Sudoku Players' Forum (clone)

Sukaku Explainer wrote:Unique Rectangle type 3 (with Naked Pair)
The cells r1c7,r3c7,r3c3,r1c3 form a Unique Rectangle with the values 8 and 9. There are exactly two ways of placing the values 8 and 9 in the cells of the Unique Rectangle, forming two possible configurations. In both configurations, each row, column or block touched by the Unique Rectangle contains each of the two values 8 and 9 exactly once. As a result, if one of these two configurations were part of the solution, it could then be replaced by the other one to get a second valid solution.
Because a valid sudoku cannot have more than one solution, none of the two configurations of the Unique Rectangle can be valid. This implies that either r3c3 or r1c3 contains one of the values 2 or 7. It follows that either r3c3 or r1c3 forms a Naked Pair with r2c3 on the values 2 and 7 in the block.

Code: Select all

*-------------------------------------------------*
| 3    1468-2  #89+2   | 125 46  2456  |#89 14 7  |
| 146  146-27  *27     | 9   8   2467  | 5  14 3  |
| 1489 5       #89+7   | 13  347 47    |#89 2  6  |
|----------------------+---------------+----------|
| 2    3        1      | 4   79  79    | 6  8  5  |
| 7    9        6      | 8   5   1     | 2  3  4  |
| 458  48       58     | 6   2   3     | 7  9  1  |
|----------------------+---------------+----------|
| 568  268      4      | 235 36  2568  | 1  7  9  |
| 689  268      3      | 7   1   2689  | 4  5  28 |
| 1589 1278     589-27 | 25  49  24589 | 3  6  28 |
*-------------------------------------------------*