2006 August 25 Nightmare

[unkx80]

Hi, this is my first post in any sudoku forum. Please pardon me if I breached any etiquette rules or whatsoever. =)

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

After applying some easy techniques (naked single, hidden single, naked subset, pointing pair/triple), my solver arrived at:

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   |
'---------------------'---------------------'---------------------'

The empty rectangle for digit 3, marked with *, allows the removal of the possible value 3 at the # square. Then the rest is just naked singles and hidden singles.

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! =)

[Ruud]

Hi, welcome aboard!

Sometimes you will find a sudoku that allows you to bypass a whole series of tricks with incremental difficulty and solve it in a single blow. I am trying to avoid these in my Nightmare series, but occasionaly one slips trough the net.

For the Benchmark, the puzzle should have no alternatives. There are a few coloring alternatives for this ER step.

Ruud