Better Almost-XY-Wing Example

Advanced methods and approaches for solving Sudoku puzzles

Better Almost-XY-Wing Example

Postby Bud » Sat Nov 29, 2008 9:35 am

This is a better example of the Almost-XY-Wing Pattern since it is the only advanced technique I used to solve the puzzle. I am adopting the name Almost-XY-Wing to resolve the question of whether this should be considered an example of a 3 ALS-XY-Wing or a 2 ALS-XZ. This is almost as eay to spot as an XY-Wing if you consider it the former, which I am going to identify it as. The pivot r1c5 is an ALS which contains both restricted common digits 35. The second ALS is r7c5 and contains 58. where 8 is the common digit. If a cell with condidates 58 were present in box 2, this would be a XY-Wing, but again the ALS 568 in r12c4 is just as good. This eliminates 8 from c4b8 and the puzzle is solved using basic techniques.

Almost-XY-Wing Example
Code: Select all
 |------------------+-------------------+-----------------|
 |   7    49  349   |  56    35     1   |   8  569    2   |
 |   1     2   39   | 568     4   3568  |   7  569   59   |
 |  56    56    8   |   9     2     7   |   3    1    4   |
 |------------------+-------------------+-----------------|
 | 45689 45689  2   |  47     1   568   | 569    3   78   |
 |   3   4568   1   |  47     9     2   |  56   45   78   |
 | 45689   7   49   |   3    58   568   |   2  459    1   |
 |------------------+-------------------+-----------------|
 |   2   1489   5   |  1-8   38   389   | 149    7    6   |
 |  89     3    7   | 15=8    6     4   | 159    2   59   |
 |  49   149    6   |   2     7    59   | 1459   8    3   |
 |------------------+-------------------+-----------------|


The puzzle is Sudoku9981 Expert Book 33 #8.
Bud
 
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Re: Better Almost-XY-Wing Example

Postby tarek » Sat Nov 29, 2008 10:14 am

Bud wrote:I am adopting the name Almost-XY-Wing to resolve the question of whether this should be considered an example of a 3 ALS-XY-Wing or a 2 ALS-XZ.

I can understand that these cases are easier to spot. I will not support the Almost xy wing name though.

There is so much talk about ALMOSTING in other threads that signify something other than that what you are after.

It is also worth noting that an XY wing can be considered the most basic example of an ALS XY rule & the ALS XZ rule.

tarek
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Re: Better Almost-XY-Wing Example

Postby aran » Sat Nov 29, 2008 12:54 pm

Bud wrote:This is a better example of the Almost-XY-Wing Pattern since it is the only advanced technique I used to solve the puzzle. I am adopting the name Almost-XY-Wing to resolve the question of whether this should be considered an example of a 3 ALS-XY-Wing or a 2 ALS-XZ. This is almost as eay to spot as an XY-Wing if you consider it the former, which I am going to identify it as. The pivot r1c5 is an ALS which contains both restricted common digits 35. The second ALS is r7c5 and contains 58. where 8 is the common digit. If a cell with condidates 58 were present in box 2, this would be a XY-Wing, but again the ALS 568 in r12c4 is just as good. This eliminates 8 from c4b8 and the puzzle is solved using basic techniques.

Almost-XY-Wing Example
Code: Select all
 |------------------+-------------------+-----------------|
 |   7    49  349   |  56    35     1   |   8  569    2   |
 |   1     2   39   | 568     4   3568  |   7  569   59   |
 |  56    56    8   |   9     2     7   |   3    1    4   |
 |------------------+-------------------+-----------------|
 | 45689 45689  2   |  47     1   568   | 569    3   78   |
 |   3   4568   1   |  47     9     2   |  56   45   78   |
 | 45689   7   49   |   3    58   568   |   2  459    1   |
 |------------------+-------------------+-----------------|
 |   2   1489   5   |  1-8   38   389   | 149    7    6   |
 |  89     3    7   | 15=8    6     4   | 159    2   59   |
 |  49   149    6   |   2     7    59   | 1459   8    3   |
 |------------------+-------------------+-----------------|

The puzzle is Sudoku9981 Expert Book 33 #8.

Bud, just for interest :
568(r1c45+r2c4)=3r1c5-(3=8)r7c5 =><8>r78c4
aran
 
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Postby daj95376 » Sat Nov 29, 2008 2:55 pm

Bud, My memory is swiss cheese anymore ... and getting worse. For instance, I can't remember the last time you presented an advanced technique after exhausting lesser techniques first. I'm sorry for my bad memory!
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