Notation xy-wing

Advanced methods and approaches for solving Sudoku puzzles

Notation xy-wing

Postby ArkieTech » Tue Aug 04, 2015 9:15 pm

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
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Re: Notation xy-wing

Postby David P Bird » Wed Aug 05, 2015 10:18 am

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. :D

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
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