Does anyone know if anywhere, there is a list of ALS Rings that I can peruse over, preferably rings of varying lengths, and in a format that they can be loaded into Hodoku (so I can get a visual on them).
Thanks in advance.
ALS Loops/Rings
12 posts
• Page 1 of 1
Re: ALS Loops/Rings
by StrmCkr » Wed Oct 01, 2025 3:33 am
Als xz 2 rcc rule => ring
als xy 3 rcc rule => ring
n als n rcc => ring
To view it easier treat als as aic
First and last node are weakn inferences its a ring
https://reddit.com/r/sudoku/w/ALS-terminology
I have all this on my reddit wiki summerizing the 20 years of data on this forum
als xy 3 rcc rule => ring
n als n rcc => ring
To view it easier treat als as aic
First and last node are weakn inferences its a ring
https://reddit.com/r/sudoku/w/ALS-terminology
I have all this on my reddit wiki summerizing the 20 years of data on this forum
Some do, some teach, the rest look it up.
stormdoku
stormdoku
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StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by Wepwawet » Thu Oct 02, 2025 12:09 am
Thanks, but the link you supplied had little info that I am not already aware of, most of it, as usual being overkill on techno babble, but, I guess, that is your style. My advice is to keep it simple and cease employing so many acronyms, and if they are used, have an appendum at the end to explain what they mean, otherwise, it is meaningless to most of the readership, and a huge turn off for most of them, rushing them to read something else.
That aside, you missed the gist of my request in my post, what I was looking for was a list, or a compendium of examples, for what you call N-ALS / N-RCC Ring Structures (and why for God's sake wasn't it called something like ALS Chain Continuous Loop, that regular Sudoku advocates could relate to).
It appears that they (N-ALS / N-RCC Ring Structures) are not that common.
That aside, you missed the gist of my request in my post, what I was looking for was a list, or a compendium of examples, for what you call N-ALS / N-RCC Ring Structures (and why for God's sake wasn't it called something like ALS Chain Continuous Loop, that regular Sudoku advocates could relate to).
It appears that they (N-ALS / N-RCC Ring Structures) are not that common.
Wept
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Wepwawet - Posts: 35
- Joined: 19 November 2019
Re: ALS Loops/Rings
by StrmCkr » Thu Oct 02, 2025 1:48 am
Cause loops are from Niceloops not aic, (niceloops arent used any more) .
Als are part of Aic not niceloops.
Aic closed systems are rings, the name is just "als Ring" for display
When you have a collection als Nodes ie N of them in chain from you have n-1 weak inferences connecting them
When first and last have also have another weak inference we now have exactlly N weak inferences.
Which is the ring rule for als past size 3 hence the rule name.
Examples
my solver has these coded there is a large number of them, they are fairly common.
The wiki has examples for als xz (2rcc rule) , als xy (3 rcc rule) projecting to larger node counts isnt to hard
Like this:
(a=b) r1c1 - (b=d) r1c5 - (c=f) r5c5 - (f=a)r5c1 -ring
Ill post some grid examples tommarow.
Ps
The acronyms are defined at the start of the parent topics and carried onward throught the subtopics. My readers are haveing little issue reading the topics and following.
Yes i perfer technical, as every time i reduce the content down to less wordy people apply it wrong and more issies arive. All lthe topics have been Eli5 endlessly as most of reddit followers arent math savy in a method thats math based..
Als are part of Aic not niceloops.
Aic closed systems are rings, the name is just "als Ring" for display
When you have a collection als Nodes ie N of them in chain from you have n-1 weak inferences connecting them
When first and last have also have another weak inference we now have exactlly N weak inferences.
Which is the ring rule for als past size 3 hence the rule name.
Examples
my solver has these coded there is a large number of them, they are fairly common.
The wiki has examples for als xz (2rcc rule) , als xy (3 rcc rule) projecting to larger node counts isnt to hard
Like this:
(a=b) r1c1 - (b=d) r1c5 - (c=f) r5c5 - (f=a)r5c1 -ring
Ill post some grid examples tommarow.
Ps
The acronyms are defined at the start of the parent topics and carried onward throught the subtopics. My readers are haveing little issue reading the topics and following.
Yes i perfer technical, as every time i reduce the content down to less wordy people apply it wrong and more issies arive. All lthe topics have been Eli5 endlessly as most of reddit followers arent math savy in a method thats math based..
Some do, some teach, the rest look it up.
stormdoku
stormdoku
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StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by Wepwawet » Thu Oct 02, 2025 2:50 am
I understand the Nice Loop terminology is no longer used, hence me not including the word Nice.
I look forward to you posting some examples of some ALS rings. preferably, those consisting of more that 3 ALS's.
Thanks, in advance.
I look forward to you posting some examples of some ALS rings. preferably, those consisting of more that 3 ALS's.
Thanks, in advance.
Wept
-
Wepwawet - Posts: 35
- Joined: 19 November 2019
Re: ALS Loops/Rings
by StrmCkr » Thu Oct 02, 2025 3:47 pm
note: all the following examples are from a max BFS of 8.
