Uniqueness & XY/XYZ wing

Advanced methods and approaches for solving Sudoku puzzles

Uniqueness & XY/XYZ wing

Postby tarek » Thu Feb 02, 2006 4:52 pm

if a "Quanum cell was formed" from the 2 cells in a Type2/3 Unique rectangle, can we extend the chain of events so that the quantum cell can form an XY wing or an XYZ wing ???!!!! (xz in box yz in line or vice versa)

Thanx

Tarek
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Postby Carcul » Thu Feb 02, 2006 5:30 pm

Yes Tarek. Consider the following (hypotethical) simple example:

Code: Select all
 . .  . | .   .  .   | . . .
 . .  . | 67  .  67  | . . .
 . .  . | .   .  .   | . . .   
--------+------------+------
 . .  . | .   .  .   | . . .
 . .  . | .   .  .   | . . .
 . .  . | .   .  .   | . . .
--------+------------+------
 . 24 . | 267 .  367 | . . .
 . .  . | .   .  .   | . . .
 . X  . | .   34 .   | . . .

We have:

[r9c2]-4-[r7c2]-2-[r7c4]=2|3=[r7c6]-3-[r9c5]-4-[r9c2] => r9c2<>4.

The two cells r7c46 function as a bivalue one, because if r7c4 is not "2" then r7c6 must be "3", and vice-versa.

Regards, Carcul
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Postby tarek » Thu Feb 02, 2006 5:40 pm

Thanx Carcul,

It sounds logical, interesting stuff to add to my solver.

Tarek
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