Extension of xyz-wing

Advanced methods and approaches for solving Sudoku puzzles

Postby ronk » Fri Feb 24, 2006 11:41 pm

tarek wrote:the ALS xz rule specifies an "x" and a "z" which is fine and understandable.

dfhwze mentioned something which also correct that the consensus was that for for an wxyz wing, the "w" is actually the candidate constrained to a sector with a wz cell which goes to say that in a vwxyz, the "v" is the candidate that should be constrained to a sector with a vz cell.

If bennys had followed that line of thinking, we might today have the insanity of an xz-rule, a wz-rule, a vz-rule, etc.

tarek wrote:so the example from an ALS xz rule point of view is as ronk mentioned...
Code: Select all
 .   .   .   | .   .   .
 wyz wyz .   |wxyz *   * 
 .   .   .   | .   xz  . 


however from the general consensus about wings, this should be:
Code: Select all
 .   .   .   | .   .   .
 xyz xyz .   |wxyz *   * 
 .   .   .   | .   wz  . 

I think most people quickly understand that the letters are just placeholders. Exchanging 'w' and 'x' in one of the above produces the other. If you have a classical wxyz and see 1234 in the "pilot cell", do you assume w=1?

tarek wrote:for a classic wing IMO:
1. ALS1 should have ONLY one cell containing all candidates of the ALS (& that cell is the only cell containing "x" according to ALS xz opinion, or the only cell containing a "w" according to the general consensus of understanding wxyz wings) - that should serve as the pilot cell.

I have no problem with that being a requirement of the "classical" wxyz-wing.

tarek wrote:2. ALS2 should be a bivalued cell which is EXACTLY xz according to the ALS xz rule or exactly wz according to the general consesus of understanding wxyz wings(or vz if VWXYZ or uz if UVWXYZ).

That is precisely where a re-description should occur IMO ... so that the candidate constrained to one unit (group, sector) is always 'x'.

As our base of knowledge expands, it becomes prudent to occasionally re-describe the old knowledge base in order to unify the entire knowledge base. This doesn't invalidate the old knowledge base.

Ron
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Postby dfhwze » Sat Feb 25, 2006 12:36 pm

xyz-wing , wxyz-wing , vwxyz-wing .... are all ALS'es with 1 single-location-candidate in it , couldn't we just call these ALS type 1 ?
and when there are 2 single-location-candidates in it ALS type 2 , and so on?

but how far can we go ? in the end we'll have an ALS with 4 of these candidates in it, who on earth can find something like this without a pc ?
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Postby tarek » Sat Feb 25, 2006 3:42 pm

ronk wrote:
tarek wrote:2. ALS2 should be a bivalued cell which is EXACTLY xz according to the ALS xz rule or exactly wz according to the general consesus of understanding wxyz wings(or vz if VWXYZ or uz if UVWXYZ).
That is precisely where a re-description should occur IMO ... so that the candidate constrained to one unit (group, sector) is always 'x'.
I have no problem in using benny's xz rules for these wings, however I think that to avoid confusion we should change the x into something else outside "uvwxyz" to avoid all confusion. some greek letter maybe ??!!!

z does not cause any confusion as it is the last letter of the alphabet & it is constant in all patterns & both opinions.

so my suggestion would be changing it into (ALS "new letter"z) rule where "new letter" replaces x.
dfhwze wrote:and when there are 2 single-location-candidates in it ALS type 2 , and so on?
I think there is a source of confusion too with ALS- xy rule also, but that is a different story......


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Postby Mike Barker » Tue Feb 28, 2006 2:39 pm

I think the question of how to define an XYZ, WXYZ, etc. wing boils down to two questions:
1) What is a definition which provides an intermediate (?) player with an effective tool
2) What definition makes the best bridge from a beginning to an advanced player?

In regards to the first question, I ran my solver with both the restricted and generalized definitions using a randomly generated set of 1000 runs (using suexg from http://magictour.free.fr/sudoku.htm). In the restricted case only 10 puzzles were advanced. In the generalized case 151 puzzles were advanced. I performed the same test with Top1465 with 39 puzzles in the first case and 304 puzzles in the second. Clearly the generalized descriptions is much more effective at advancing the solution. Of course a 4-candidate cell is easier to spot than a 4-candidate ALS, but given the significant difference in effectiveness and the fact that even relative beginners will be looking for 4-candidate locked sets, it seems worthwhile to use the generalized definition.

I think tarek has the best argument for the generalized definition, that is, that it is a simple form of an ALS reduction. A beginner starts with finding naked locked sets (as well as other techniques). A natural extension is what to do if s/he finds n+1 candidates in n cells - search for a bivalued cell which contains the same candidates and perform the mYZ reductions. Got that down - the next step is to advance to all of the ALS reductions. The argument could also begin with an XY-wing, but nothing requires that the next step require an XYZ pilot. Since the progression should proceed to ALS, it still seems to make more sense (to my primitive mind) to focus on the ALS nature of the technique.
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