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peterj · Joined: 26 Mar 2010 Posts: 974 Location: London, UK

This was a very interesting puzzle with lots of xy action!

This was my natural solve path for 3 steps...

tlanglet · Posted: Mon Jun 14, 2010 12:13 am Post subject:

I am not a xy-chain type of person. I only find them when looking to extend a potential xy-wing such as occurred in my last step for this puzzle.

My first step is something of a mess. I hope the post is understandable since I am not aware of proper notation. Finally the deletion provide by this step is not effective, and would have been accomplished by a following step in any case, but it was mountain that had to be climbed.

JC Van Hay · Joined: 13 Jun 2010 Posts: 494 Location: Charleroi, Belgium

A shorter one step proof :

peterj · Joined: 26 Mar 2010 Posts: 974 Location: London, UK

JC - I have not been initiated into the world of SIS and appropriate notation! Can you point me somewhere where I can learn?
Peter

JC Van Hay · Joined: 13 Jun 2010 Posts: 494 Location: Charleroi, Belgium

Peter,

SIS = Strong (Inference) Set = set in which at least one element is true.

The candidates in a cell, the candidates for a single digit in a unit are said to be native SIS while the guardians in a Broken Wings pattern, the endpoints of an AIC chain ... are said to be derived SISWIS = Weak (Inference) set = set in which at most one element is true.

The candidates in a cell, the candidates for a single digit in a unit, or a subset of these are native WIS; derived WIS are used in full tagging, for example.Some references :

Definitions

http://sudoku.com.au/

http://forum.enjoysudoku.com/

If further information is wanted, don't hesitate to ask.

JC

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Can you put it in pictures while we grapple with the notation JC ?

Luke451 · Posted: Mon Jun 14, 2010 7:49 pm Post subject:

ronk · Joined: 07 May 2006 Posts: 398

Luke451 · Posted: Mon Jun 14, 2010 9:56 pm Post subject:

ronk · Joined: 07 May 2006 Posts: 398

An m-ring between 2 wings:

Marty R. · Posted: Tue Jun 15, 2010 4:30 am Post subject:

SIS, WIS, M-Rings, etc. notwithstanding Wink

, either way of breaking up the 17 DP in boxes 36 results in r5c5=1, which solves the puzzle.

JC Van Hay · Joined: 13 Jun 2010 Posts: 494 Location: Charleroi, Belgium

. Forgive me for the grappling. I thought I were using well-known notations.

Of course, here, as noted by Luke451 and Ronk, the ordered list of strong sets is a concise way to represent an AIC chain. It is exactly similar to a path in a B/B plot. By application of the Sudoku rules, the AIC chain is easily reconstructed. In case of an AIC net, the reconstruction is much more involved and an ad-hoc diagram is needed as in the 9-SIS MUG above. For further examples of notations and diagrams, see Allan Barker's website at http://sudokuone.com/.

As an application, Marty's move may be written as a

Here the reconstruction needed the applications of the Sudoku rules 4 times and the uniqueness rule once.

JC

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Thanks JC and thanks Luke - for me certainly a new way of looking at sudoku. Will go to that Alan Barker page you recommended JC.

daj95376 · Joined: 23 Aug 2008 Posts: 3854

I migrated from NL notation to AIC notation because I found it easier to understand what was happening in a chain. Now, with the use of SIS notation, I see that a chain can be reduced to its fundamental strong links and still be understandable. It is certainly a more compact notation than either of the two former notations.

What my solver found: