Renban Sudoku: How to Solve Consecutive Runs
A Renban Sudoku draws a coloured line through several cells. The digits on that line form a run of consecutive numbers, in any order.
A three-cell line might therefore contain 2, 3, and 4. It could appear as 4, 2, 3 or in any other order. The line does not make an ascending path. It only names the set of values that must appear on it.
The line names a set, not a direction
The length of a Renban line tells you the size of its run. A three-cell line must contain one of 1–3 through 7–9. The line may turn a corner, but it never asks the digits to rise as you follow it.
Here the highlighted line reads 6, 8, 7 as it travels around the corner. It is still a valid 6–7–8 run. The coloured path says those three digits belong together; it does not say where each member belongs.
Let known members choose the run
The other line on this board already has a 3 and a 5. For a three-cell Renban, there is only one consecutive set that contains both: 3, 4, 5. The remaining cell is therefore 4.
Use ordinary Sudoku to choose positions
Once a line has narrowed to a set, put those candidates only where the ordinary grid allows them. A row, column, or box can remove one member from a cell, and that restriction travels along the Renban line. The line gives membership; ordinary Sudoku gives position.
Try it
The practice board uses the same two three-cell lines. Watch for a line with two known members, then use its consecutive set before making ordinary Sudoku placements.
Where to go next
Arrow also marks a line of cells, but asks for an exact sum rather than a consecutive set. Thermometer uses a path in the other direction: its digits must rise from bulb to tip.
If you want the version where most of the grid is hidden while you solve, fog of war Sudoku is that. Everything published so far is on the Learn index.
Sudoku Fog is on Android — What Sudoku Fog is, Get it on Google Play.