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Empty rectangle

A box where a digit forms an L, paired with a strong link outside.

An empty rectangle is a configuration inside a box where the candidate cells for a digit all lie on a single row and a single column within the box — forming an L (or +) shape. The remaining four 'off-axis' cells of the box have no candidate for the digit.

By itself, the pattern says: within this box, the digit will appear either somewhere on this row or somewhere on this column. Combined with a strong link elsewhere (a row or column where the digit has exactly two candidates, one of them lining up with the L), it pinches a specific cell where the digit can be removed.

When to look for it

Empty rectangles are pretty common in advanced puzzles. Scan each box for an L-shape and then look for strong links in lines outside it.

How to apply it

  1. Find a box where a digit's candidates all lie on one row + one column inside the box.
  2. Look for a strong link in a row or column elsewhere that pairs with the empty rectangle.
  3. The intersection of the other end of the strong link with the empty rectangle's axis gives the elimination.

Example

2
Box 2's 2-candidates form an L. The strong link in column 1 forces a single elimination.