What is this technique classified as?

Advanced methods and approaches for solving Sudoku puzzles

What is this technique classified as?

Postby 999_Springs » Wed Aug 15, 2007 2:58 pm

Code: Select all
...|...|...
...|..X|...
X**|.X.|***
|--+---+---
|..|..*|...
|..|..*|...
|..|..*|...
|--+---+---
X**|..*|...
.**|..*|...
..X---X|...

X---X = strong link
* = elimination
(Found in Times Super-Fiendish 10.8.07 in sevens before I found the x-wing)


Is this classified as 3 strong links or bidirectional cycle or both or a type of fish with a long name?
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Postby Mauricio » Wed Aug 15, 2007 5:29 pm

To me it would be a fishy pattern, but I don't know if it has been classified yet.
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Re: What is this technique classified as?

Postby ronk » Wed Aug 15, 2007 6:20 pm

999_Springs wrote:Is this classified as 3 strong links or bidirectional cycle or both or a type of fish with a long name?

Illustrating your example in the style of The Ultimate FISH Guide ...
Code: Select all
 /  .  . | /  /  X2| .  .  .
 /  .  . | /  /  X | .  .  .
 X  *  * | X2 X *X2| *  *  *
---------+---------+---------- 
 /  .  . | .  .  * | .  .  .
 /  .  . | .  .  * | .  .  .
 /  .  . | .  .  * | .  .  .
---------+---------+---------- 
 X  *  * | .  .  * | .  .  .
 X2 *  * | .  .  * | .  .  .
 /  X2 X | /  /  X | /  /  /

 'X'  <=> candidate in 999_Springs' illustration
 "X2" <=> additional permissible candidate (as in 'X' too)
 '/'  <=> empty cell
 '*'  <=> elimination cell
 '.'  <=> candidate may or may not exist

As a fish (constraint sets): (unfinned) mutant swordfish r9c1b2\r3c6b7

Note that r3c6<>X is also true. See Fig 3E at the above link for a permuted rcb\rcb swordfish exemplar.

As a chain: multi-coloring, continuous loop, x-cycle, or bidirectional x-cycle

r7c1 =X= r3c1 -X- r3c5 =X= r2c6 -X- r9c6 =X= r9c3 -X- Loop (nice loop notation, assuming X2 cells are empty)

As a "grouped chain":

r78c1 =X= r3c1 -X- r3c456 =X= r2c456 -X- r9c6 =X= r9c23 -X- Loop (with X2 candidates)

[edits: 1) thanks to tarek for seeing typos; 2) added illustration and "grouped chain"]
Last edited by ronk on Thu Aug 16, 2007 7:08 am, edited 1 time in total.
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