Advanced methods and approaches for solving Sudoku puzzles

This thread is more general than the ALS examples in this puzzle. It is about finding weak links between cells which are not in the same house by means of ER boxes and using these cells in a pattern that can help solve the puzzle. Strong and intermediate links have frequently been used for this purpose, but in many cases a weak link is sufficient. In this puzzle the first ALS-XZ (marked with an asterisk) that I used is also an XYZ-Wing. The ER boxes 8 and 9. confirm that the 2's in r1c9 and r6c6 are peers. These same ER boxes also show that the 7 in r6c6 is a peer of the 7's in r13c9, which is necessary to make the cell elimination in r3c9. The cells in the second ALS-XZ are marked with ^. The 8's in r9c9 and r3c9 are peers because of ER box 9. These are combined into aa ALS 368. The 4's in r7c5 and r4c9 are also peers. because of the ER box 9. These are combined into an ALS 346. The restrictive common digit for these two ALS's is 3 and the common digit is 6. Therefore 6 can be eliminated from r9c5, and 6 must be in r7c5 and r8c1. The other eliminations that I made are beyond the scope of this post.

Code: Select all
|-----------------+-----------------+-----------------|
|  79    8    5   |   1    3    4   |  29   67* 267*  |
|   3    6    2   |  89    7   89   |   4    1    5   |
|  79    4    1   |   2    5    6   |  89   37  3-78^ |
|-----------------+-----------------+-----------------|
|   5    2    8   |   6    9    1   |   7   34   34^  |
|   4    9    7   |   3    8    5   |   6    2    1   |
|   1    3    6   |  47   24   27*  |   5    8    9   |
|-----------------+-----------------+-----------------|
|   2    5  349   | 4789  46^ 3789  |   1  467  4678  |
|  68    7   49   | 489    1  289   |   3    5  2468  |
|  68^   1   34   |   5  24-6 2378  |  28    9  24678 |
|-----------------+-----------------+-----------------|

The original puzzle is Sudoku9981 Extreme Book20 #2.
Bud

Posts: 56
Joined: 24 August 2008

### Re: 2 ER-Linked ALS-XZ Example

Bud wrote:This thread is more general than the ALS examples in this puzzle. It is about finding weak links between cells which are not in the same house by means of ER boxes and using these cells in a pattern that can help solve the puzzle. Strong and intermediate links have frequently been used for this purpose, but in many cases a weak link is sufficient. In this puzzle the first ALS-XZ (marked with an asterisk) that I used is also an XYZ-Wing. The ER boxes 8 and 9. confirm that the 2's in r1c9 and r6c6 are peers. These same ER boxes also show that the 7 in r6c6 is a peer of the 7's in r13c9, which is necessary to make the cell elimination in r3c9. The cells in the second ALS-XZ are marked with ^. The 8's in r9c9 and r3c9 are peers because of ER box 9. These are combined into aa ALS 368. The 4's in r7c5 and r4c9 are also peers. because of the ER box 9. These are combined into an ALS 346. The restrictive common digit for these two ALS's is 3 and the common digit is 6. Therefore 6 can be eliminated from r9c5, and 6 must be in r7c5 and r8c1. The other eliminations that I made are beyond the scope of this post.

Code: Select all
|-----------------+-----------------+-----------------|
|  79    8    5   |   1    3    4   |  29   67* 267*  |
|   3    6    2   |  89    7   89   |   4    1    5   |
|  79    4    1   |   2    5    6   |  89   37  3-78^ |
|-----------------+-----------------+-----------------|
|   5    2    8   |   6    9    1   |   7   34   34^  |
|   4    9    7   |   3    8    5   |   6    2    1   |
|   1    3    6   |  47   24   27*  |   5    8    9   |
|-----------------+-----------------+-----------------|
|   2    5  349   | 4789  46^ 3789  |   1  467  4678  |
|  68    7   49   | 489    1  289   |   3    5  2468  |
|  68^   1   34   |   5  24-6 2378  |  28    9  24678 |
|-----------------+-----------------+-----------------|

The original puzzle is Sudoku9981 Extreme Book20 #2.

Bud, a very fine set of moves.
aran

Posts: 334
Joined: 02 March 2007