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X - Wing

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X - Wing

Postby strmckr on Sun May 10, 2009 9:05 pm

two rows / columns where there is only 4 digits.

the dgits of N form a rectangle shape.

where each digit see one digit on the opposite row.

the elliminations occur in opposite direction to where the digits line up.

( if its two rows. eliminate on columns,
if its two columns eliminate on rows)

to understand how the elimiantion works

try placing a N on the board, the opposit corner is always true.

thus no matter which way the rectangle solves the x's are never true


Code: Select all
/  /  N | / / / | / / N
.  .  x | . . . | . . x
.  .  x | . . . | . . x
--------+-------+-------
/  /  N | / / / | / / N
.  .  x | . . . | . . x
.  .  x | . . . | . . x
--------+-------+-------
.  .  x | . . . | . . x
.  .  x | . . . | . . x
.  .  x | . . . | . . x


KEY: '/' <=> cells void of candidate 'N'
'N' <=> cells with candidate 'N'; all are required
"-X" <=> potential eliminations of candidate 'N'
Last edited by strmckr on Tue Aug 04, 2009 12:44 am, edited 1 time in total.
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Re: X - Wing

Postby strmckr on Sun May 10, 2009 9:21 pm

Example on Rows

digit 1

on Rows 4 and 7 there is only 2 locations per row where the digits 1 are
they form a rectangle shape.
eliminate all the ones on the columns.

Code: Select all
.-----------------.-------------------------.--------------------.
| 1    1346  2    | 146     46-1     7      | 9     5       8    |
| 7    456   4589 | 45689   45689    4689   | 1     2       3    |
| 189  1456  4589 | 145689  245689-1  3     | 467   467     47   |
:-----------------+-------------------------+--------------------:
| 5    9     48   | 7     1248@     1248@   | 3     48      6    |
| 128  147   478  | 14689  234689-1  24689-1| 478   4789    4579 |
| 3    47    6    | 489     489      5      | 478   1       2    |
:-----------------+-------------------------+--------------------:
| 9    57    579  | 2       1456789@ 14689@ | 4678  346789  479  |
| 6    8     3    | 459     4579     49     | 247   479     1    |
| 4    2     1    | 3       6789     689    | 5     6789    79   |
'-----------------'-------------------------'--------------------'

1 r47 c56 => r135c5,r5c6<>1
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