{3 RCC} Ring Rule examples:
ALS - XY: A=r17c7 {138}, B=r7c3 {37}, C=r3c2378 {13457}, X:(AB =3), (BC =7), (CA =1) => r7c258 <> 3
ALS - XY: A=r1c7 {18}, B=r7c37 {378}, C=r3c2378 {13457}, X:(AB =8), (BC =7), (CA =1) => r7c258 <> 3
ALS - XY: A=r2c9 {45}, B=r8c169 {2457}, C=r3c1278 {13457}, X:(AB =5), (BC =7), (CA =4) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r17c7 {138}, B=r7c37 {378}, C=r3c2378 {13457}, X:(AB =8), (BC =7), (CA =1) => r7c258 <> 3
ALS - XY: A=r7c23578 {234678}, B=r3c1278 {13457}, C=r8c1 {27}, X:(AB =4), (BC =7), (CA =2) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r1c27 {128}, B=r7c23578 {234678}, C=r3c278 {1345}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r38c1 {127}, B=r7c23578 {234678}, C=r3c278 {1345}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p23589 {234578}, B=r7c37 {378}, C=r1c57 {128}, X:(AB =7), (BC =8), (CA =2) => r7c258 <> 3
ALS - XY: A=r38c1 {127}, B=r7c23578 {234678}, C=r3c1278 {13457}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r3c1278 {13457}, B=r8c169 {2457}, C=b9p12578 {234568}, X:(AB =7), (BC =5), (CA =4) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p235789 {1234578}, B=r7c23578 {234678}, C=r3c278 {1345}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p23589 {234578}, B=r3c1278 {13457}, C=r7c23578 {234678}, X:(AB =7), (BC =4), (CA =2) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p235789 {1234578}, B=r7c23578 {234678}, C=r3c1278 {13457}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
{N RCC} Ring Rule Examples:
ALS - Ring: (1=7)r3c1-(7)r8c1=(245)r8c169-(5=4)r2c9-(4)r3c8=(351)r3c278-(1)r3c1 => r3c7 <> 5; r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=8)r1c7-(8=3)r7c7-(3=7)r7c3-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2=1)r2c5-(1)r2c1 => r7c258 <> 3
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5=4)r2c9-(4)r3c8=(351)r3c278-(1)r3c1 => r3c7 <> 5; r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2=7)r8c1-(7)r3c1=(1354)r3c1278-(4=5)r2c9-(5)r8c9=(42)r8c69-(2)r8c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (3=4)r1c4-(4)r1c3=(37)r17c3-(7)r8c1=(245)r8c169-(5)r2c9=(43)r2c49-(3)r1c4 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (4=5)r2c9-(5=4)r8c9-(4)r8c6=(27)r8c16-(7)r3c1=(1354)r3c1278-(4)r2c9 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(72)r38c1-(2)r8c6=(45)r8c69-(5=4)r2c9-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r7c258,r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r8c6=(45)r8c69-(5=4)r2c9-(4)r3c8=(1357)r3c1278-(7)r8c1=(42)r8c16-(2)r8c6 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=8)r1c7-(8=2)r1c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7=3)r7c3-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7)r7c3=(38)r7c37-(8=1)r1c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1=2)r1c5-(2)r1c2=(34587)b1p23589-(7=3)r7c3-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1=2)r1c5-(2)r1c2=(34587)b1p23589-(7)r7c3=(38)r7c37-(8=1)r1c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5=4)r2c9-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=7)r3c1-(7=2)r8c1-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2=8)r1c2-(8)r2c2=(3457)b1p3589-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (2)r1c2=(34587)b1p23589-(7=3)r7c3-(3=8)r7c7-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (1)r1c7=(82)r1c27-(2)r1c5=(18)r1c57-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c23=(672)b7p234-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r7c258,r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c23=(276)b7p234-(6)r7c58=(3784)r7c3578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r7c258,r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3=7)r7c3-(7)r3c3=(34582)b1p23589-(2)r1c5=(81)r1c57-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r2c1=(17)r23c1-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7=3)r7c3-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7)r7c3=(38)r7c37-(8=1)r1c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7)r7c3=(38)r7c37-(8)r1c7=(21)r1c57-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7)r7c3=(83)r7c37-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1=2)r1c5-(2)r1c2=(34587)b1p23589-(7)r7c3=(83)r7c37-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r8c1=(24)r8c16-(4=2)r7c6-(2)r7c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(38)r17c7-(8)r7c7=(37)r7c37-(7)r3c3=(34582)b1p23589-(2)r1c5=(81)r1c57-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3=7)r7c3-(7)r3c3=(3458)b1p3589-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1=8)r1c7-(8)r7c7=(37)r7c37-(7)r3c3=(3458)b1p3589-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7)r7c3=(38)r7c37-(8)r1c7=(21)r1c57-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7)r7c3=(83)r7c37-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3562)r2378c2-(2)r8c1=(73)b7p34-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2=1)r2c5-(1)r2c1 => r7c258 <> 3
ALS - Ring: (2)r1c2=(583)r123c2-(3)r13c3=(47)r13c3-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (3=4)r1c4-(4)r1c3=(123587)b1p234578-(7)r8c1=(245)r8c169-(5)r2c9=(43)r2c49-(3)r1c4 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(43)r13c3-(3)r7c3=(72)b7p34-(2)r7c2 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(38)r17c7-(8)r7c7=(37)r7c37-(7)r3c3=(3458)b1p3589-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r78c2=(367)b7p235-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r8c1=(71)r38c1-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(134572)b1p345789-(2)r8c1=(73)b7p34-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2=(345781)b1p235789-(1)r2c1 => r7c258 <> 3
ALS - Ring: (1)r3c1=(72)r38c1-(2)r8c6=(45)r8c69-(5)r8c8=(23684)b9p12578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=7)r3c1-(7)r8c1=(245)r8c169-(5)r8c8=(23684)b9p12578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(473)b1p379-(3)r7c3=(72)b7p34-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (2)r1c2=(583)r123c2-(3)r78c2=(267)b7p245-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (2=7)r8c1-(7)r3c1=(1354)r3c1278-(4)r78c8=(23685)b9p12578-(5)r8c9=(42)r8c69-(2)r8c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (4)r3c8=(1357)r3c1278-(7)r8c1=(24)r8c16-(4=5)r8c9-(5)r8c8=(23684)b9p12578-(4)r3c8 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r8c1=(263)b7p245-(3)r7c3=(72)b7p34-(2)r7c2 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r39c7=(1258)r1349c7-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r78c2=(3568)r2378c2-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r3c1=(72)r38c1-(2)r8c6=(45)r8c69-(5)r8c8=(23684)b9p12578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5)r8c8=(23684)b9p12578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(34578)b1p35789-(8=2)r1c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=7)r3c1-(7)r3c3=(34582)b1p23589-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(473)b1p379-(3)r7c3=(72)b7p34-(2)r7c2=(36784)r7c23578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (2=8)r1c2-(8)r2c2=(3457)b1p3589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r8c6=(45)r8c69-(5)r8c8=(23684)b9p12578-(4)r3c8=(1357)r3c1278-(7)r8c1=(42)r8c16-(2)r8c6 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(82)r1c27-(2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(3451)r3c2378-(1)r1c7 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r2c1=(134578)b1p345789-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1=8)r1c7-(8)r7c7=(376)r7c357-(6)r7c28=(23487)r7c23678-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r3c1=(345782)b1p235789-(2)r1c5=(18)r1c57-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r3c1 => r7c258 <> 3
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5)r8c8=(23684)b9p12578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(72)r38c1-(2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(3451)r3c2378-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(34578)b1p35789-(8=2)r1c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (3)r2c28=(584)r2c289-(4)r3c8=(1357)r3c1278-(7)r8c1=(245)r8c169-(5)r2c9=(43)r2c49-(3)r2c28 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(38)r17c7-(8)r7c7=(376)r7c357-(6)r7c28=(23487)r7c23678-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c35=(76)r7c35-(6)r7c28=(23487)r7c23678-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r3c1=(473)b1p379-(3)r23c2=(582)r123c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r1c2=(583)r123c2-(3)r13c3=(47)r13c3-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)b9p2578=(24568)b9p25678-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r8c1=(71)r38c1-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c2358=(24678)r7c23568-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2=(345781)b1p235789-(1)r2c1 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2=(345781)b1p235789-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(473)b1p379-(3)r23c2=(582)r123c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r1c2=(34587)b1p23589-(7)r7c3=(23486)r7c23678-(6)r7c5=(378)r7c357-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (2)r1c2=(583)r123c2-(3)r78c2=(267)b7p245-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r8c1=(24)r8c16-(4)r8c89=(35672)r8c12589-(2)r7c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(345782)b1p235789-(2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(3451)r3c2378-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2=(345781)b1p235789-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
- Code: Select all
.--------------.-------------.---------------.
