can somone please explain this to me better

Advanced methods and approaches for solving Sudoku puzzles

can somone please explain this to me better

Postby Kunegochu » Wed Jan 23, 2008 8:42 am

i am really confused about the methods of solving the more complicted sudokus i only can solve the sudokus that use cross hatching and other easy methods but i dont get how x wing and other more difficult ways work i have looked on the internet but all the explantions are confusing... can somone please explain in a way that i can understand?
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Postby Pat » Wed Jan 23, 2008 10:10 am

Kunegochu wrote:i am really confused about the methods of solving the more complicted sudokus

i only can solve the sudokus that use cross hatching and other easy methods
but i dont get how x wing and other more difficult ways work

i have looked on the internet
but all the explantions are confusing...

can somone please explain in a way that i can understand?

    hi Kunegochu

    X-wing is explained here
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Can someone please explain this to me better

Postby Cec » Wed Jan 23, 2008 11:40 pm

Hi Kunegochu,

Notwithstanding various descriptions of the X-Wing pattern throughout the forum I too had trouble understanding this technique. Thanks to another member whose name I've misplaced, I came across the following explanation which helped me considerably.

The X-Wing pattern requires a particular candidate to appear twice and only twice either in two rows and sharing the same two columns in which case the eventual exclusions of an identical candidate occur in these same two columns or, using the same logic, where a particular candidate appears twice and only twice in two columns and sharing the same two rows then the exclusions occur in rows.

In the following grid, the 3's form an X-Wing pattern in rows 6 and 9, columns 3 and 8 (these cells are marked with an asterisk). Under the above definition, this enables the remaining 3's in columns 3 and 8 to be excluded from the cells marked (A)

Code: Select all
 *--------------------------------------------------------------------*
 | 13     8      49     | 7      135    15     | 49     6      2      |
 | 136    39  (A)13469  | 13     2      8      | 459    7      59     |
 | 7      5      2      | 49     49     6      | 3      1      8      |
 |----------------------+----------------------+----------------------|
 | 4      139    8      | 19     6      7      | 59     2      359    |
 | 56     19     56     | 2      1489   3      | 7      48     49     |
 | 2      7     *39     | 5      489    49     | 6     *348    1      |
 |----------------------+----------------------+----------------------|
 | 135    6      7      | 134    1345   2      | 8      9      34     |
 | 8      4   (A)135    | 6      1359   159    | 2   (A)35     7      |
 | 9      2     *35     | 8      7      45     | 1     *345    6      |
 *--------------------------------------------------------------------*


In addition to Pat's above guidance I hope this also helps.

Cec
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Postby HATMAN » Thu Jan 24, 2008 12:38 am

For plain vanilla sudoku I think of this as "the corners of a rectangle"

The more restained ones such as X or Windoku have applications of the technique that are less visually obvious.
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Postby daj95376 » Thu Jan 24, 2008 2:03 am

What the heck. Count me in as well.

Code: Select all
+--------------------------------------------------------------------+
|  2      14     3     |  5      49     7     |  19     6      8     |
|  6      5      14    |  249    2349   8     |  139    12     7     |
|  8      7      9     |  12     1236   136   |  5      4      23    |
|----------------------+----------------------+----------------------|
|  7      2      16    |  3      5      16    |  8      9      4     |
|  14     9      5     |  1247   8      146   |  137    12     236   |
|  3      8      146   |  1247   1246   9     |  17     5      26    |
|----------------------+----------------------+----------------------|
|  14     6      8     |  149    1349   134   |  2      7      5     |
|  5      14     7     |  8      14     2     |  6      3      9     |
|  9      3      2     |  6      7      5     |  4      8      1     |
+--------------------------------------------------------------------+

Code: Select all
Candidate grid for digit 4:  X-Wing r18\c25

Rows 1 & 8: two candidates per row, and two common columns -- 2 & 5
other candidates in columns 2 & 5 can be eliminated
+-----------------------------------+
|  . *4  .  |  . *4  .  |  .  .  .  |
|  .  .  4  |  4 -4  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  4  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  4  |
|  4  .  .  |  4  .  4  |  .  .  .  |
|  .  .  4  |  4 -4  .  |  .  .  .  |
|-----------+-----------+-----------|
|  4  .  .  |  4 -4  4  |  .  .  .  |
|  . *4  .  |  . *4  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  4  .  .  |
+-----------------------------------+

Code: Select all
Candidate grid for digit 4:  X-Wing c16\r57

Columns 1 & 6: two candidates per column, and two common rows -- 5 & 7
other candidates in rows 5 & 7 can be eliminated
+-----------------------------------+
|  .  4  .  |  .  4  .  |  .  .  .  |
|  .  .  4  |  4  4  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  4  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  .  .  |  .  .  4  |
| *4  .  .  | -4  . *4  |  .  .  .  |
|  .  .  4  |  4  4  .  |  .  .  .  |
|-----------+-----------+-----------|
| *4  .  .  | -4 -4 *4  |  .  .  .  |
|  .  4  .  |  .  4  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  4  .  .  |
+-----------------------------------+
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