## Technique Help

Advanced methods and approaches for solving Sudoku puzzles

### Technique Help

I am new to the forum but i have been playing Sudoku for over a year now. I had no idea there where special techniques and I would appreciate if someone would explain some of them. I am an intermediate Sudoku-er(or whatever it is called). I also dont understand those green things that you put on messages what are those bunch of numbers?
viper

Posts: 2
Joined: 28 December 2005

Start with the general sources at the top of this list. It might take some time to learn all the different terminology and get used to the different diagrams used to explain the techniques on this forum, but don't let this scare you away. I'm sure you'll have lots of fun exploring the new techniques.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

Thanks a lot! I will check that out

I read the first one and didnt understand most of it lol could you explain it to me (short version). What is an X-wing?
viper

Posts: 2
Joined: 28 December 2005

I'm not sure I can do any better than the existing descriptions, but here goes. A column X-wing consists of two columns where a digit only occurs twice in each column and makes a box. In this example the digit, 4, only appears in columns 5 and 8 in rows 2 and 7.
Code: Select all
`+-----------+------------------+-----------------+| 5   4  8  |    2   1     67  |  67   3      9  || 9   6  3  | 57-4  47X     8  |   1  24X 257-4  || 2   1  7  |    3   9    456  |  46   8    456  |+-----------+------------------+-----------------+| 6  37  2  |    1   5     47  |   8   9    347  || 4  37  1  |    8   6      9  |   2   5     37  || 8   5  9  |   47   2      3  | 467   1    467  |+-----------+------------------+-----------------+| 3   8  6  | 57-4  47X 157-4  |   9  24X  12-4  || 1   9  4  |    6   3      2  |   5   7      8  || 7   2  5  |    9   8     14  |   3   6     14  |+-----------+------------------+-----------------+`

In order for "4" to appear in both columns it must appear in r2c5 and r7c8 or it must appear in r2c8 and r7c5 since it can't appear twice in the same row. If r2c4 were to contain a "4", then neither r2c5 nor r2c8 could contain a "4", therefore r2c4 cannot contain a "4". The same is true for any cell in rows 2 and 7 expect those cells in columns 5 and 8 (r2c9, r7c4, r7c6, and r7c9 cannot contain "4").

In general, let "X" indicate the only places where a digit is located in two columns (the "/"s indicate cells which do not contain the digit). If the "X"s form a box, then the digit can be eliminated from all cells in the rows which contains the "X"s except for those in the two columns. The possible eliminations are indicated with "*". The same thing occurs with row X-wings except that the "/" are in rows and the eliminations are in columns.
Code: Select all
` . . . | . / . | . / .  * * * | * X * | * X *  . . . | . / . | . / .  ------+-------+------  . . . | . / . | . / .  . . . | . / . | . / .  . . . | . / . | . / .  ------+-------+------  * * * | * X * | * X *  . . . | . / . | . / .  . . . | . / . | . / . `
Last edited by Mike Barker on Fri Nov 24, 2006 10:48 am, edited 1 time in total.
Mike Barker

Posts: 458
Joined: 22 January 2006

Very good description Mike, this is the kind of description that I think should exist in the ultimate fish guide. Minor typo though:
Mike Barker wrote: If r2c5 were to contain a "4", then neither r2c5 nor r2c8 could contain a "4", therefore r2c5 cannot contain a "4".

Lots of 'r2c5' there... might distract newbies.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

### X-wing explained by example

viper wrote:could you explain it to me (short version). What is an X-wing?

X-wing - example -

Code: Select all
` . . . | 9 7 4 | . 6 .  4 1 6 | 5 3 8 | 9 7 2  . 7 . | 1 6 2 | 4 3 . -------+-------+------ 7 2 4 | 8 1 9 | 3 5 6  1 5 3 | 2 4 6 | 7 . .  6 9 8 | 7 5 3 | 2 1 4 -------+-------+------ . 4 . | 3 9 1 | 6 2 .  . . 1 | 6 . 7 | 5 4 .  . 6 . | 4 . 5 | . . . `

the 8 for r3
has only two possible places - c1 , c9

and in r7,
this digit also has only two possible places -
which are in the same two Columns

so,
those two Rows
will definitely provide two 8s in those two Columns;
which is the full quota of 8s for any two Columns.

exclude 8 in those two Columns
outside of those two Rows.

Pat

Posts: 3674
Joined: 18 July 2005

RW, thanks for the correction. I've updated the post. I agree that this is what we want-detailed descriptions in the Ultimate fish guide, I have been distracted by other things.

Pat, excellent example of a "row" X-wing. It belongs in the Ultimate guide. Here are the pencil marks and eliminations:
Code: Select all
`+-----------------+-----------+-----------------+| 235-8  38   25  | 9   7  4  | 18   6    15-8  ||     4   1    6  | 5   3  8  |  9   7       2  ||   589X  7   59  | 1   6  2  |  4   3      58X |+-----------------+-----------+-----------------+|     7   2    4  | 8   1  9  |  3   5       6  ||     1   5    3  | 2   4  6  |  7  89     9-8  ||     6   9    8  | 7   5  3  |  2   1       4  |+-----------------+-----------+-----------------+|    58X  4   57  | 3   9  1  |  6   2      78X || 239-8  38    1  | 6  28  7  |  5   4    39-8  || 239-8   6  279  | 4  28  5  | 18  89  1379-8  |+-----------------+-----------+-----------------+`
Mike Barker

Posts: 458
Joined: 22 January 2006

Hi Viper,

I found myself in exactly the same position as yourself earlier this year. Using the information that Mike Barker had posted at the top of this list, I hooked into the solving guide below:

http://www.sudocue.net/guide.php

I found (and find) this document very useful, as it is well written and has worked examples for each technique that is explained.

To practice the (let me call them intermediate) techniques of X-Wings, Swordfish, Jellyfish and Quads the following selection of puzzles, The Superior Plus thread, is ideal:

http://forum.enjoysudoku.com/viewtopic.php?t=4414

best wishes

Andrewd
andrewd

Posts: 7
Joined: 27 July 2006

The X-wing definitions here & Pat's beautiful true example (which looks at you in the eye) will be added to the ultimate fish guide.....

tarek

tarek

Posts: 2761
Joined: 05 January 2006

### X-wing explained by example

i thought 58 known cells was quite high --
but recently, daj95376 has provided a better example, with 63 known cells !!

X-wing -- example --

Code: Select all
` 1 8 . | 2 . 7 | 9 . 5  . 5 9 | . . 1 | 8 2 7  . 7 2 | 5 8 9 | . 1 . -------+-------+------ 7 1 8 | 6 2 4 | 5 9 3  2 6 4 | 9 5 3 | 1 7 8  9 3 5 | 7 1 8 | 2 . . -------+-------+------ 8 9 . | 1 . 5 | 7 . 2  5 2 1 | . 7 6 | . 8 9  . 4 7 | 8 9 2 | . 5 1 `

the 3 for r3
has only two possible places -- c1 , c7

and in r9,
this digit also has only two possible places -
which are in the same two Columns

so,
those two Rows
will definitely provide two 3s in those two Columns;
which is the full quota of 3s for any two Columns.

exclude 3 in those two Columns
outside of those two Rows.

Pat

Posts: 3674
Joined: 18 July 2005