| 6 28 34 | 34 12 5 | 18 7 9 |
| 12 358 9 | 34 12 7 | 6 3458 45 |
| 17 35 347 | 6 9 8 | 135 345 2 |
:--------------+-------------+---------------:
| 8 7 6 | 9 4 1 | 25 25 3 |
| 3 1 2 | 7 5 6 | 4 9 8 |
| 4 9 5 | 2 8 3 | 7 1 6 |
:--------------+-------------+---------------:
| 9 236 37 | 5 367 24 | 38 3468 1 |
| 27 236 8 | 1 367 24 | 9 3456 45 |
| 5 4 1 | 8 36 9 | 23 236 7 |
'--------------'-------------'---------------'
{3 RCC} Ring Rule examples:
ALS - XY: A=r17c7 {138}, B=r7c3 {37}, C=r3c2378 {13457}, X:(AB =3), (BC =7), (CA =1) => r7c258 <> 3
ALS - XY: A=r1c7 {18}, B=r7c37 {378}, C=r3c2378 {13457}, X:(AB =8), (BC =7), (CA =1) => r7c258 <> 3
ALS - XY: A=r2c9 {45}, B=r8c169 {2457}, C=r3c1278 {13457}, X:(AB =5), (BC =7), (CA =4) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r17c7 {138}, B=r7c37 {378}, C=r3c2378 {13457}, X:(AB =8), (BC =7), (CA =1) => r7c258 <> 3
ALS - XY: A=r7c23578 {234678}, B=r3c1278 {13457}, C=r8c1 {27}, X:(AB =4), (BC =7), (CA =2) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r1c27 {128}, B=r7c23578 {234678}, C=r3c278 {1345}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r38c1 {127}, B=r7c23578 {234678}, C=r3c278 {1345}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p23589 {234578}, B=r7c37 {378}, C=r1c57 {128}, X:(AB =7), (BC =8), (CA =2) => r7c258 <> 3
ALS - XY: A=r38c1 {127}, B=r7c23578 {234678}, C=r3c1278 {13457}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=r3c1278 {13457}, B=r8c169 {2457}, C=b9p12578 {234568}, X:(AB =7), (BC =5), (CA =4) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p235789 {1234578}, B=r7c23578 {234678}, C=r3c278 {1345}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p23589 {234578}, B=r3c1278 {13457}, C=r7c23578 {234678}, X:(AB =7), (BC =4), (CA =2) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - XY: A=b1p235789 {1234578}, B=r7c23578 {234678}, C=r3c1278 {13457}, X:(AB =2), (BC =4), (CA =1) => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
{N RCC} Ring Rule Examples:
ALS - Ring: (1=7)r3c1-(7)r8c1=(245)r8c169-(5=4)r2c9-(4)r3c8=(351)r3c278-(1)r3c1 => r3c7 <> 5; r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=8)r1c7-(8=3)r7c7-(3=7)r7c3-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2=1)r2c5-(1)r2c1 => r7c258 <> 3
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5=4)r2c9-(4)r3c8=(351)r3c278-(1)r3c1 => r3c7 <> 5; r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2=7)r8c1-(7)r3c1=(1354)r3c1278-(4=5)r2c9-(5)r8c9=(42)r8c69-(2)r8c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (3=4)r1c4-(4)r1c3=(37)r17c3-(7)r8c1=(245)r8c169-(5)r2c9=(43)r2c49-(3)r1c4 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (4=5)r2c9-(5=4)r8c9-(4)r8c6=(27)r8c16-(7)r3c1=(1354)r3c1278-(4)r2c9 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(72)r38c1-(2)r8c6=(45)r8c69-(5=4)r2c9-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r7c258,r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r8c6=(45)r8c69-(5=4)r2c9-(4)r3c8=(1357)r3c1278-(7)r8c1=(42)r8c16-(2)r8c6 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=8)r1c7-(8=2)r1c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7=3)r7c3-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7)r7c3=(38)r7c37-(8=1)r1c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1=2)r1c5-(2)r1c2=(34587)b1p23589-(7=3)r7c3-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1=2)r1c5-(2)r1c2=(34587)b1p23589-(7)r7c3=(38)r7c37-(8=1)r1c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5=4)r2c9-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=7)r3c1-(7=2)r8c1-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2=8)r1c2-(8)r2c2=(3457)b1p3589-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (2)r1c2=(34587)b1p23589-(7=3)r7c3-(3=8)r7c7-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (1)r1c7=(82)r1c27-(2)r1c5=(18)r1c57-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c23=(672)b7p234-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r7c258,r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c23=(276)b7p234-(6)r7c58=(3784)r7c3578-(4)r3c8=(351)r3c278-(1)r1c7 => r28c8 <> 4; r7c258,r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3=7)r7c3-(7)r3c3=(34582)b1p23589-(2)r1c5=(81)r1c57-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r2c1=(17)r23c1-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7=3)r7c3-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7)r7c3=(38)r7c37-(8=1)r1c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7)r7c3=(38)r7c37-(8)r1c7=(21)r1c57-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3457)b1p3589-(7)r7c3=(83)r7c37-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1=2)r1c5-(2)r1c2=(34587)b1p23589-(7)r7c3=(83)r7c37-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r8c1=(24)r8c16-(4=2)r7c6-(2)r7c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(38)r17c7-(8)r7c7=(37)r7c37-(7)r3c3=(34582)b1p23589-(2)r1c5=(81)r1c57-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3=7)r7c3-(7)r3c3=(3458)b1p3589-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1=8)r1c7-(8)r7c7=(37)r7c37-(7)r3c3=(3458)b1p3589-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7)r7c3=(38)r7c37-(8)r1c7=(21)r1c57-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(82)r1c25-(2)r1c2=(34587)b1p23589-(7)r7c3=(83)r7c37-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(3562)r2378c2-(2)r8c1=(73)b7p34-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2=1)r2c5-(1)r2c1 => r7c258 <> 3
ALS - Ring: (2)r1c2=(583)r123c2-(3)r13c3=(47)r13c3-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (3=4)r1c4-(4)r1c3=(123587)b1p234578-(7)r8c1=(245)r8c169-(5)r2c9=(43)r2c49-(3)r1c4 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(43)r13c3-(3)r7c3=(72)b7p34-(2)r7c2 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(38)r17c7-(8)r7c7=(37)r7c37-(7)r3c3=(3458)b1p3589-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r78c2=(367)b7p235-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r8c1=(71)r38c1-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c5=(28)r1c25-(8)r2c2=(134572)b1p345789-(2)r8c1=(73)b7p34-(3)r7c7=(81)r17c7-(1)r1c5 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2=(345781)b1p235789-(1)r2c1 => r7c258 <> 3
