Forcing chains: Terminology and Definition

Advanced methods and approaches for solving Sudoku puzzles

Re: Forcing chains: Terminology and Definition

Postby ronk » Tue Mar 21, 2006 11:33 am

Jeff wrote:Alternative Inference Loop- a nice loop with all links that make strong and weak inferences alternatively to yield a deduction in the form of an inclusion or exclusion , eg. x-cycle, x-wing & Turbot fish.

x-cycle - a chain in which all nodes are linked by a single digit 'x' with links that make alternative strong and weak inferences to yield deduction(s). A x-cycle can be of any length. It can be continuous or discontinuous. The following patterns are subsets of x-cycles:

I think you meant the words "Alternating" ... "alternately" ... and "alternate" ... respectively.
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Re: Forcing chains: Terminology and Definition

Postby Jeff » Tue Mar 21, 2006 4:04 pm

Thanks Ronk.
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Re: Forcing chains: Terminology and Definition

Postby ronk » Sat Mar 25, 2006 11:32 pm

Jeff wrote:Bilocation/Bilocation Plot - a diagram ...
LOL. Been writing "b/b" too long?

Simple Colouring and Multiple Colouring - a discontinuous x-cycle of length n.
Continuous x-cycles exist in colouring.

Turbot chain - a discontinuous x-cycle of length n.
A discontinuous x-cycle of length n, where n = 5, 7, 9, ...
... OR ...
A discontinuous x-cycle of odd length n >= 5.
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Re: Forcing chains: Terminology and Definition

Postby Jeff » Sun Mar 26, 2006 4:15 am

Thanks Ronk.

ronk wrote:LOL. Been writing "b/b" too long?

I was wondering what LOL (Is it Lots of Love?:D ) stands for so I looked it up and found a few different meanings as follows:

Code: Select all
Lots of Love       Laugh Out Loud   Life of Loan
Lots of Lag        Loss of Life     Little Old Lady
Lots of Luck       Land O' Lakes    Language of Literature
Lack of Love       Learn Online     Land of Legends
List of Lists      Loads of Love    Lower Operating Limit
Lords of Legend    Live-On-Line     Loyal Orange Lodge
Load of Laughs     Lots of Losers   Low Order Language
Laughing On Line   Log On Later     Legend of Lothian
Legend of Legaia   Love On Line     Language of Love
League of Losers   Lord Oh Lord     Life of the Land
Loss of Lock       Land of Lincoln  Living on Line
Lautes Online      Lands of Lore    Lying Out Loud
Lips on Lips       Love of Life     Ladies of Lallybroch
Loss of Load       Loss of Light    Laughing Out Loud
Last or Least      List of Lights   League of Lightness
Lawyers on Line    Less of Lip      Lewd Obscene Language
Loss of Line       Lot of Lamers    Leaning Over Laughing
Lunatics on Line   Longitudinal Output Level
Love of Literacy   Limited Operational Life
List of Links      Lots Of Laughs/Laughter

ronk wrote:Continuous x-cycles exist in colouring.

Could you give an example?
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Re: Forcing chains: Terminology and Definition

Postby ronk » Sun Mar 26, 2006 6:45 am

Jeff wrote:
ronk wrote:Continuous x-cycles exist in colouring.

Could you give an example?

A multi-coloring example from #871 of the top1465:

84...9..1....8.2......7..4...1..4....83....6...9.....4...7...3..1.8....5.2..3.4..
Code: Select all
 8     4     2567 | 256   256    9    | 3     57    1
 15679 35679 567  | 4     8      1356 | 2     579   679
 1569  3569  256  | 1256  7      12356| 5689  4     689
------------------+-------------------+------------------
 2567  567   1    | 2569  2569   4    | 5789  25789 3
 4     8     3    | 1259  1259   7    | 159   6     29
 2567  567   9    | 3     1256   8    | 157   1257  4
------------------+-------------------+------------------
 569   569   4568 | 7     124569 1256 | 1689  3     2689
 3     1     467  | 8     2469   26   | 679   279   5
 5679  2     568  | 1569  3      156  | 4     1789  6789

 .  .  A  |  .  .  .  |  .   a  .
 7  7 -7  |  .  .  .  |  .  -7  B
 .  .  .  |  .  .  .  |  .   .  .
----------+-----------+-----------
 7  7  .  |  .  .  .  |  7   7  .
 .  .  .  |  .  .  .  |  .   .  .
 7  7  .  |  .  .  .  |  7   7  .
----------+-----------+-----------
 .  .  .  |  .  .  .  |  .   .  .
 .  .  c  |  .  .  .  |  7   7  .
 C  .  .  |  .  .  .  |  .  -7  b

... for exclusions r2c3<>7, r2c8<>7, and r9c8<>7

Jeff wrote:I was wondering what LOL (Is it Lots of Love?:D ) stands for ...

