Between Lines Sudoku: Rules and Solving Strategy

Understand the endpoint range

Between Lines Sudoku keeps the classic requirement that every row, column, and 3 by 3 box contains 1 through 9 once. A marked line has two special endpoint cells, often shown as circles or diamonds. Every cell between those endpoints along the line must contain a digit strictly between the endpoint values. If the endpoints are 2 and 8, interior cells may contain 3, 4, 5, 6, or 7. The endpoints may appear in either order, so 8 at one end and 2 at the other creates the same range. Strictly between means the interior cannot repeat either endpoint. The interior digits do not usually need to be ordered and may repeat only when ordinary Sudoku units allow it. Shapedoku uses symbols without numerical magnitude, so Between Lines is not part of its classic format. The variant still rewards the same habit of combining one added rule with rows, columns, and boxes.

Use line length to restrict endpoint gaps

A long line needs enough distinct available values between its endpoints, especially when several interior cells share a row, column, or box. If four interior cells all see one another, the endpoint gap must leave at least four different digits between them. Endpoints 3 and 7 allow only 4, 5, and 6, which is not enough for four mutually visible cells. Endpoints 2 and 8 allow five interior values and may work. Even when interior cells do not all share a unit, the candidate range still narrows them sharply. Extreme endpoint digits such as 1 and 9 create the widest range, while close endpoints may be impossible for anything longer than a short line. Before assigning exact digits, list the possible endpoint pairs that provide a large enough range. Then use the endpoints' own rows, columns, and boxes to remove pairs. A placed low endpoint may immediately force the other endpoint high, or vice versa.

Intersect ranges when lines and units overlap

Once the endpoints are partly known, apply the resulting range to every interior cell. Suppose one endpoint is 3 and the other can be 7, 8, or 9. An interior cell may initially take 4 through 8, but a crossing box may remove 7 and 8, leaving a much smaller set. Shared cells on two Between Lines must satisfy both ranges. If one line restricts a cell to 3 through 6 and another restricts it to 5 through 8, the shared cell can only be 5 or 6. That intersection may create a pair or single in its row. Interior placements also constrain the endpoints. If a line already contains an interior 8, one endpoint must be 9 and the other must be below 8. Update the logic in both directions rather than treating endpoints as the only source of information. Full Notes are useful on complex boards, but keep the active range visible so a locally legal digit does not violate the line.

1. Identify the two endpoints and every interior cell on each line.
2. List endpoint pairs that leave a wide enough numerical range.
3. Remove endpoint pairs that conflict with rows, columns, or boxes.
4. Restrict each interior cell to digits strictly between the endpoints.
5. Intersect the ranges of cells shared by multiple lines.
6. Use confirmed interior extremes to push one endpoint lower and the other higher.