ALS - Ring: (1)r3c1=(72)r38c1-(2)r8c6=(45)r8c69-(5)r8c8=(23684)b9p12578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=7)r3c1-(7)r8c1=(245)r8c169-(5)r8c8=(23684)b9p12578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(473)b1p379-(3)r7c3=(72)b7p34-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (2)r1c2=(583)r123c2-(3)r78c2=(267)b7p245-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (2=7)r8c1-(7)r3c1=(1354)r3c1278-(4)r78c8=(23685)b9p12578-(5)r8c9=(42)r8c69-(2)r8c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (4)r3c8=(1357)r3c1278-(7)r8c1=(24)r8c16-(4=5)r8c9-(5)r8c8=(23684)b9p12578-(4)r3c8 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r8c1=(263)b7p245-(3)r7c3=(72)b7p34-(2)r7c2 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r39c7=(1258)r1349c7-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r78c2=(3568)r2378c2-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r3c1=(72)r38c1-(2)r8c6=(45)r8c69-(5)r8c8=(23684)b9p12578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5)r8c8=(23684)b9p12578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(34578)b1p35789-(8=2)r1c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1=7)r3c1-(7)r3c3=(34582)b1p23589-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(473)b1p379-(3)r7c3=(72)b7p34-(2)r7c2=(36784)r7c23578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3,r7c8 <> 3; r8c2 <> 2
ALS - Ring: (2=8)r1c2-(8)r2c2=(3457)b1p3589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r8c6=(45)r8c69-(5)r8c8=(23684)b9p12578-(4)r3c8=(1357)r3c1278-(7)r8c1=(42)r8c16-(2)r8c6 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(82)r1c27-(2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(3451)r3c2378-(1)r1c7 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c3=(72)b7p34-(2)r2c1=(134578)b1p345789-(8)r2c8=(3451)b3p5678-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1=8)r1c7-(8)r7c7=(376)r7c357-(6)r7c28=(23487)r7c23678-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r3c1=(345782)b1p235789-(2)r1c5=(18)r1c57-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r3c1 => r7c258 <> 3
ALS - Ring: (1)r3c1=(27)r38c1-(7)r8c1=(245)r8c169-(5)r8c8=(23684)b9p12578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(72)r38c1-(2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(3451)r3c2378-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(34578)b1p35789-(8=2)r1c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (3)r2c28=(584)r2c289-(4)r3c8=(1357)r3c1278-(7)r8c1=(245)r8c169-(5)r2c9=(43)r2c49-(3)r2c28 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(38)r17c7-(8)r7c7=(376)r7c357-(6)r7c28=(23487)r7c23678-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c35=(76)r7c35-(6)r7c28=(23487)r7c23678-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r3c1=(473)b1p379-(3)r23c2=(582)r123c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(351)r3c278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r1c2=(583)r123c2-(3)r13c3=(47)r13c3-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)b9p2578=(24568)b9p25678-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r8c1=(71)r38c1-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r1c7=(83)r17c7-(3)r7c2358=(24678)r7c23568-(8)r7c7=(37)r7c37-(7)r3c3=(3451)r3c2378-(1)r1c7 => r7c258 <> 3
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r7c3=(38)r7c37-(8)r1c7=(12)r1c57-(2)r1c2=(345781)b1p235789-(1)r2c1 => r7c258 <> 3
ALS - Ring: (1)r2c1=(27)r28c1-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2=(345781)b1p235789-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(473)b1p379-(3)r23c2=(582)r123c2-(2)r7c2=(36784)r7c23578-(4)r3c8=(3571)r3c1278-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r1c2=(34587)b1p23589-(7)r7c3=(23486)r7c23678-(6)r7c5=(378)r7c357-(8)r1c7=(12)r1c57-(2)r1c2 => r7c258 <> 3
ALS - Ring: (2)r1c2=(583)r123c2-(3)r78c2=(267)b7p245-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r8c1=(24)r8c16-(4)r8c89=(35672)r8c12589-(2)r7c2 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r3c1=(345782)b1p235789-(2)r7c2=(36784)r7c23578-(4)r3c8=(1357)r3c1278-(7)r3c3=(3451)r3c2378-(1)r3c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2=(345781)b1p235789-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
Last edited by StrmCkr on Thu Oct 02, 2025 5:24 pm, edited 1 time in total.
Some do, some teach, the rest look it up.
stormdoku
stormdoku
-
StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by StrmCkr » Thu Oct 02, 2025 5:00 pm
- Code: Select all
.---------------------.---------------.-----------------.
| 1689 169 4 | 168 18 2 | 5 3 7 |
| 258 257 3 | 9 4 57 | 6 1 28 |
| 12568 12567 15678 | 3 178 567 | 24 289 2489 |
:---------------------+---------------+-----------------:
| 148 3 18 | 28 5 9 | 7 24 6 |
| 459 59 2 | 7 6 3 | 8 49 1 |
| 7 69 68 | 4 28 1 | 23 5 239 |
:---------------------+---------------+-----------------:
| 1256 12567 1567 | 126 9 467 | 234 268 23458 |
| 256 4 9 | 26 3 8 | 1 7 25 |
| 3 8 167 | 5 127 467 | 9 26 24 |
'---------------------'---------------'-----------------'
{N RCC} Ring Rule Examples:
ALS - Ring: (1)r4c3=(689)b4p389-(9)r6c9=(238)r6c579-(8)r13c5=(172)r139c5-(2)r9c89=(4671)r9c3689-(1)r4c3 => r3c3 <> 1, 8; r4c1 <> 8; r9c5 <> 7; r7c3 <> 1
ALS - Ring: (1)r4c3=(86)r46c3-(6)r6c2=(2398)r6c2579-(8)r13c5=(172)r139c5-(2)r9c89=(4671)r9c3689-(1)r4c3 => r3c3 <> 1, 8; r4c1 <> 8; r9c5 <> 7; r7c3 <> 1
ALS - Ring: (1)r4c3=(896)b4p389-(6)r6c2=(2398)r6c2579-(8)r13c5=(172)r139c5-(2)r9c89=(4671)r9c3689-(1)r4c3 => r3c3 <> 1, 8; r4c1 <> 8; r9c5 <> 7; r7c3 <> 1
ALS - Ring: (1)r4c3=(82)r4c34-(2)r78c4=(168)r178c4-(8)r13c5=(172)r139c5-(2)r9c89=(4671)r9c3689-(1)r4c3 => r4c1 <> 8; r9c5 <> 7; r37c3 <> 1
ALS - Ring: (1)r4c3=(82)r4c34-(2=8)r6c5-(8)r13c5=(172)r139c5-(2)r9c89=(4671)r9c3689-(1)r4c3 => r4c1 <> 8; r9c5 <> 7; r37c3 <> 1
Some do, some teach, the rest look it up.
stormdoku
stormdoku
-
StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by StrmCkr » Thu Oct 02, 2025 5:06 pm
- Code: Select all
.-------------------.----------------.------------------.
