German Whispers Sudoku: How to Solve Lines That Jump by Five
German Whispers Sudoku adds green lines to an ordinary Sudoku grid. Any two digits that sit next to each other along a line must differ by at least 5. A 1 can sit beside a 6, 7, 8 or 9. A 4 can only sit beside a 9.
The rule at a glance:
- Neighbours along a green line differ by 5 or more.
- 5 can never appear on a German Whispers line.
- The digits alternate between low (1–4) and high (6–9) as you follow the line.
- 4 can only sit beside 9, and 6 can only sit beside 1.
- Two cells on the same line that are not neighbours on it are not restricted by the line. Only the next cell along it counts.
In Sudoku Fog the lines can step diagonally as well as sideways, and the normal Sudoku rules still apply to every cell.
Why 5 is missing and the line swings high and low
A 5 would need a neighbour at least five away from it. That means 0 or 10, and neither exists, so no cell on a German line can hold a 5.
The same arithmetic splits the rest of the digits in two. A low digit (1–4) can only reach a high one (6–9), and a high digit can only reach a low one. Read any German line from one end and the digits go high, low, high, low, or low, high, low, high, without exception.
The digits near 5 have the fewest partners
How far a digit sits from 5 decides how many neighbours it can have:
| Digit | Possible neighbours on the line |
|---|---|
| 1 | 6, 7, 8, 9 |
| 2 | 7, 8, 9 |
| 3 | 8, 9 |
| 4 | 9 |
| 6 | 1 |
| 7 | 1, 2 |
| 8 | 1, 2, 3 |
| 9 | 1, 2, 3, 4 |
The digits far from 5 have plenty of partners and the ones next to it have only one. A 4 in the middle of a line needs a 9 on both sides, which only works if those two cells share no row, column or box.
That tightness is where the line does its work. On the first line, the cell beside the given 3 is a plain Sudoku single, 8. The cell on the 8’s other side has three Sudoku candidates, 3, 4 and 5, and the line rejects two of them.
Each digit on the line narrows the next cell
On most cells the line will not name a digit outright. It cuts the candidates down, and the row, column and box do the rest. Every digit you place on the line then starts the same work on its neighbour.
The 3 you just placed has an empty cell on its other side. Its row also holds an 8 by now, because the cell beside the given 1 on the second line is a Sudoku single. That leaves 6 or 9. A 6 is only three away from the 3.
Try it
The practice board has two four-cell lines. Start near the given 3 and follow the line from there: each digit you place narrows the next cell.
Where to go next
Renban also draws a line through cells, but asks for the opposite: digits that sit close together as a set. Kropki marks single pairs of cells instead of a whole line, and Sudoku Fog pairs it with German Whispers in one of its mixed variants.
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.