sudokUI › Sudoku techniques › Unique Rectangle Type 5
Unique Rectangle Type 5 in sudoku
A rectangle in exactly two boxes where one corner holds only X and Y and the other three each hold exactly X, Y and Z.
Why it works
If none of the three 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 other cells seeing all three.
How to spot it
Start from a bivalue cell and look for a rectangle whose other three corners each show the same pair plus one shared extra candidate.
Worked example
Unique Rectangle Type 5: one of r5c9, r8c8, r8c9 must be 5 to avoid the deadly pattern, so 5 is removed from cells seeing all of them. So 5 is removed from r9c9.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Unique Rectangle Type 5 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 5, the puzzle's difficulty rating grows by 100. Its class is Hard. It is needed in 1 in 16,000 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 6 · Hidden Rectangle · Avoidable Rectangle Type 1 · Avoidable Rectangle Type 2 · Extended Rectangle