Renban Sudoku: Rules and Solving Strategy

Understand consecutive sets without fixed order

Renban Sudoku follows the normal rule that every row, column, and 3x3 box contains the digits 1 through 9 once. Colored or outlined Renban lines add another condition: the digits on each line form one consecutive set with no repeats. A four-cell line might contain 2, 3, 4, and 5 in any order, or 5, 6, 7, and 8 in any order. It cannot contain 2, 3, 5, and 6 because the set has a gap. Unlike Thermo Sudoku, Renban digits do not need to rise from one end to the other. Position alone tells you nothing about which value is larger. If two line cells share a row, column, or box, the ordinary no-repeat rule also applies, but the Renban rule already requires distinct digits across the entire line. Shapedoku uses shapes without numerical order, so it does not include Renban lines. Classic candidate discipline still transfers cleanly between the games.

List the possible ranges from the line length

A line of length N can use only consecutive ranges of N digits. For a four-cell line, the possible sets are 1 to 4, 2 to 5, 3 to 6, 4 to 7, 5 to 8, and 6 to 9. If one cell is already 8, only ranges containing 8 survive: 5 to 8 or 6 to 9. Every other cell on the line can then be restricted to the union of those ranges, which removes 1 through 4 immediately. If another cell cannot contain 9 because of its column, the 6 to 9 range may still survive because 9 could occupy a different line cell. Eliminate a whole range only when some required digit has no possible position anywhere on the line. This distinction matters. Renban solving is about complete sets, not simply giving every cell a local interval. Track the surviving ranges beside the line and update them whenever a candidate disappears.

Use endpoints, overlaps, and shared units

Long lines are naturally restrictive because they have fewer possible ranges. A seven-cell Renban can be only 1 to 7, 2 to 8, or 3 to 9. If it contains a confirmed 1, the entire set becomes 1 to 7 and digits 8 and 9 can be removed from every other line cell. Overlapping Renban lines can also control shared cells. If a shared cell belongs to one line restricted to 1 through 4 and another restricted to 4 through 7, that cell must be 4. Lines passing through one box may create hidden subsets because their required range digits must fit into a limited collection of box cells. After fixing a range, do not place its digits arbitrarily. Use classic rows, columns, and boxes to decide their order. On a difficult puzzle, write full candidates and mark the active range separately. A candidate can belong to the range but still be impossible in one particular cell because of a crossing unit.

1. Count the cells on each Renban line.
2. List every consecutive range of that length from 1 through 9.
3. Remove ranges that exclude a confirmed line digit.
4. Remove a range when one of its required digits has no legal line position.
5. Intersect ranges when a cell belongs to more than one line.
6. Use ordinary Sudoku logic to place the surviving range digits in their exact cells.