the additional rule as a safe exclusion.
• Only check rows and columns and overlook the special marking of the puzzle.
• Enter a number that fits locally but violates the special rule.
• Fail to update candidates after each new entry.
• Read a marking incorrectly or apply it to the wrong cells.

Tips for beginners

• Start like a normal Sudoku with well-filled rows, columns, and regions.
• Then check the special rule specifically. This often leads to early safe exclusions.
• Always think: Which numbers are truly allowed, and which are excluded by a rule?
• Enter a number only when it can be unambiguously derived.
• If stuck, change perspective: from rows to columns, from regions to the special rule, or from individual cells to candidates.

Asterisk Sudoku is especially good for practicing thinking in additional regions. The special rule is simple but creates many useful connections across the grid.