sudokUI › Sudoku techniques › Empty Rectangle
Empty Rectangle in sudoku
Grouped Nice Loop · how it fits
A box's candidates for X lie only on one row and one column; a column (or row) conjugate pair outside the box has one end on that row (or column).
Why it works
With the end on the row, X in the box lies either on that row, making the other end X, or on the column; so any cell on that column outside the box that sees the other end loses X. Swap row and column otherwise.
How to spot it
Look for a box where four cells forming a rectangle have no candidate X, leaving X along both one row and one column.
Worked example
Empty Rectangle on 5: in box 1 every 5 lies on one row and one column, and r1c5, r6c5 are the only two places for 5 in their line. If r6c5 is 5, r6c2 in its row is not. If not, r1c5 is 5, so the box's 5 cannot share its row and must lie on the column through r6c2, which again is not 5. So 5 is removed from r6c2.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Empty Rectangle and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.
In a puzzle's rating
Each time the solver needs Empty Rectangle, the puzzle's difficulty rating grows by 120. Its class is Hard. It is needed in 1 in 32 puzzles that sudokUI generates. How the rating works.