## Chain Notation in my Trace

Advanced methods and approaches for solving Sudoku puzzles

### Chain Notation in my Trace

(DB in the sequel) link to Whips.html. I have some questions &
observations. For one thing I am working on a new Log format or Trace is
what I like to call it from the influence of John Welch's
"Systematic Sudoku" Blog at:

http://sysudoku.com/sysudoku-traces/

I am a fan of any systematic approach to solving Sudoku. I have read
and studied most of Denis Berthier's book 'Hidden Logic of Sudoku
(Second Edition)' (HLOS2 in the sequel) I particularly like the way he
defines chains and in particular 3D Chains. At the same time I am giving
you a tidbit on the Trace Format (Log if you prefer) that I use.

I prefer a numbered line format. This allows those reading the Trace to
reference items by line number. Also I use a further numbering of
actual operations with a 's' number. I will at some point do a
complete write-up on my Trace - perhaps referencing my 'BigSudoku' Blog
to that if it is acceptable. The part I want to focus on now is
the way I think all chains can be represented as in lines 20-35 below.
I use 'k' instead of 'n' when I am referring to a candidate in a cell
(which I prefer to call square) If I reference the complete contents of
a cell as in r2c3 I would reference that as 'n23' So that deviates a
bit from DB. Also using essentially the concept of DB's 3D 'nrc' chain
notation becomes 'krc' for me, but same idea. I also prefer to not
use the curly braces. So DB would write n3{r4r3}c5 for the first link
of the chain, I believe there is already a Sudoku precedent to write
that simply as n3r43c5 or with my preference k3r43c5.

Now I prefer to take this a step further to make the links even clearer.
DB in HLOS2 refers to the odd parts of the links (left-linking candidate)
as being numbered 1,3,5... and the even parts of the links (right-linking
candidate) as being numbered 2,4,6.

I believe it makes it even more clear to break the link into two numnbered
candidates with the next line of '--' demarcating the link.

01 k3r4c5=a
02 k3r3c5=A
--

For one thing it allows your eyes to easily scan the candidates and verify
that they are linked because only one part is changing. In this case the
row number. Also it is perhaps even clearer that you start with the cell
that has r4. I also like to use a chain parity notation of a letter where
the lower-case stands for the False candidate and the upper case stands for
the True candidate. I do this with a '=' to the parity. There may be
other punctuation you could use. This is called by DB a 'tagging' Robert
Hanson of 3D-Medusa fame also uses similar notation. I like the way DB
names the chains and their length as being the number of cell involved.

I believe chains of all types can be represented in this way. Also with the
presentation I use it is easy to show the target as being linked to the left
most candidate and right most candidate. Also the block-square notation can
be written to the side for those links inside those 3x3 blocks where the
linking might be harder to visualize. I show it on the first and last
candidates in the chains just to show what it might look like.

but will do that in further posts.

Code: Select all
`01 http://denis.berthier.pagesperso-orange.fr/HLS/Whips.html02 03 4.1) First whip example0405 .---------------.---------------.-------------.06 | 4     1   6   | 37    2   5   | 89   89  37 |07 | 8     7   23  | 4     1   9   | 23   5   6  |08 | 235   35  9   | 8     37  6   | 237  1   4  |09 :---------------+---------------+-------------:10 | 6     4   37  | 1     37  8   | 5    2   9  |11 | 1     9   8   | 5     4   2   | 37   6   37 |12 | 357   2   357 | 9     6   37  | 1    4   8  |13 :---------------+---------------+-------------:14 | 79    68  1   | 67    5   47  | 489  3   2  |15 | 237   38  4   | 27    9   1   | 6    78  5  |16 | 2579  56  257 | 2367  8   347 | 49   79  1  |17 '---------------'---------------'-------------'18 1920 XY-4 Chain21 ----------->22 01 k3r4c5=a k3b5s223 02 k3r3c5=A24 --25 03 k3r3c2=a26 04 k5r3c2=A27 --28 05 k5r3c1=a29 06 k2r3c1=A30 --31 07 k2r2c3=a32 08 k3r2c3=A k3b1s633 --34    k3r4c3=X35 -----------<36 s01 r3c3-3`
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA

### Re: Chain Notation in my Trace

I forgot to mention that the candidates diagram is NOT the original one as Denis Bethier's URL on Whips as he defines them. I started with his example and applied various operations to get to the point where I was ready to apply the chain shown there. Hope that helps?
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA

### Re: Chain Notation in my Trace

Just to give a hint on where I want to go with this discussion is that I believe there is a shorter Whip that makes the same elimination and that there is a 't' candidate that is not articulated in the chain shown. And two issues with that 't' candidate. Is it needed in the logic of the chain and should it be shown or not shown?
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA

### Re: Chain Notation in my Trace

[Withdrawn: topic moved to another post.]
Last edited by daj95376 on Mon Nov 11, 2013 7:04 am, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Chain Notation in my Trace

daj95376 wrote:_

Your sequence [22-34] corresponds to a chain with memory:

Code: Select all
` a         A          a A          aa A         a A(3)r4c5 = (3*)r3c5 - (3=5)r3c2 - (*35=2)r3c1 - (2=3)r2c3  =>  r4c3<>3`

There are those who might write it as a chain with an ALS:

Code: Select all
` a         A         a AA          a A(3)r4c5 = (3)r3c5 - (3=52)r3c21 - (2=3)r2c3  =>  r4c3<>3`

However, most would consider an Empty Rectangle as a more desirable alternative:

Code: Select all
` a         A         a          A(3)r4c5 = (3)r3c5 - (3)r3c12 = (3)r2c3  =>  r4c3<>3`

Your statement "36 s01 r3c3-3" appears to be a typo for the above conclusion.

Line 36 is my conclusion and I forgot to mention I was using '-' to replace '<>'
I have been using s01, s02, s03, ... numbering to list the actual operations
on the grid. I have never hear the term 'chain with memory'
Your first chain appears to me to be Eureka notation - am I correct in that?

Thanks for responding!
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA

### Re: Chain Notation in my Trace

daj95376 wrote:_

Your sequence [22-34] corresponds to a chain with memory:

Code: Select all
` a         A          a A          aa A         a A(3)r4c5 = (3*)r3c5 - (3=5)r3c2 - (*35=2)r3c1 - (2=3)r2c3  =>  r4c3<>3`

There are those who might write it as a chain with an ALS:

Code: Select all
` a         A         a AA          a A(3)r4c5 = (3)r3c5 - (3=52)r3c21 - (2=3)r2c3  =>  r4c3<>3`

However, most would consider an Empty Rectangle as a more desirable alternative:

Code: Select all
` a         A         a          A(3)r4c5 = (3)r3c5 - (3)r3c12 = (3)r2c3  =>  r4c3<>3`

Your statement "36 s01 r3c3-3" appears to be a typo for the above conclusion.

Oops! It was worse than I thought - My Bad - You are Right it is r4c3-3 or r4c3<>3 if you prefer!
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA