Hidden Unique Rectangle
The Hidden Unique Rectangle is a sharper form of the unique rectangle. Both defend against the same deadly pattern — two digits sitting in four cells across two rows, two columns and two boxes, freely swappable and so giving two solutions. Where the plain version reads the pattern off naked candidates, the hidden version uses a strong link on the extra digit, letting you act even when the marks are less obvious.
The idea
Take a rectangle whose four corners all still hold the two "floor" digits, say 2 and 9. One corner also carries extra candidates; the diagonally opposite corner is a pure {2,9} cell. Look along the row and the column that join those two corners. If, in both of those units, the digit 9 appears in only the two rectangle cells — a strong link each way — then setting the {2,9} corner to 2 would force the deadly pattern. To avoid two solutions, that corner must be 9, not 2, and you place it.
A worked example
Corners r2c3, r2c8, r6c3, r6c8 all contain 2 and 9; r6c8 is a bare {2,9} cell while r2c3 carries extras. In column 8, 9 sits only in r2c8 and r6c8; in row 6, 9 sits only in r6c3 and r6c8. Both are strong links on 9 through the bare corner. If r6c8 were 2, the four cells would form the swappable 2/9 square. Since the puzzle is unique, r6c8 must be 9.
9 is confined to two cells in column 8 and in row 6 (solid) — two strong links meeting at the bare {2,9} corner. Making it 2 would complete the deadly 2/9 rectangle, so it is forced to 9.
Step by step
- Find the rectangle — four cells in two rows, two columns and two boxes sharing two floor digits.
- Pick the bare corner that holds only the two floor digits.
- Test the strong links — one floor digit must be confined to the rectangle in both the connecting row and column.
- Place the other digit in the bare corner to dodge the deadly pattern.
Common mistakes
- Weak links won't do. The digit must be truly confined to the two rectangle cells in each unit, not merely present there.
- Wrong corner. The forced placement is on the bare {floor,floor} corner, reached through the two strong links.
- Variant grids. As with all uniqueness logic, cages or diagonals can void the deadly-pattern assumption — keep it to standard grids.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.