The New Sudoku Players' Forum

[daj95376]

There was a time when I use to post puzzles.

Code: Select all

 +-----------------------+
 | . . 7 | . . . | . . . |
 | . 1 8 | . . 6 | 9 7 . |
 | 5 9 2 | . . . | 6 . . |
 |-------+-------+-------|
 | . . . | 9 . . | 5 . 7 |
 | . . . | . . . | 8 1 6 |
 | . 7 . | . . 5 | . . . |
 |-------+-------+-------|
 | . 2 6 | 7 5 . | 1 . . |
 | . 8 . | . 9 . | . 2 . |
 | . . . | 8 4 . | . . 9 |
 +-----------------------+


Play this puzzle online at the Daily Sudoku site

[ArkieTech]

I remember fondly

Code: Select all

 *--------------------------------------------------------------------*
 | 346    46     7      | 1234   1238   9      | 24     5      12348  |
 | 34     1      8      | 5      23     6      | 9      7      234    |
 | 5      9      2      | 134    1378   478    | 6      348    1348   |
 |----------------------+----------------------+----------------------|
 | 2468   46     13     | 9      1268   48     | 5      34     7      |
 | 24     5      9      | 234    237    47     | 8      1      6      |
 | 68     7      13     | 14     68     5      | 24     9      234    |
 |----------------------+----------------------+----------------------|
 | 9      2      6      | 7      5      3      | 1      48     48     |
 | 7      8      4      | 6      9      1      | 3      2      5      |
 | 1      3      5      | 8      4      2      | 7      6      9      |
 *--------------------------------------------------------------------*
net
2r1c7-r1c4=r5c4-(2=4)r5c1-r2c1=r2c9-r7c9=4r7c8
||
4r1c7-----------r3c8
     -r1c2=r4c2-r4c8=4r7c8 => 4r7c8; ste


[JC Van Hay]

Interpretations of Dan's solution ...

1. Colouring C7 with the complementary colours a,A gives

a : r6c7,r5c1,r1c4=2 and r1c7,r4c1,r1c2=4
A : r1c7,r5c4=2 and r6c7,r5c1,r1c2,r2c9=4
a=A :=> -2r1c59,-2r5c5 and -4r1c149,-4r3c89,-4r4c18

or

Code: Select all

+-----------------+---------------------+---------------------+
| 36-4   6(4A) 7  | 13-4(2a) 138-2  9   | (2A4a) 5     138-24 |
| 3(4a)  1     8  | 5        23     6   | 9      7     23(4A) |
| 5      9     2  | 134      1378   478 | 6      38-4  138-4  |
+-----------------+---------------------+---------------------+
| 268-4  6(4a) 13 | 9        1268   48  | 5      3-4   7      |
| (2a4A) 5     9  | 34(2A)   37-2   47  | 8      1     6      |
| 68     7     13 | 14       68     5   | (2a4A) 9     234    |
+-----------------+---------------------+---------------------+
| 9      2     6  | 7        5      3   | 1      48    48     |
| 7      8     4  | 6        9      1   | 3      2     5      |
| 1      3     5  | 8        4      2   | 7      6     9      |
+-----------------+---------------------+--------------------+

2. Chain[6] : WRing{(4=2)r1c7-2r1c4=2r5c4-(2=4)r5c1-4r4c2=4r1c2}-[4r2c1=4r2c9 and (2=4)r6c7]

WR :=> -2r1c59,-2r5c5,-4r4c1,-4r1c149
4r1c7=4r2c9 :=> -4r3c89
4r4c2=4r6c7 :=> -4r4c8 [equivalent to Skyscraper(4C27)]

Therefore, r7c8=8;stte

[Marty R.]

Code: Select all

 *--------------------------------------------------------------------*
 | 346    46     7      | 1234   1238   9      | 24     5      12348  |
 | 34     1      8      | 5      23     6      | 9      7      234    |
 | 5      9      2      | 134    1378   478    | 6      348    1348   |
 |----------------------+----------------------+----------------------|
 | 2468   46     13     | 9      1268   48     | 5      34     7      |
 | 24     5      9      | 234    237    47     | 8      1      6      |
 | 68     7      13     | 14     68     5      | 24     9      234    |
 |----------------------+----------------------+----------------------|
 | 9      2      6      | 7      5      3      | 1      48     48     |
 | 7      8      4      | 6      9      1      | 3      2      5      |
 | 1      3      5      | 8      4      2      | 7      6      9      |
 *--------------------------------------------------------------------*

Two steps.