| 147 8 5 | 3 9 167 | 2467 124 1267 |
| 6 2 1347 | 147 5 8 | 47 134 9 |
| 1479 1347 13479 | 1467 2 167 | 5 8 1367 |
:-------------------+----------------+------------------:
| 1457 9 147 | 267 8 2567 | 3 1245 1256 |
| 3 1567 17 | 2679 4 25679 | 269 1259 8 |
| 8 456 2 | 69 1 3 | 469 7 56 |
:-------------------+----------------+------------------:
| 1459 1345 6 | 1289 7 129 | 289 2359 235 |
| 2 137 13789 | 5 6 19 | 789 39 4 |
| 579 57 789 | 289 3 4 | 1 6 257 |
'-------------------'----------------'------------------'
{3 RCC} Ring Rule examples:
ALS - XY: A=r7c46789 {123589}, B=r8c8 {39}, C=r8c6 {19}, X:(AB =3), (BC =9), (CA =1) => r7c1 <> 5, 9; r8c37 <> 9; r7c2,r9c9 <> 5
ALS - XY: A=r9c1234 {25789}, B=r8c2368 {13789}, C=r9c1239 {25789}, X:(AB =7), (BC =8), (CA =2) => r7c1 <> 5, 9; r8c37,r9c4 <> 9; r7c2,r9c9 <> 5
ALS - XY: A=b9p12345 {235789}, B=r8c2368 {13789}, C=r9c1239 {25789}, X:(AB =7), (BC =8), (CA =2) => r7c1 <> 5, 9; r8c37,r9c4 <> 9; r7c2,r9c9 <> 5
ALS - XY: A=b8p136 {1289}, B=b9p12359 {235789}, C=r9c1234 {25789}, X:(AB =8), (BC =7), (CA =2) => r8c7,r9c4 <> 9; r7c12,r9c9 <> 5
ALS - XY: A=b8p136 {1289}, B=b9p12359 {235789}, C=b9p12345 {235789}, X:(AB =8), (BC =7), (CA =2) => r8c7,r9c4 <> 9; r7c12,r9c9 <> 5
ALS - XY: A=b8p136 {1289}, B=r12567c7 {246789}, C=b9p12345 {235789}, X:(AB =8), (BC =7), (CA =2) => r8c7,r9c4 <> 9; r7c12,r9c9 <> 5
ALS - XY: A=r234567c4 {1246789}, B=b9p12359 {235789}, C=r9c1234 {25789}, X:(AB =8), (BC =7), (CA =2) => r8c7,r9c4 <> 9; r7c12,r9c9 <> 5
ALS - XY: A=b7p56789 {135789}, B=r8c8 {39}, C=r8c6 {19}, X:(AB =3), (BC =9), (CA =1) => r7c1 <> 5, 9; r8c37 <> 9; r7c2,r9c9 <> 5
Some do, some teach, the rest look it up.
stormdoku
stormdoku
-
StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by StrmCkr » Thu Oct 02, 2025 5:11 pm
- Code: Select all
.------------------.-------------------.-------------------.
| 6 34589 579 | 12457 14579 29 | 347 34789 3479 |
| 349 34589 579 | 457 4579 6 | 1 34789 2 |
| 49 1 2 | 47 3 8 | 6 479 5 |
:------------------+-------------------+-------------------:
| 29 259 59 | 6 47 347 | 8 1 347 |
| 1 6 3 | 247 8 29 | 5 2479 479 |
| 8 7 4 | 123 19 5 | 23 239 6 |
:------------------+-------------------+-------------------:
| 5 34 1 | 8 2 347 | 9 6 347 |
| 7 234 8 | 9 6 34 | 234 5 1 |
| 2349 2349 6 | 3457 457 1 | 2347 2347 8 |
'------------------'-------------------'-------------------'
{2 RCC rule}
VWXYZ - Ring: A=b2p2457 {14579}, B=r6c5 {19}, X:(AB=9), (BA=1) => r1c4 <> 4, 5, 7
{3 RCC rule}
ALS - XY: A=b2p23457 {124579}, B=r5c6 {29}, C=r6c5 {19}, X:(AB =2), (BC =9), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=b2p2457 {14579}, B=r1c6 {29}, C=b5p68 {129}, X:(AB =9), (BC =2), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=r1c2356789 {12345789}, B=r5c6 {29}, C=r6c5 {19}, X:(AB =2), (BC =9), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=r23569c4 {123457}, B=r5c6 {29}, C=r6c5 {19}, X:(AB =2), (BC =9), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=b2p23457 {124579}, B=b2p12457 {124579}, C=r6c5 {19}, X:(AB =2), (BC =9), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=r1c235789 {1345789}, B=r1c6 {29}, C=b5p68 {129}, X:(AB =9), (BC =2), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=b2p2457 {14579}, B=b5p23478 {123479}, C=b5p68 {129}, X:(AB =9), (BC =2), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=r23569c4 {123457}, B=b2p12457 {124579}, C=r6c5 {19}, X:(AB =2), (BC =9), (CA =1) => r1c4 <> 4, 5, 7
ALS - XY: A=r1c2356789 {12345789}, B=b2p12457 {124579}, C=r6c5 {19}, X:(AB =2), (BC =9), (CA =1) => r1c4 <> 4, 5, 7
{N RCC rule}
ALS - Ring: (1)r1c5=(4579)b2p2457-(9=2)r1c6-(2=9)r5c6-(9=1)r6c5-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r1c5=(345789)r1c235789-(9=2)r1c6-(2=9)r5c6-(9=1)r6c5-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(34572)r23569c4-(2)r1c4=(14579)b2p12457-(9=2)r1c6-(2)r5c6=(91)b5p68-(1)r6c4 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r1c5=(345789)r1c235789-(9=2)r1c6-(2)r1c4=(14579)b2p12457-(9=1)r6c5-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r1c5=(45792)b2p23457-(2)r1c4=(14579)b2p12457-(9)r6c5=(13472)b5p23478-(2)r5c6=(91)b5p68-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(34572)r23569c4-(2)r1c4=(1345789)r1c2345789-(9=2)r1c6-(2)r5c6=(91)b5p68-(1)r6c4 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(34572)r23569c4-(2)r1c4=(14579)b2p12457-(9=2)r1c6-(2=9)r5c6-(9=1)r6c5-(1)r6c4 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(34572)r23569c4-(2=9)r5c6-(9=2)r1c6-(2)r1c4=(14579)b2p12457-(9=1)r6c5-(1)r6c4 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r1c5=(3457892)r1c2356789-(2)r1c4=(14579)b2p12457-(9)r6c5=(13472)b5p23478-(2)r5c6=(91)b5p68-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(239)r6c478-(9)r6c5=(13472)b5p23478-(2)r1c4=(14579)b2p12457-(9=2)r1c6-(2)r5c6=(91)b5p68-(1)r6c4 => r1c8 <> 9
ALS - Ring: (1)r6c4=(34572)r23569c4-(2)r1c4=(1345789)r1c2345789-(9=2)r1c6-(2=9)r5c6-(9=1)r6c5-(1)r6c4 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(239)r6c478-(9)r5c89=(472)r5c489-(2=9)r5c6-(9=2)r1c6-(2)r1c4=(14579)b2p12457-(9=1)r6c5-(1)r6c4 => r1c8 <> 9
ALS - Ring: (1)r1c5=(345789)r1c235789-(9=2)r1c6-(2)r1c4=(14579)b2p12457-(9)r6c5=(13472)b5p23478-(2)r5c6=(91)b5p68-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r1c5=(4579)b2p2457-(9)r6c5=(13472)b5p23478-(2)r1c4=(1345789)r1c2345789-(9=2)r1c6-(2)r5c6=(91)b5p68-(1)r1c5 => r1c4 <> 4, 5, 7
ALS - Ring: (1)r6c4=(239)r6c478-(9)r6c5=(13472)b5p23478-(2)r1c4=(1345789)r1c2345789-(9=2)r1c6-(2)r5c6=(91)b5p68-(1)r6c4 => r1c8 <> 9
Some do, some teach, the rest look it up.
