Empty Rectangle
A box where a digit's candidates lie entirely along one row or one column, plus a strong link on that digit elsewhere, force an elimination on the intersection cell.
Advanced sudoku technique
What it is
An Empty Rectangle (ER) is a 3×3 box where digit X's candidates are confined to exactly ONE row OR ONE column inside the box — the rest of the box has no X candidates. (The 'rectangle' is the empty 2×3 or 3×2 region inside the box that DOESN'T hold any X.) Combine the ER with a strong link on X somewhere else: a row or column outside the box where X fits in only two cells, and one of those cells sits in the ER's column-of-confinement (or row-of-confinement). The chain: that strong-link cell is X, or the other end of the strong link is X. Either way, the elimination cell — the intersection of the strong link's outer end with the ER's confinement axis — drops X.
When to use it
On master and evil-tier puzzles. Spot it by scanning each box for a digit whose candidates form a single-row or single-column strip.
Worked example
In box 5, digit 2's candidates all lie in column 5 (inside the box). In row 3, digit 2 has strong link R3C5↔R3C8. If R3C5 = 2, box 5's column-5 strip can't hold 2 anywhere — but box 5 must contain 2 somewhere, contradiction. If R3C8 = 2 instead, the chain forces box 5's 2 to be in column 5. Either way, R3C8's column drops 2 in any cell that sees both the ER and R3C8.
Try it
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