W-Wing (24) + transport (4=2)r1c7-r1c4=r5c4-(2=4)r5c1-r12c1=r1c2=>r1c149<>4
Skyscraper, c27=>r4c8<>4

[David P Bird]

Code: Select all

 *-------------------*---------------------*-------------------*
 |  346  h46   7     | 1234  a1238   9     | 24    5     2348  |
 | g34    1    8     | 5      23     6     | 9     7    f234   |
 |  5     9    2     | 134   b1378  b47-8  | 6    c348   1348  |
 *-------------------*---------------------*-------------------*
 |  2468 i46   13    | 9      126-8 j48    | 5     34    7     |
 |  24    5    9     | 234    237    47    | 8     1     6     |
 |  68    7    13    | 14     6-8    5     | 24    9     234   |
 *-------------------*---------------------*-------------------*
 |  9     2    6     | 7      5      3     | 1    d48   e48    |
 |  7     8    4     | 6      9      1     | 3     2     5     |
 |  1     3    5     | 8      4      2     | 7     6     9     |
 *-------------------*---------------------*-------------------*

Just (4)s and (8)s

(8)r1c5 = (8)r3c56 - (8)r3c8 = (8-4)r7c8 = (4)r7c9 - (4)r2c9 = (4)r2c1 - (4)r1c2 = (4)r4c2 - (4=8)r4c6
=> r3c6,r46c5 <> 8 sste

[Luke]

I remember fondly

Code: Select all

 *--------------------------------------------------------------------*
 | 346    46     7      | 1234   1238   9      | 24     5      12348  |
 | 34     1      8      | 5      23     6      | 9      7      234    |
 | 5      9      2      | 134    1378   478    | 6      348    1348   |
 |----------------------+----------------------+----------------------|
 | 2468   46     13     | 9      1268   48     | 5      34     7      |
 | 24     5      9      | 234    237    47     | 8      1      6      |
 | 68     7      13     | 14     68     5      | 24     9      234    |
 |----------------------+----------------------+----------------------|
 | 9      2      6      | 7      5      3      | 1      48     48     |
 | 7      8      4      | 6      9      1      | 3      2      5      |
 | 1      3      5      | 8      4      2      | 7      6      9      |
 *--------------------------------------------------------------------*
net
2r1c7-r1c4=r5c4-(2=4)r5c1-r2c1=r2c9-r7c9=4r7c8
||
4r1c7-----------r3c8
     -r1c2=r4c2-r4c8=4r7c8 => 4r7c8; ste


Isn't this what's known as "bifurcation"?

[ArkieTech]

Code: Select all

2r1c7-r1c4=r5c4-(2=4)r5c1-r2c1=r2c9-r7c9=4r7c8
||
4r1c7-----------r3c8
     -r1c2=r4c2-r4c8=4r7c8 => 4r7c8; ste

Isn't this what's known as "bifurcation"?

I don't know. I am still in "learning mode".

[JC Van Hay]

Code: Select all

2r1c7-r1c4=r5c4-(2=4)r5c1-r2c1=r2c9-r7c9=4r7c8
||
4r1c7-----------r3c8
     -r1c2=r4c2-r4c8=4r7c8 => 4r7c8; ste

Isn't this what's known as "bifurcation"?

I don't know. I am still in "learning mode".

No, AFAICT, Dan's chain is a "dynamic forcing chain" due to the "4r1c7-4r3c8" allowing, with -4r4c8, =4r7c8 (memory effect).
Notes : in the interpretations I gave of Dan's solution, I replaced the SISs 4C8+4R7 by (24)r6c7. Furthermore, as it is well clear from Marty's solution, the W-Ring and the Skyscraper are all that is needed to solve this puzzle!

[daj95376]

From Jeff's definitions, I interpret a network to be a forcing chain where secondary/memory eliminations are used to reach the final conclusion. Dan's solution matches my usage.

I tried calling it a Kraken Cell, but ronk insisted that term only applied to cells containing three or more candidates. As for other terms, I thought that it also worked as a Double-Implication Chain, but I believe that usage applied to bilocation and not bivalue. Besides, Sudopedia updated the definition of Double-Implication Chain and my usage was called the "old way".

