## Almost X-Wing Example in Loop

Advanced methods and approaches for solving Sudoku puzzles

### Almost X-Wing Example in Loop

Here is a puzzle I made. The solution is probably the most ordered solution that can exist('all traveling triples'), but What I find interesting is the neat loop following. After Simple Sudoku could give no more hints I found the folowing elimination and looked at it through two 'different' chains.

I just entered the solution and deleted numbers until Simple Sudoku said the puzzle had multiple solutions if I deleted another number.

Code: Select all
`Original Puzzle: *-----------* |1..|..6|.89| |...|.2.|4.6| |...|.8.|...| |---+---+---| |9..|.45|6.8| |6..|...|...| |.4.|.7.|..2| |---+---+---| |..1|...|...| |567|...|23.| |.3.|5.7|...| *-----------*After basic logic and coloring:*--------------------------------------------------------------------*| 1      2      34     | 47     5      6      | 37     8      9      || 378    589    389    | 179    2      139    | 4      157    6      || 347    59     6      | 1479   8      1349   | 1357   2      357    ||----------------------+----------------------+----------------------|| 9      17     23     | 23     4      5      | 6      17     8      || 6      17     258    | 189    139    1289   | 13579  4      357    || 38     4      358    | 6      7      189    | 1359   159    2      ||----------------------+----------------------+----------------------|| 48     89     1      | 23     36     24     | 5789   5679   57     || 5      6      7      | 1489   19     1489   | 2      3      14     || 2      3      489    | 5      16     7      | 89     69     14     |*--------------------------------------------------------------------*`

I found the following loop with an almost x wing. For a good explanation check this forum(Almost X-Wing) and this forum(Multiple implication and grouped nodes).

Here are some pictures:

In the picture above:
[r4c3]-3-[r6c1]=3=[Almost X-Wing:r23c16]-3-[r3c79]=3=[r1c7]-3-[r56c7]=3=[r5c9]-3-[r5c5]=3=[r4c4]-3-[r4c3] => [r4c3]<>3

Where the extra -3's around the x-wing are those exclude by the x-wing and its locked candidates.

In the picture above:
[r4c3]-3-[r4c4]=3=[r5c5]-3-[r5c9]=3=[r56c7]-3-[r13c7]=3=[r3c9](-3-[r3c1])-3-[r3c6]=3=[r2c6]-3-[r2c13|(r3c1)]=3=[r1c3]-3-[r4c3] => [r4c3]<>3

Where you really have to follow the chain in a particular direction to see the conclusion easily.
doduff

Posts: 32
Joined: 29 May 2006

### Re: Almost X-Wing Example in Loop

Code: Select all
`*--------------------------------------------------------------------*| 1      2     *34     | 47     5      6      |*37     8      9      || 378    589    389    | 179    2      139    | 4      157    6      || 347    59     6      | 1479   8      1349   | 1357   2      357    ||----------------------+----------------------+----------------------|| 9      17    -23     | 23     4      5      | 6      17     8      || 6      17     258    | 189    139    1289   | 13579  4      357    ||#38     4     *358    | 6      7      189    |*1359   159    2      ||----------------------+----------------------+----------------------|| 48     89     1      | 23     36     24     | 5789   5679   57     || 5      6      7      | 1489   19     1489   | 2      3      14     || 2      3      489    | 5      16     7      | 89     69     14     |*--------------------------------------------------------------------*`

...or you could just use a finned r16c37 x-wing (fin = r6c1). Either the fin is 3 or the x-wing is true, and either one will eliminate the 3 in r4c3.
Myth Jellies

Posts: 593
Joined: 19 September 2005

The coloring is not "needed":

Code: Select all
` *--------------------------------------------------------------------* | 1      2      34     | 347    5      6      | 37     8      9      | | 378    589    389    | 1379   2      139    | 4      157    6      | | 347    59     6      | 13479  8      1349   | 1357   2      357    | |----------------------+----------------------+----------------------| | 9      17     23     | 23     4      5      | 6      17     8      | | 6      17     2358   | 12389  139    12389  | 13579  4      357    | | 38     4      358    | 6      7      1389   | 1359   159    2      | |----------------------+----------------------+----------------------| | 48     89     1      | 234    36     234    | 5789   5679   57     | | 5      6      7      | 1489   19     1489   | 2      3      14     | | 2      3      489    | 5      16     7      | 89     69     14     | *--------------------------------------------------------------------*`

[r4c3](-3-[r4c4]-2-[r7c4])-3-[r6c1]-8-[r7c1]-4-[r7c4](-3-[r5c4])-3-
[r123c4]=3=[r23c6]-3-[r56c6]=3=[r5c5]-3-[r5c79]=3=[r6c7]-3-[r1c7]
=3=[r1c3]-3-[r4c3], => r4c3<>3 and the puzzle is solved.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Man... Everytime I find something that I think is cool, someone shows me an easier way to reach the same conclusion!

Thanks for pointing that stuff out to me.
doduff

Posts: 32
Joined: 29 May 2006