sudokUI › Sudoku techniques › Unique Rectangle Type 6
Unique Rectangle Type 6 in sudoku
A rectangle in exactly two boxes: two opposite corners hold only X and Y, the others hold extras too, and its two rows, or two columns, have no other X.
Why it works
If a corner with extras were X, the rest of the rectangle would be forced into X and Y only, and swapping them would give a second solution. Assuming the puzzle has exactly one solution, X is removed from both corners with extras.
How to spot it
With bivalue corners on a diagonal, check whether X or Y forms a conjugate pair inside the rectangle in both rows or both columns.
Worked example
Unique Rectangle Type 6: 6 is confined to the rectangle in both rows; placing it in a roof corner would force the deadly pattern, so 6 is removed from r5c9, r6c6.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Unique Rectangle Type 6 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 Unique Rectangle Type 6, the puzzle's difficulty rating grows by 100. Its class is Hard. It is needed in 1 in 300 puzzles that sudokUI generates. How the rating works.
More uniqueness
BUG+1 · Unique Rectangle Type 1 · Unique Rectangle Type 2 · Unique Rectangle Type 3 · Unique Rectangle Type 4 · Unique Rectangle Type 5 · Hidden Rectangle · Avoidable Rectangle Type 1 · Avoidable Rectangle Type 2 · Extended Rectangle