From Sudopedia, the free Sudoku reference guide

From Sudopedia

The Empty Rectangle is a single-digit solving technique which uses the absence of candidates to perform an elimination.

An alternative term is hinge, which was actually coined before the term Empty Rectangle, but to a smaller audience. The acronym ER is used by many players.

How it works

Take a look at this diagram:

.-------.-------.-------.
| . . . | . . . | . . . |
| - A - | - - - | - B - |
| . . . | . . . | . . . |
:-------+-------+-------:
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
:-------+-------+-------:
| . . . | . . . | - X - |
| . * . | . . . | X . X |
| . . . | . . . | - X - |
'-------'-------'-------'

Row 2 has a strong linked pair of candidates in cells A and B. Call that candidate x. Box 9 has all candidates x confined to 1 boxcol and 1 boxrow. The 4 cells without candidate x form the Empty Rectangle (marked with a dash). When x is true in A, x is false in r8c2. When x is false in A, it is true in B, and hence the remaining candidates x in box 9 are confined to row 8, causing x to be false in r8c2. Thus x can never be true in r8c2, and so can be eliminated from r8c2.

This technique is a special case of Grouped Turbot Fish.

See Also

• 2-String Kite