## Rectangle Elimination

The Rectangle Elimination strategy can eliminate a single candidate in the corner of a rectangle.

### Credits

Rectangle Elimination was introduced on Andrew Stuart's Sudoku Wiki with credit to Ken Reek.

### Introduction

To use Rectangle Elimination, you must first find a row or column that contains exactly two of a given candidate, and the two cells are not in the same box. If the cells that you found are in the same row, then look in their columns for a cell that isn't in the same box and that has the same candidate. Similarly, if they are in the same column, then look in their rows for a cell that isn't in the same box and that has the same candidate. When you find such a cell, treat it as the third corner of a rectangle. Each of the three corners needs to be in a different box.

Now check what would happen in the box that contains the fourth corner if the other corners that it can see were both set to that candidate. If none of that candidate would remain anywhere in that box, you have found a contradiction. You can't remove the candidate from the row or column where it appears exactly twice, but you can remove it from the rectangle corner cell in the column or row where it appears more than twice.