Consecutive Sudoku: Rules and Solving Strategy

Consecutive Sudoku links orthogonal neighbors that differ by one

Consecutive Sudoku uses the normal rule that every row, column, and 3x3 box contains 1 through 9 exactly once. Marks placed between orthogonally adjacent cells indicate that the two digits are consecutive, meaning their difference is exactly 1. A marked pair could therefore be 1 and 2, 2 and 3, 3 and 4, and so on, in either order. Many Consecutive Sudoku puzzles also use a negative constraint: every consecutive orthogonal pair is marked, so an unmarked border means the two cells are not consecutive. Always read the puzzle instructions to confirm whether that negative rule is active, because some setters mark only selected consecutive pairs. Start by translating each mark into a short candidate relationship. If one cell is 6, its marked neighbor must be 5 or 7. If the neighbor's row already contains 7, it is forced to 5. If an unmarked edge is subject to the negative rule, a placed 6 removes 5 and 7 from the touching cell instead.

Use chains of marks to restrict ranges

Several consecutive clues in a row can be much stronger than one isolated mark. If three cells form a chain of two consecutive marks, the values must step by one at each link, although the direction can change. Candidate ranges become useful. Suppose the middle cell is limited by Sudoku to 2 or 8. Its two marked neighbors must come from 1 or 3 when the middle is 2, or 7 or 9 when the middle is 8. Crossing row and box restrictions may eliminate one whole branch. End digits are especially informative because 1 has only one consecutive partner, 2, and 9 has only one, 8. A marked neighbor of a solved 1 or 9 is therefore immediate. Under a negative constraint, the same edge digits create clean exclusions: an unmarked neighbor of 1 cannot be 2, and an unmarked neighbor of 9 cannot be 8. Keep candidate support precise. Do not remove 5 from a cell merely because its marked partner could be 4; remove it only if every allowed value in the partner cell would make the pair impossible.

Blend Consecutive Sudoku with classic techniques

The extra adjacency rule is most useful when it creates ordinary Sudoku patterns. A consecutive mark may reduce a cell from three candidates to two, forming a naked pair with another cell in the same box. A negative edge may remove the last position for a digit in a row and create a hidden single. After every placement, update four kinds of information: the row, the column, the box, and all orthogonal adjacency relationships. Central cells can affect up to four neighbors, so they often produce larger cascades than edge cells. Full Notes are worthwhile on harder puzzles because every local change can alter several candidate sets. Shapedoku does not use numerical adjacency, since its nine glowing shapes have no numerical order, but the candidate discipline transfers perfectly. Make one justified elimination, clean the nearby Notes, and immediately look for the simpler classic consequence. This keeps Consecutive Sudoku from feeling like two puzzles layered together. The extra rule is not a separate stage; it is another source of eliminations feeding the same candidate map.

1. Apply classic row, column, and box eliminations first.
2. For every marked edge, restrict the two cells to values that differ by exactly one.
3. Confirm whether unmarked edges also mean non-consecutive before using negative clues.
4. Use 1 and 9 aggressively because each has only one possible consecutive partner.
5. Track chains of several marked cells as candidate ranges rather than guessing an order.
6. After each adjacency deduction, rescan for singles, pairs, and locked candidates.