stormdoku
stormdoku
-
StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by StrmCkr » Thu Oct 02, 2025 5:22 pm
- Code: Select all
.---------------.-----------.--------------.
| 8 29 5 | 6 17 3 | 79 12 4 |
| 1 7 4 | 9 2 5 | 3 68 68 |
| 29 3 6 | 4 17 8 | 5 12 79 |
:---------------+-----------+--------------:
| 3469 469 2 | 5 8 1 | 67 346 367 |
| 56 8 7 | 2 3 4 | 1 9 56 |
| 345 145 13 | 7 6 9 | 8 345 2 |
:---------------+-----------+--------------:
| 356 156 8 | 13 9 2 | 4 7 356 |
| 2346 246 9 | 8 5 7 | 26 36 1 |
| 7 25 13 | 13 4 6 | 29 58 589 |
'---------------'-----------'--------------'
{3 RCC rule} { note: noticed my above posts didn't have the "ring" in my output code fixed it for this one. }
ALS - XY - Ring: A=r257c9 {3568}, B=r2c8 {68}, C=r8c8 {36}, X:(AB =8), (BC =6), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r8c78 {236}, B=r2579c9 {35689}, C=r9c7 {29}, X:(AB =3), (BC =9), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r57c9 {356}, B=r2c9 {68}, C=r28c8 {368}, X:(AB =6), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2579c9 {35689}, B=r89c7 {269}, C=r8c8 {36}, X:(AB =9), (BC =6), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r5c9 {56}, C=r149c7 {2679}, X:(AB =5), (BC =6), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b9p345 {2356}, B=b6p16 {567}, C=r19c7 {279}, X:(AB =5), (BC =7), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r8c78 {236}, B=r2579c9 {35689}, C=r89c7 {269}, X:(AB =3), (BC =9), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r5c9 {56}, B=r14c7 {679}, C=b9p3457 {23569}, X:(AB =6), (BC =9), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r5c9 {56}, B=r2c9 {68}, C=r2468c8 {34568}, X:(AB =6), (BC =8), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=b6p16 {567}, B=r1c7 {79}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b9p345 {2356}, B=b6p16 {567}, C=r189c7 {2679}, X:(AB =5), (BC =7), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b9p345 {2356}, B=b6p16 {567}, C=r149c7 {2679}, X:(AB =5), (BC =6), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r8c78 {236}, B=r23579c9 {356789}, C=r19c7 {279}, X:(AB =3), (BC =7), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r8c78 {236}, B=b6p1268 {34567}, C=r19c7 {279}, X:(AB =3), (BC =7), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r1c27 {279}, B=r3c9 {79}, C=r9c289 {2589}, X:(AB =7), (BC =9), (CA =2) => r8c2 <> 2
ALS - XY - Ring: A=r149c7 {2679}, B=r5c9 {56}, C=b9p3457 {23569}, X:(AB =6), (BC =5), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r19c7 {279}, B=b6p16 {567}, C=b9p3457 {23569}, X:(AB =7), (BC =5), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r23579c9 {356789}, B=r1c7 {79}, C=b9p457 {2369}, X:(AB =7), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r23579c9 {356789}, B=r189c7 {2679}, C=r8c8 {36}, X:(AB =7), (BC =6), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r25c9 {568}, B=r2c8 {68}, C=r468c8 {3456}, X:(AB =8), (BC =6), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=b6p16 {567}, B=r189c7 {2679}, C=b9p35 {356}, X:(AB =7), (BC =6), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p16 {567}, B=r14c7 {679}, C=b9p3457 {23569}, X:(AB =6), (BC =9), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b9p345 {2356}, B=r2579c9 {35689}, C=r9c7 {29}, X:(AB =3), (BC =9), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r259c9 {5689}, C=r9c7 {29}, X:(AB =5), (BC =9), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=r8c78 {236}, B=r23579c9 {356789}, C=r189c7 {2679}, X:(AB =3), (BC =7), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r8c78 {236}, B=b6p268 {3456}, C=r149c7 {2679}, X:(AB =3), (BC =6), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r8c78 {236}, B=b6p1268 {34567}, C=r189c7 {2679}, X:(AB =3), (BC =7), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r8c78 {236}, B=b6p1268 {34567}, C=r149c7 {2679}, X:(AB =3), (BC =6), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r149c7 {2679}, B=b6p16 {567}, C=b9p3457 {23569}, X:(AB =7), (BC =5), (CA =2) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r19c7 {279}, B=b6p1268 {34567}, C=b9p457 {2369}, X:(AB =7), (BC =3), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r19c7 {279}, B=r23579c9 {356789}, C=b9p457 {2369}, X:(AB =7), (BC =3), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b6p1268 {34567}, B=r1c7 {79}, C=b9p457 {2369}, X:(AB =7), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b6p1268 {34567}, B=r189c7 {2679}, C=r8c8 {36}, X:(AB =7), (BC =6), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=r9c27 {259}, C=r289c8 {3568}, X:(AB =9), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2579c9 {35689}, B=r9c278 {2589}, C=r28c8 {368}, X:(AB =9), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r5c9 {56}, B=r2c9 {68}, C=b9p34579 {235689}, X:(AB =6), (BC =8), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r2579c9 {35689}, C=r89c7 {269}, X:(AB =3), (BC =9), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r259c9 {5689}, C=r89c7 {269}, X:(AB =5), (BC =9), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=r1c257 {1279}, B=r9c289 {2589}, C=r3c59 {179}, X:(AB =2), (BC =9), (CA =1) => r8c2 <> 2
ALS - XY - Ring: A=r1c27 {279}, B=r489c7 {2679}, C=r9c289 {2589}, X:(AB =7), (BC =9), (CA =2) => r8c2 <> 2
