sudokUI › Sudoku techniques › Unique Rectangle Type 2
Unique Rectangle Type 2 in sudoku
A rectangle in exactly two boxes where two corners hold only X and Y and the other two each hold exactly X, Y and Z.
Why it works
If neither corner were Z, the rectangle would hold only X and Y, and swapping them would give a second solution. Assuming the puzzle has exactly one solution, at least one is Z, so Z is removed from every other cell that sees both.
How to spot it
Find two bivalue cells with the same pair on a rectangle, then check whether both remaining corners add the same single extra candidate.
Worked example
Unique Rectangle Type 2: to avoid the deadly pattern on 4/7, one of r5c4/r6c4 must be 6, so 6 is removed from cells seeing both. So 6 is removed from r4c4.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Unique Rectangle Type 2 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 2, the puzzle's difficulty rating grows by 100. Its class is Hard. It is needed in 1 in 330 puzzles that sudokUI generates. How the rating works.
More uniqueness
BUG+1 · Unique Rectangle Type 1 · Unique Rectangle Type 3 · Unique Rectangle Type 4 · Unique Rectangle Type 5 · Unique Rectangle Type 6 · Hidden Rectangle · Avoidable Rectangle Type 1 · Avoidable Rectangle Type 2 · Extended Rectangle