Empty Rectangle
A box where a digit's candidates form a cross rather than a rectangle, combined with a strong link elsewhere.
What it is
An Empty Rectangle describes a box in which a digit's candidates all lie in one row and one column of the box, leaving a 2×2 corner empty. That shape means the digit in the box lies either on that row or on that column. Combined with a line elsewhere where the digit has exactly two candidates, this forces an elimination at the intersection point.
How to spot it
Scan boxes for a digit whose candidates avoid one 2×2 corner entirely, so they form an L or cross shape. Then find a row or column outside the box where the digit has exactly two candidates, one of which aligns with the box's row or column. The elimination sits where the remaining candidate's line crosses the box's other line.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 4/7, 4/8, 5/8, 9/6, 9/8
- Digits
- 7
- Eliminations
- 4/6
Press a marked square to point it out on the board above.
Why it matters
The Empty Rectangle is the most flexible of the single-digit techniques because the box pattern is common. It is harder to see than a Skyscraper, but it applies in positions where nothing simpler does.
Frequently asked questions
What exactly is empty about it?
One 2×2 corner of the box contains no candidates for the digit. The remaining candidates form a cross of one row and one column, which is the shape the technique needs.
Is this related to the Skyscraper?
Yes. All three — Skyscraper, Two-String Kite and Empty Rectangle — are short single-digit chains. They differ only in how the two strong links are arranged.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
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