sudokUI › Sudoku techniques › Unique Rectangle Type 3
Unique Rectangle Type 3 in sudoku
A rectangle in exactly two boxes: two corners hold only X and Y, the others share a unit, and their extras and K other cells' candidates there total K+1 digits.
Why it works
Assuming the puzzle has exactly one solution, one corner takes an extra, or swapping X and Y would give a second solution. That corner and the K cells use up the K+1 digits, which are removed from that unit's remaining cells outside the rectangle.
How to spot it
When the two corners with extras share a unit, look there for cells whose candidates are all among those extras.
Worked example
Unique Rectangle Type 3: the roof extras of r3c4, r3c5, r7c4, r7c5 act as one pseudo-cell and form a locked set with r7c6, clearing those digits from the rest of the unit. So 6 is removed from r7c7.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Unique Rectangle Type 3 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 3, the puzzle's difficulty rating grows by 100. Its class is Hard. It is needed in 1 in 200 puzzles that sudokUI generates. How the rating works.
More uniqueness
BUG+1 · Unique Rectangle Type 1 · Unique Rectangle Type 2 · Unique Rectangle Type 4 · Unique Rectangle Type 5 · Unique Rectangle Type 6 · Hidden Rectangle · Avoidable Rectangle Type 1 · Avoidable Rectangle Type 2 · Extended Rectangle