As for my solver's solutions to this puzzle, I favor/chose the following:

Code: Select all

 after basics
 +-----------------------------------------------------------------------+
 |  346   *46     7      |  1234   1238   9      | *24     5      12348  |
 |  34     1      8      |  5      23     6      |  9      7      234    |
 |  5      9      2      |  134    1378   478    |  6      348    1348   |
 |-----------------------+-----------------------+-----------------------|
 |  2468  *46     13     |  9      1268   48     |  5      3-4    7      |
 |  24     5      9      |  234    237    47     |  8      1      6      |
 |  68     7      13     |  14     68     5      | *24     9      234    |
 |-----------------------+-----------------------+-----------------------|
 |  9      2      6      |  7      5      3      |  1      48     48     |
 |  7      8      4      |  6      9      1      |  3      2      5      |
 |  1      3      5      |  8      4      2      |  7      6      9      |
 +-----------------------------------------------------------------------+
 # 55 eliminations remain

 c27r1   Skyscraper                      <> 4    r4c8

 after additional basics
 +--------------------------------------------------------------+
 |  346  a46    7     |  23-4  18    9     |  24    5     18    |
 |  34    1     8     |  5     23    6     |  9     7     234   |
 |  5     9     2     | e34    178   78    |  6     48    1348  |
 |--------------------+--------------------+--------------------|
 |  2468 b46    1     |  9     268   48    |  5     3     7     |
 | c24    5     9     | d23    237   47    |  8     1     6     |
 |  68    7     3     |  1     68    5     |  24    9     24    |
 |--------------------+--------------------+--------------------|
 |  9     2     6     |  7     5     3     |  1     48    48    |
 |  7     8     4     |  6     9     1     |  3     2     5     |
 |  1     3     5     |  8     4     2     |  7     6     9     |
 +--------------------------------------------------------------+
 # 38 eliminations remain

 XY-Chain:  (4=6)r1c2 - (6=4)r4c2 - (4=2)r5c1 - (2=3)r5c4 - (3=4)r3c4  =>  r1c4<>4

 -or-

 S-Wing:    (2)r1c4 = r5c4 - (2=4)r5c1 - r4c2 = (4)r1c2  =>  r1c4<>4


According to the Sudopedia Mirror on this site, the definition of Bifurcation involves a contradiction for one candidate forcing a strongly-linked (companion) candidate to be true. That's definitely not the outcome in Dan's solution.

[Luke]

No, AFAICT, Dan's chain is a "dynamic forcing chain" due to the "4r1c7-4r3c8" allowing, with -4r4c8, =4r7c8 (memory effect).

I'm guessing that bifurcation is distinguished from a forcing chain. Bifurcation is choosing one of the two candidates of a bivalue cell and following it along either to a solution or a contradiction. A forcing chain follows each in turn until a common outcome is reached. How does that sound as a simplification?

Either way seems unattractive to me, unless I'm missing something.

[daj95376]

No, AFAICT, Dan's chain is a "dynamic forcing chain" due to the "4r1c7-4r3c8" allowing, with -4r4c8, =4r7c8 (memory effect).

I'm guessing that bifurcation is distinguished from a forcing chain. Bifurcation is choosing one of the two candidates of a bivalue cell and following it along either to a solution or a contradiction. A forcing chain follows each in turn until a common outcome is reached. How does that sound as a simplification?

Either way seems unattractive to me, unless I'm missing something.

I've been chastized severely in the past for saying that I believe that an AIC and a specific forcing chain structure are equivalent. On that note, please pretend that I didn't say the following:

Forcing Chain version of Skyscraper elimination:

Code: Select all

(4)r6c7                      - (4)r4c8
(4)r6c7 = r1c7 - r1c2 = r4c2 - (4)r4c8


The forcing chain says that the two possible states for <4> in r6c7 lead to a common outcome; r4c8<>4.

AIC/X-Chain version of Skyscraper:

Code: Select all

(4)r6c7 = r1c7 - r1c2 = r4c2  =>  r4c8<>4


For the AIC, r4c8=4 forces both ends of the chain false ... so it can be eliminated.

You say TOE-MAY-TOE and I say toe-may-toe.

[Marty R.]

You say TOE-MAY-TOE and I say toe-may-toe.

Doesn't one of you say toe-MAH-toe?

[DonM]

(Please assume that IMO is at the beginning of every paragraph )

This discussion is another indication as to how much has been lost with the complete wiping out of the Eureka forum. I feel like I'm living in a sudoku parallel universe where issues are being discussed as if they are new (where they were put to bed long ago) and methods that were long ago put in their place are being resurrected as if something new to use alongside more credible manual-solving methods (for a given puzzle difficulty).

Fwiw, the original Players' Forum gave us the gift of so many basic and advanced solving methods, but Eureka gave of us the gift of advanced manual solving and the best approaches to it. (Of course, there was cross-pollination between the two forums.) Around 2007, we had many discussions on the issues of assumptivity and bifurcation. (These discussions included some of the best manual solvers and math theorists.)