ALS - XY - Ring: A=r149c7 {2679}, B=b6p268 {3456}, C=b9p457 {2369}, X:(AB =6), (BC =3), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r149c7 {2679}, B=b6p1268 {34567}, C=b9p457 {2369}, X:(AB =7), (BC =3), (CA =2) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b6p268 {3456}, B=r14c7 {679}, C=b9p457 {2369}, X:(AB =6), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b6p1268 {34567}, B=r14c7 {679}, C=b9p457 {2369}, X:(AB =6), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=r89c7 {269}, C=b9p35 {356}, X:(AB =9), (BC =6), (CA =3) => r47c9 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=b9p3457 {23569}, C=r289c8 {3568}, X:(AB =9), (BC =5), (CA =3) => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2579c9 {35689}, B=r9c278 {2589}, C=r289c8 {3568}, X:(AB =9), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r257c9 {3568}, B=r2468c8 {34568}, C=r289c8 {3568}, X:(AB =8), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r257c9 {3568}, B=r9c279 {2589}, C=r289c8 {3568}, X:(AB =8), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=b9p3457 {23569}, C=r2579c9 {35689}, X:(AB =5), (BC =9), (CA =3) => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=r2468c8 {34568}, C=r257c9 {3568}, X:(AB =5), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p16 {567}, B=r2457c9 {35678}, C=r2468c8 {34568}, X:(AB =7), (BC =8), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b9p345 {2356}, B=r23579c9 {356789}, C=r19c7 {279}, X:(AB =3), (BC =7), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r2359c9 {56789}, C=r19c7 {279}, X:(AB =5), (BC =7), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=r148c7 {2679}, B=r19c2 {259}, C=r9c789 {2589}, X:(AB =9), (BC =5), (CA =2) => r8c2 <> 2
ALS - XY - Ring: A=r23579c9 {356789}, B=r2457c9 {35678}, C=r28c8 {368}, X:(AB =7), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r23579c9 {356789}, B=r1c7 {79}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =3) => r47c9 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=r23457c9 {356789}, C=r28c8 {368}, X:(AB =9), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2579c9 {35689}, B=b9p34578 {235689}, C=r28c8 {368}, X:(AB =9), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2579c9 {35689}, B=r9c27 {259}, C=b9p45789 {235689}, X:(AB =9), (BC =5), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=r9c279 {2589}, C=r289c8 {3568}, X:(AB =8), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=r2468c8 {34568}, C=r2457c9 {35678}, X:(AB =5), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r259c9 {5689}, B=r89c7 {269}, C=b9p35 {356}, X:(AB =9), (BC =6), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=r19c2 {259}, B=r14c7 {679}, C=b9p4789 {25689}, X:(AB =9), (BC =6), (CA =5) => r8c2 <> 2
ALS - XY - Ring: A=b6p16 {567}, B=r24579c9 {356789}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r7c124 {1356}, B=r9c27 {259}, C=r2579c9 {35689}, X:(AB =5), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r23579c9 {356789}, C=r189c7 {2679}, X:(AB =3), (BC =7), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=b9p345 {2356}, B=r2359c9 {56789}, C=r189c7 {2679}, X:(AB =5), (BC =7), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=r148c7 {2679}, B=r19c2 {259}, C=b9p4789 {25689}, X:(AB =9), (BC =5), (CA =2) => r8c2 <> 2
ALS - XY - Ring: A=r19c7 {279}, B=r23579c9 {356789}, C=b9p3457 {23569}, X:(AB =7), (BC =5), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=r19c7 {279}, B=r2359c9 {56789}, C=b9p3457 {23569}, X:(AB =7), (BC =5), (CA =2) => r47c9 <> 6
ALS - XY - Ring: A=b6p1268 {34567}, B=r2457c9 {35678}, C=r28c8 {368}, X:(AB =7), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r23579c9 {356789}, B=r24579c9 {356789}, C=b9p457 {2369}, X:(AB =7), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r23579c9 {356789}, B=r23457c9 {356789}, C=r28c8 {368}, X:(AB =9), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r23579c9 {356789}, B=r189c7 {2679}, C=b9p35 {356}, X:(AB =7), (BC =6), (CA =3) => r47c9 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=b9p34578 {235689}, C=r289c8 {3568}, X:(AB =9), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r257c9 {3568}, B=b9p34579 {235689}, C=r289c8 {3568}, X:(AB =8), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=b9p34579 {235689}, C=r257c9 {3568}, X:(AB =5), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=b9p3457 {23569}, C=r24579c9 {356789}, X:(AB =5), (BC =9), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2359c9 {56789}, B=r1c7 {79}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=b6p16 {567}, B=r2457c9 {35678}, C=b9p34579 {235689}, X:(AB =7), (BC =8), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p1268 {34567}, B=r24579c9 {356789}, C=b9p457 {2369}, X:(AB =7), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=b9p3457 {23569}, C=b9p45789 {235689}, X:(AB =9), (BC =5), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=r2579c9 {35689}, B=b9p34579 {235689}, C=r289c8 {3568}, X:(AB =8), (BC =5), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=b9p34579 {235689}, C=r2579c9 {35689}, X:(AB =5), (BC =9), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b6p136 {3567}, B=b9p34579 {235689}, C=r2457c9 {35678}, X:(AB =5), (BC =8), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r2359c9 {56789}, B=r189c7 {2679}, C=b9p35 {356}, X:(AB =7), (BC =6), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=b6p16 {567}, B=r24579c9 {356789}, C=b9p34579 {235689}, X:(AB =7), (BC =8), (CA =5) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=r7c124 {1356}, B=b9p3457 {23569}, C=r2579c9 {35689}, X:(AB =5), (BC =9), (CA =3) => r47c9,r8c12 <> 6
ALS - XY - Ring: A=b6p136 {3567}, B=b9p34579 {235689}, C=r24579c9 {356789}, X:(AB =5), (BC =9), (CA =3) => r4c89 <> 6; r9c9 <> 5
ALS - XY - Ring: A=b7p12459 {123456}, B=r19c2 {259}, C=r148c7 {2679}, X:(AB =5), (BC =9), (CA =2) => r8c2 <> 2
ALS - XY - Ring: A=r23579c9 {356789}, B=r24579c9 {356789}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =3) => r47c9 <> 6
ALS - XY - Ring: A=r23459c9 {356789}, B=b9p3457 {23569}, C=r2579c9 {35689}, X:(AB =5), (BC =9), (CA =3) => r47c9 <> 6
ALS - XY - Ring: A=r23459c9 {356789}, B=b9p3457 {23569}, C=r24579c9 {356789}, X:(AB =5), (BC =9), (CA =3) => r47c9 <> 6
ALS - XY - Ring: A=r2359c9 {56789}, B=r24579c9 {356789}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =5) => r47c9 <> 6
ALS - XY - Ring: A=r2359c9 {56789}, B=r24579c9 {356789}, C=b9p3457 {23569}, X:(AB =7), (BC =9), (CA =5) => r47c9 <> 6
{N RCC rule} this list is not complete its huge.
