sudokUI › Sudoku techniques › Hidden Rectangle
Hidden Rectangle in sudoku
A rectangle in exactly two boxes with X and Y in every corner, one holding nothing else, and X confined to rectangle corners in the opposite corner's row and column.
Why it works
If the opposite corner were Y, X would be forced into the two neighbouring corners and Y into the bivalue cell, letting X and Y swap for a second solution. Assuming the puzzle has exactly one solution, Y is removed from the opposite corner.
How to spot it
From a bivalue cell, check the opposite corner: one of the two digits must form a conjugate pair in both that corner's row and column.
Worked example
Hidden Rectangle: r9c6 holds only 35, and 5 is confined to the rectangle in r6c5's row and column; r6c5 cannot be 3 or the deadly pattern appears.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Hidden Rectangle 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 Hidden Rectangle, the puzzle's difficulty rating grows by 100. Its class is Hard. It is needed in 1 in 29 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 · Unique Rectangle Type 6 · Avoidable Rectangle Type 1 · Avoidable Rectangle Type 2 · Extended Rectangle