Consecutive Sudoku – Hard

Consecutive Sudoku

Consecutive Sudoku is a variant of the classic 9x9 Sudoku where certain neighboring cells are marked as consecutive. Two numbers are consecutive if they differ by exactly 1, for example, 4 and 5 or 8 and 9.

The normal Sudoku rules still apply. Additionally, marks between two orthogonally adjacent cells indicate that the two numbers must be consecutive. In the usual form of this variant, the opposite also applies: if there is no mark between two neighboring cells, these two numbers cannot be consecutive.

Basic Rules

• 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.
• A mark between two adjacent cells means: The two numbers differ by exactly 1.
• In the standard complete Consecutive rule, if a mark is missing between two adjacent cells, consecutive numbers are excluded there.
• The numbers 1 and 9 are not consecutive.

Solving Strategies

1. Evaluate marked neighbors

If a cell is filled with 7 and its neighbor is connected by a Consecutive mark, the neighbor can only be 6 or 8.

In the following example, row 1, column 1 is marked with row 1, column 2. These two cells must therefore be consecutive.

Row 1, column 2 is next to 7. Because of the mark, it can only be 6 or 8. However, a 6 already exists in the same row. Therefore, 6 is excluded, and row 1, column 2 must be 8.

2. Consider unmarked neighbors

In complete Consecutive puzzles, the absence of a mark is also important. If there is no mark between two neighboring cells, they cannot contain numbers that differ by 1.

This means, for example: next to a 5 without a mark, 4 or 6 cannot be present. This negative information is often just as important as the visible marks.

3. Use edge numbers strategically

Numbers 1 and 9 each have only one consecutive neighbor. Next to a marked 1, only a 2 can be present. Next to a marked 9, only an 8 can be present. This often leads to quick, secure conclusions.

Typical solving process

1. Solve first using normal Sudoku steps in rows, columns, and blocks.
2. Then check marked neighbors with known numbers.
3. Reduce candidates to direct neighbors of known numbers.
4. Use missing marks as exclusions in fully marked scenarios.
5. Pay special attention to 1 and 9 since they have only one Consecutive neighbor each.
6. Update candidates after each new entry.

Common mistakes

• Relying too early on guessing rather than using the additional rule as a reliable exclusion.
• Only checking rows and columns and overlooking the special markings of the puzzle.
• Entering a number that, while locally fitting, violates the special rule.
• Not updating candidates after each new entry.
• Misreading a mark or applying it to the wrong cells.

Tips for beginners

• Start like a normal Sudoku with well-filled rows, columns, and regions.
• Then carefully check the special rule. These are often where early secure exclusions arise.
• Always ask yourself: Which numbers are truly allowed, and which are excluded by the rule?
• Enter a number only when it can be clearly derived.
• If stuck, change perspective: from rows to columns, from regions to the special rule, or from individual cells to candidates.

Consecutive Sudoku is particularly easy to solve when connections are not just viewed as additional information but as active exclusion tools. Every marked and unmarked neighbor can change candidates.