I have been programming a (not very powerful) solver and I just added empty rectangles into the list of rules used. Sometimes I will randomly select nightmares to have an idea how many hard sudokus my solver can solve. Currently some nightmares cannot be solved by my solver and most require application of several advanced rules. However, by using one empty rectangle, I think the 2006 August 25 nightmare can be solved quite easily.
Starting from:
Code: Select all
000900001800001760030007002090002006000000000600300050700800090062500004100004000
Code: Select all
.---------------------.---------------------.---------------------.
| 245 7 6 | 9 23458 358 | 345 348 1 |
| 8 245 459 | 24 *2345 1 | 7 6 *39 |
| 459 3 1 | 46 4568 7 | 459 48 2 |
:---------------------+---------------------+---------------------:
| 345 9 34578 | 147 4578 2 | 34 1347 6 |
| 2345 12458 34578 | 1467 456789 589 | 349 12347 3789 |
| 6 12 478 | 3 4789 89 | 12 5 789 |
:---------------------+---------------------+---------------------:
| 7 45 345 | 8 12 6 | 12 9 *35 |
| 39 6 2 | 5 17 39 | 8 17 4 |
| 1 58 3589 | 27 #39 4 | 6 *237 *357 |
'---------------------'---------------------'---------------------'
Incidentally, I saw the Benchmark Sudoku List (http://www.sudoku.com/forums/viewtopic.php?t=3834) by Ruud. Perhaps this example can be added into this benchmark list as an example of empty rectangles.
Please correct me if I am wrong. Thanks! =)