Dutch Whispers Sudoku: How to Solve Lines That Jump by Four
Dutch Whispers Sudoku adds orange lines to an ordinary Sudoku grid. Any two digits that sit next to each other along a line must differ by at least 4. A 1 can sit beside 5, 6, 7, 8 or 9. A 5 can only sit beside 1 or 9.
The rule at a glance:
- Neighbours along an orange line differ by 4 or more.
- 5 can appear on a Dutch Whispers line, but only next to 1 or 9.
- 4 and 6 can never be neighbours on the line.
- Apart from 5, the digits alternate between low (1–4) and high (6–9).
- 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.
How Dutch Whispers differs from German Whispers
German Whispers asks for a gap of 5. Dutch Whispers asks for 4. With the smaller gap a 5 becomes possible, since 1 and 9 are both four away from it, and pairs exactly four apart, like 6 and 2 or 9 and 5, become legal. Every digit ends up with one more partner than it has on a German line.
| Digit | Neighbours on a Dutch line | On a German line |
|---|---|---|
| 1 | 5, 6, 7, 8, 9 | 6, 7, 8, 9 |
| 2 | 6, 7, 8, 9 | 7, 8, 9 |
| 3 | 7, 8, 9 | 8, 9 |
| 4 | 8, 9 | 9 |
| 5 | 1, 9 | none |
| 6 | 1, 2 | 1 |
| 7 | 1, 2, 3 | 1, 2 |
| 8 | 1, 2, 3, 4 | 1, 2, 3 |
| 9 | 1, 2, 3, 4, 5 | 1, 2, 3, 4 |
The middle of the table is still the tight part. Every neighbour of a 5 must be a 1 or a 9, and a 4 or a 6 has two options instead of one.
Low and high still alternate, except around 5
Two low digits (1–4) are at most 3 apart, and so are two high digits (6–9), so neither pair can sit side by side. Read a Dutch line from one end and the digits swing high, low, high, low, the same as on a German line.
The exception is 5. It sits between the two halves, and its neighbours are 1 or 9, so a line can read 1, 5, 9 or 9, 5, 1 and break the pattern for one cell. When a cell on a Dutch line could be 5, check whether each of its neighbours on the line can still be a 1 or a 9. Often one of them can’t, and the 5 goes.
Start beside a given digit
A given digit on the line is the best place to begin, because every candidate next to it has to be four or more away from it.
Take the empty cell diagonally beside the given 2. Its row, column and box leave 5 or 8. A 5 would be only three away from the 2, so the cell is 8.
The same 2 has a second neighbour on the line. With the 8 now in its row, Sudoku leaves that cell 5 or 6, and the line removes the 5 for the same reason. The cell is 6, a pair a German line would never allow.
Try it
The practice board has two four-cell lines. One is the line from the examples above; the other starts from a given 3. A digit may appear twice on one line, as long as the two cells share no row, column or box.
Where to go next
German Whispers is the stricter version of the same line, and most of what works here works there. Renban draws a line through cells too, but asks for digits that sit close together as a set.
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.