## Notation xy-wing

Advanced methods and approaches for solving Sudoku puzzles

### Notation xy-wing

Notation xy-wing

This will be an attempt to explain the notation I use to describe the setting of clues and the removal of candidates necessary to solve a Sudoku puzzle. The objective is to provide a method to describe to others a solution that you see. So a notation must be able to communicate or be understood by others. To me that is the only rule.

As an example, the following puzzle can be solved --reduced to singles-- with an xy-wing with pinchers located in r3c8 and r4c4 connected by r4c8 will remove a candidate 2 in r3c4. This will reduce the puzzle to singles.

Code: Select all
` *-----------------------------------------------------------* | 48    58    3     | 7     24    15    | 12    9     6     | | 46    2     1     | 9     46    8     | 7     5     3     | | 9     7     56    | 6-2   3     15    | 4    a12    8     | |-------------------+-------------------+-------------------| | 3     6     4     |c28    128   9     | 5    b18    7     | | 128   58    2578  | 4     178   6     | 18    3     9     | | 18    9     78    | 5     178   3     | 6     4     2     | |-------------------+-------------------+-------------------| | 7     3     28    | 1     9     4     | 28    6     5     | | 5     4     9     | 68    68    2     | 3     7     1     | | 268   1     268   | 3     5     7     | 9     28    4     | *-----------------------------------------------------------*`

The objective is to prove the removal of 2 in r3c4.
if r3c8 is a 2 then the objective is met.
if r3c8(a) is not a 2 then it has to be 1 this is shown in notation as (2=1)r3c8
with r3c8 a 1 then r4c8(b) must be an 8 adding to our notation we get (2=1)r3c8-(1=8)r4c8
if r4c8 is an 8 then r4c4(c) must be a 2 forcing the removal of a 2 in r3c4 Objective met. our notation becomes (2=1)r3c8-(1=8)r4c8-(8=2)r4c4
Many use the => notation which means "therefore" (2=1)r3c8-(1=8)r4c8-(8=2)r4c4 => -2r3c4
I like to use brackets to show a proof followed by a result.

[(2=1)r3c8-(1=8)r4c8-(8=2)r4c4]-2r3c4

The semicolon represents the end of a step. ste means "singles to end" so we complete our notation with

[(2=1)r3c8-(1=8)r4c8-(8=2)r4c4]-2r3c4; ste

For fun try going backwards starting with if r4c4 is not 2 then....

Comments and further posts are welcome. Maybe we can learn better ways to communicate Sudoku solutions.
dan

ArkieTech

Posts: 2978
Joined: 29 May 2006
Location: NW Arkansas USA

### Re: Notation xy-wing

ArkieTech, When the Daily Sudoku site crashed in 2012 and a number of you turned to this forum, there was reluctance for contributors to conform to any notation standard so a large variety of styles started to appear.

As this produces obvious disadvantages I, and later DonM, tried to provide guidance and were fairly comprehensively ignored.
< Here >
you wrote:The beautiful thing about Eureka notation is it is like writing. Each person can have and enjoy his own style. Which hopefully others can understand.

After that 'please keep your nose out' comment by and large I complied as after all, the Puzzles section is effectively your domain (BTW well done for keeping it up). But can we now take it that after 3 years' experience of notation mayhem you've had a change of heart and are now trying to standardise?

DPB
David P Bird
2010 Supporter

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Joined: 16 September 2008
Location: Middle England