LOL. It's common internet slang for "laughing out loud" or "lots of laughs."
http://en.wikipedia.org/wiki/LOL_(Internet_slang) [edit: the parenthetical is part of the link, but BBCode won't pick it up.]
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Re: Forcing chains: Terminology and Definition

Postby Jeff » Sun Mar 26, 2006 9:57 am

ronk wrote:A multi-coloring example from #871 of the top1465:

Thanks Ronk for the example, I must have missed this one. Could you point me to the thread or description where this continous colouring technique is discussed?
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Re: Forcing chains: Terminology and Definition

Postby Jeff » Sun Mar 26, 2006 10:06 am

ronk wrote:LOL. It's common internet slang for "laughing out loud" or "lots of laughs."
http://en.wikipedia.org/wiki/LOL_(Internet_slang) [edit: the parenthetical is part of the link, but BBCode won't pick it up.]

Thanks Ronk. Link added to 'Favorites'.
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Postby Mike Barker » Sun Mar 26, 2006 2:02 pm

There is a "Grounded X-wing" in the initial post. Also in a list of X-cycles, I've always a continuous 6-node 2-tailed Turbot fish and its higher order brethren as well as grouped brethren as separate from a 222 Swordfish (simple or finned):
Code: Select all
 . . X | . . X
 . . . | . . .
 X . . | . . .
------+------
 . . . | . . X
 . . . | . . .
 X . . | X . .

Is it truly separate or just something already listed? I also include 2222 Jellyfish, etc.

Most grouped X-cycles are just grouped somethings, with two notable exceptions: finned N*N fish and box/box locked candidates (grouped 4-node continuous). Would it makes sense to include these as well? Note as I understand it, a box/line locked candidate is somewhat akin to a grouped naked single so unless you're including 1-node continuous X-cycles, it doesn't appear to make the list.

Finally, in the list of xy-chains such critters as naked pairs, 222 naked triples, etc could also be included. Here grouping aka Almost Locked Sets could also be included.
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Re: Forcing chains: Terminology and Definition

Postby ronk » Sun Mar 26, 2006 3:12 pm

Jeff wrote:Could you point me to the thread or description where this continous colouring technique is discussed?

I don't recall ever seeing the terms "continuous" or "discontinuous" used in conjunction with coloring. I'm sure it's not a concept foreign to coloring ... and maybe it's called "closed loop" and "open loop", or something similar to that.

Following very simple rules, one just arbitrarily starts coloring anywhere on the grid. If the coloring creates a closed loop with a contradiction (identical colors in a unit) then candidates represented by that color may be eliminated. If there is no contradiction, the closed loop corresponds to the continuous chain on your b/b plots.

My one and only "bible" post on such closed loops is ... http://forum.enjoysudoku.com/viewtopic.php?p=14764#p14764

It all seems quite elementary, with the simplest case being the x-wing:
Code: Select all
 . A . | . . b
 . . . | . . .
 . a . | . . B

Since A!b (A true excludes b true) and a!B, then b=a and B=A ... and we may recolor as:
Code: Select all
 . A . | . . a
 . . . | . . .
 . a . | . . A
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Postby Jeff » Sun Mar 26, 2006 3:13 pm

Hi Mike, I am not sure if the following is relevant to your comments.

A Turbot fish always has odd number of links, so it can never be continuous. The 6-node pattern shown above is just a simple x-cycle which has been included already.

Listed below are some of the grouped nodes that can be used to make inferences within grouped networks:

    grouped x-node, Note: a grouped x-node nice loop is equivalent to an empty rectangle deduction.
    almost locked set (Lockedset+1)
    almost unique rectangle (AUR)
    almost x-wing, Note: an almost x-wing nice loop is equivalent to a fillet-O-fish.
    almost NxN fish (finned fish)
    almost BUG-Lite (BUG-Lite+2), Note: all almost unique patterns are almost BUG-Lites.
A grouped network may have one or more of the above grouped nodes embedded in a simple chain or net. Names have been used in some special cases listed below:

    Grouped x-cycle - an x-cycle with grouped x-node(s) as grouped node(s).

    Grouped xy-chain - an xy-chain with almost locked set(s) as grouped node(s).

    Strong Grouped Nice Loop - a simple nice loop with grouped x-node(s) as grouped node(s).

    Weak Grouped Nice Loop - a simple nice loop with almost locked set(s) as grouped node(s).

    AUR Nice Loop - a simple nice loop with almost unique rectangle(s) as grouped node(s).

    Almost x-wing Nice Loop - a simple nice loop with almost x-wing(s) as grouped node(s).
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