There was a lot of disagreement over what, in hindsight, appeared to be minutiae, but there was a general consensus over what was considered to be highly assumptive where assumptiveness generally refers to the level of assumptions made (ie. very close to, if not, guessing) used in a given method or in the overall approach to solving.

I used to refer to methods or patterns as either being 'what is' or 'what may be'. The least assumptive methods were 'what is' patterns such as naked pairs, x-wings, xy-wings and the like. All you had to do was recognize them and you could assume the result. When it came to chains/AICs, the 'what is' patterns could include simple chains based on transport. If one found an xy-wing and used transport to create a wider chain, then, again, the result spoke for itself.

However, as puzzles being solved became more difficult, more assumptive methods had to be developed and so you had the addition of various 'almost' patterns and finally, the use of AAICs (almost-AICs, unfortunately also called Kraken cell/row/column) and the like.

Part of the above discussion involved the premise of 'elegant' solving which partly means using the least assumptive methods for a puzzle as possible. That generally includes reserving the use of most nets for the most difficult puzzles (ie. somewhere around above ER=8.3). I don't think there's anything wrong with using nets for simpler puzzles if one is simply trying to learn how to use them- I did a lot of that in 2007- but once learned, I think that the real challenge of sudoku is to be an elegant solver: use simple methods for simple puzzles (which most of the puzzles in the section are) and reserve nets and the like for puzzles that deserve them.

During the same time there were these discussions and a lot of advanced manual solving on Eureka, there was a separate UK forum sub-section where the overall solving method was known as bifurcation or bifurcating. Generally, this always involved variations of making assumptions about what the value of a cell might be, particularly by splitting bivalue cells, and seeing where that leads. I never saw any change/improvement in the few methods that were used there and the process always seemed the same. Inevitably, variations of what are, by any measure that I know of, forcing chains (as a method-see below) would be used.

One can try to put lipstick on a pig by quoting definitions of forcing chains as found in the very old threads of Jeff (et al) where forcing chains were discussed generically and the term 'double-implication chain' was also used as a description, but the fact is that the use of forcing chains as a method as described here (http://www.sudokuassistant.co.uk/solving/solving-sudoku-forcing-chains.htm) is by any measure that I know of, bifurcating! And if one doesn't want to get their arms around that then forcing chains and/or splitting bivalue cells is highly assumptive compared to, say, a simple transport-derived chain.

PS. IMO, there are exceptions to the premise that nets are in the 'what may be' or more assumptive category. Examples of those exceptions are Empty Rectangles and Broken Wings-based solutions expressed as chains. The chains may inevitably be net-like, but the patterns are 'what is' patterns and the results are 'what is'.

[daj95376]

(Please assume that IMO is at the beginning of every paragraph )

.... I feel like I'm living in a sudoku parallel universe where issues are being discussed as if they are new (where they were put to bed long ago) and methods that were long ago put in their place are being resurrected as if something new to use alongside more credible manual-solving methods (for a given puzzle difficulty).

Yes, the discussions at the Eureka forum are lost ... and they weren't for everyone even when they existed. Learn to live with it!

BTW, congratulations on finding a link to the worst explanation of forcing chains that I've ever encountered! The site ever reversed cell locations by using [column,row]. Nice going DonM !!!

[DonM]

(Please assume that IMO is at the beginning of every paragraph )

.... I feel like I'm living in a sudoku parallel universe where issues are being discussed as if they are new (where they were put to bed long ago) and methods that were long ago put in their place are being resurrected as if something new to use alongside more credible manual-solving methods (for a given puzzle difficulty).

Yes, the discussions at the Eureka forum are lost ... and they weren't for everyone even when they existed. Learn to live with it!

I'll try Dr. Freud. Still, you might have a different perspective on the subject at hand if you had taken a little time out from programming to follow some of those discussions.

BTW, congratulations on finding a link to the worst explanation of forcing chains that I've ever encountered! The site ever reversed cell locations by using [column,row]. Nice going DonM !!!

I'm sorry that that example didn't work for you. Here are a number of others that appear to use the same (according to you 'worst') explanations. The forcing chain method as described in them is the same one I used when I started solving in late 2005. Even when I read Jeff's generic definition of forcing chains I was able to distinguish it from the forcing chain 'method'.

http://www.sudokuoftheday.com/pages/techniques-10.php
http://www.sadmansoftware.com/sudoku/forcingchain.htm
http://www.intosudoku.com/Doc/ForcingChain.html
http://www.sudoku129.com/puzzles/tips_44.php
http://sudoku.awardspace.biz/solving_sudoku_advanced.php?technique_id=Forcing%20chain