Proven Sudoku
Techniques / Single-digit patterns
Empty Rectangle
Also called ER, Turbot Fish (box-based form), Hinge.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
In one box, all the homes for a digit sit in one row and one column. The box needs that digit somewhere. So it is in that row part or that column part. Team that up with a pair of homes elsewhere and you can rule the digit out.
The exact rule, for stronger players
The rule, stated exactly: For digit d and a box B, if the candidates of d in B all lie in one row and one column of B (leaving an empty rectangle of four cells), the intersection acts as a grouped node. Combined with a conjugate pair on d elsewhere, d is eliminated from the cell seeing both the far end of the pair and the relevant line of B.
What it removes: Remove d from the cell seeing both the conjugate partner and the grouped box node.
Why it works: Whichever of the row or column within B holds d, the box node is true as a group. That grouped node forms a strong link, and the rest is a length-four chain identical to the other Turbot forms.
Worked examples
These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.
Learn these first
- Turbot FishPick one digit.
- Locked Candidates (general form)Sometimes all the spots for a digit inside one group also sit inside a second group.
Related single-digit patterns
- Multi-ColoringColouring marks a digit's spots in two shades.
- Simple ColoringPick a digit.
- SkyscraperPick a digit.
- X-ColoringColouring with an extra step.
- 2-String KitePick a digit.
How often does it come up?
Our rough estimate: common, but frequently missed because the name describes the empty cells rather than the candidate cells.