sudokUI › Sudoku techniques › Unique Rectangle Type 1
Unique Rectangle Type 1 in sudoku
Four cells forming a rectangle in exactly two boxes, where three hold only X and Y and the fourth holds X, Y and at least one other candidate.
Why it works
If the fourth cell were X or Y, the four cells would hold only X and Y, and swapping them would give a second solution. Assuming the puzzle has exactly one solution, X and Y are removed from the fourth cell.
How to spot it
Look for three bivalue cells with the same two candidates on three corners of a rectangle that lies in exactly two boxes.
Worked example
Unique Rectangle Type 1: r4c1, r4c8, r5c1, r5c8 would form a deadly pattern on 5/8; r4c8 cannot be 5 or 8.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Unique Rectangle Type 1 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 1, the puzzle's difficulty rating grows by 100. Its class is Hard. It is needed in 1 in 76 puzzles that sudokUI generates. How the rating works.
More uniqueness
BUG+1 · Unique Rectangle Type 2 · 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