Empty Rectangle
The Empty Rectangle is a compact single-digit technique that pairs a special box formation with a strong link elsewhere. It's part of the Turbot Fish family, alongside the Skyscraper and 2-String Kite, and it's worth learning for the eliminations the others can't reach.
What is an Empty Rectangle?
Look at a box for one digit. Sometimes its candidates all lie within a single row and a single column of that box — the other four cells (the "empty rectangle") hold none. That means the digit in this box is either on that row or on that column. Combine it with a strong link (a two-cell line) for the same digit elsewhere, and you can eliminate the digit at the point where the box's line and the strong link's free end meet.
In the top-left box the 3 lies only on row 2 and column 2 (blue). With a strong link for 3 in column 8 (amber), the 3 is eliminated where the box's column meets the link's free end — the red cell.
Step by step
- Scan boxes for one digit. Find a box where its candidates share a single row and column.
- Find a strong link for the same digit — a line where it has exactly two homes.
- Locate the crossing point of the box's line and the link's far end.
- Eliminate the digit there.
Common mistakes
- Candidates outside the row/column. If any of the box's candidates for the digit fall outside the single row and column, there's no empty rectangle.
- Missing the strong link. The technique needs a genuine two-cell conjugate pair elsewhere to fire.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.