ALS - Ring: (2=6)r8c7-(6=3)r8c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(56)r57c9-(6=8)r2c9-(8=6)r2c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6=7)r4c7-(7)r1c7=(92)r19c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6)r4c7=(79)r14c7-(9=2)r9c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(67)b6p16-(7=9)r1c7-(9=2)r9c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5=6)r5c9-(6=7)r4c7-(7=9)r1c7-(9)r9c7=(2365)b9p3457-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6=7)r4c7-(7)r1c7=(692)r189c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6)r4c7=(79)r14c7-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6)r4c7=(97)r14c7-(7)r1c7=(92)r19c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(67)b6p16-(7=9)r1c7-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(76)b6p16-(6)r4c7=(79)r14c7-(9=2)r9c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=6)r8c7-(6=3)r8c8-(3)r7c9=(56897)r23579c9-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2=6)r8c7-(6=3)r8c8-(3)r46c8=(4567)b6p1268-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2=6)r8c7-(6)b9p35=(35)b9p35-(5=6)r5c9-(6)r4c7=(792)r149c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=6)r8c7-(6)b9p35=(35)b9p35-(5)r5c9=(67)b6p16-(7)r1c7=(92)r19c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(56897)r23579c9-(7=9)r1c7-(9=2)r9c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9=7)r3c9-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4567)b6p1268-(7=9)r1c7-(9=2)r9c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2=9)r1c2-(9=7)r1c7-(7=9)r3c9-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r9c7=(97)r19c7-(7=6)r4c7-(6=5)r5c9-(5)r7c9=(3692)b9p3457-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(56897)r23579c9-(7=9)r1c7-(9)r9c7=(26)r89c7-(6=3)r8c8-(3)r7c9 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(5689)r2579c9-(9=7)r3c9-(7=9)r1c7-(9)r9c7=(263)b9p457-(3)r7c9 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(5689)r2579c9-(9=7)r3c9-(7)r1c7=(296)r189c7-(6=3)r8c8-(3)r7c9 => r47c9,r8c12 <> 6
ALS - Ring: (5=6)r5c9-(6=7)r4c7-(7)r1c7=(296)r189c7-(6)b9p35=(35)b9p35-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5=6)r5c9-(6)r4c7=(79)r14c7-(9)r9c7=(26)r89c7-(6)b9p35=(35)b9p35-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5=6)r5c9-(6=8)r2c9-(8=6)r2c8-(6)r48c8=(345)r468c8-(5)r5c9 => r47c9 <> 6
ALS - Ring: (5)r5c9=(67)b6p16-(7=9)r1c7-(9)r9c7=(26)r89c7-(6)b9p35=(35)b9p35-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6)r4c7=(97)r14c7-(7)r1c7=(692)r189c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5=6)r5c9-(6)r4c7=(279)r149c7-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(67)b6p16-(7)r1c7=(29)r19c7-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(76)b6p16-(6)r4c7=(79)r14c7-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(76)b6p16-(6)r4c7=(97)r14c7-(7)r1c7=(92)r19c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=6)r8c7-(6=3)r8c8-(3)r46c8=(456)b6p268-(6)r4c7=(792)r149c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2=6)r8c7-(6=3)r8c8-(3)r46c8=(4576)b6p1268-(6)r4c7=(792)r149c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2=6)r8c7-(6)b9p35=(35)b9p35-(5)r5c9=(76)b6p16-(6)r4c7=(792)r149c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(56897)r23579c9-(7=9)r1c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9=7)r3c9-(7)r1c7=(692)r189c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6=7)r4c7-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4567)b6p1268-(7=9)r1c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6)r4c7=(79)r14c7-(9=2)r9c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4576)b6p1268-(6)r4c7=(79)r14c7-(9=2)r9c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(65)b6p16-(5)r6c8=(3468)r2468c8-(8)r9c8=(52)r9c28-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7=9)r3c9-(9)r9c9=(85)r9c89-(5=2)r9c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(63)r28c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(589)r9c289-(9=7)r3c9-(7=9)r1c7-(9)r1c2=(52)r19c2-(2)r9c2 => r8c2 <> 2
ALS - Ring: (2)r9c7=(796)r149c7-(6=5)r5c9-(5)r7c9=(36)b9p35-(6)r8c7=(92)r89c7-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=5)r9c2-(5)r9c8=(683)r289c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(79)r19c7-(9)r1c7=(76)r14c7-(6=5)r5c9-(5)r7c9=(3692)b9p3457-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(97)r19c7-(7)r4c7=(4563)b6p1268-(3=6)r8c8-(6)r8c7=(92)r89c7-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(97)r19c7-(7)r4c7=(65)b6p16-(5)r7c9=(36)b9p35-(6)r8c7=(92)r89c7-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(97)r19c7-(7)r3c9=(56893)r23579c9-(3=6)r8c8-(6)r8c7=(92)r89c7-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(97)r19c7-(7=9)r3c9-(9)r9c9=(5683)r2579c9-(3)r8c8=(692)b9p457-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (3)r46c8=(4567)b6p1268-(7=9)r1c7-(9)r9c7=(26)r89c7-(6=3)r8c8-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(25)r9c27-(5)r9c8=(86)r29c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(25)r9c27-(5=8)r9c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(258)r9c278-(8=6)r2c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5)r9c2=(29)r19c2-(9=7)r1c7-(7=9)r3c9-(9)r9c9=(85)r9c89-(5)r9c2 => r8c2 <> 2
ALS - Ring: (5=6)r5c9-(6)r4c7=(97)r14c7-(7)r1c7=(296)r189c7-(6)b9p35=(35)b9p35-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5)r5c9=(76)b6p16-(6)r4c7=(79)r14c7-(9)r9c7=(26)r89c7-(6)b9p35=(35)b9p35-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (1)r3c5=(79)r3c59-(9)r9c9=(582)r9c289-(2=9)r1c2-(9)r3c1=(21)r3c18-(1)r3c5 => r8c2 <> 2
ALS - Ring: (2)r8c7=(365)b9p345-(5)r9c8=(683)r289c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r8c7 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(673)b6p136-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r8c7 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(76)b6p16-(6)r4c7=(97)r14c7-(7)r1c7=(692)r189c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(76)b6p16-(6)r4c7=(279)r149c7-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=6)r8c7-(6)b9p35=(53)b9p35-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r8c7 => r47c9 <> 6
ALS - Ring: (2=6)r8c7-(6)b9p35=(35)b9p35-(5)r59c9=(689)r259c9-(9=2)r9c7-(2)r8c7 => r47c9 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(56897)r23579c9-(7)r1c7=(29)r19c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9)r9c7=(26)r89c7-(6)r4c7=(792)r149c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9)r9c7=(267)r489c7-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6=7)r4c7-(7)r1c7=(692)r189c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6)r4c7=(79)r14c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6)r4c7=(97)r14c7-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4567)b6p1268-(7)r1c7=(29)r19c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4576)b6p1268-(6)r4c7=(79)r14c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4576)b6p1268-(6)r4c7=(97)r14c7-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (1)r1c5=(79)r1c57-(9)r9c7=(263)b9p457-(3)r7c9=(56897)r23579c9-(7=1)r3c5-(1)r1c5 => r47c9,r8c12 <> 6
ALS - Ring: (1)r1c5=(79)r1c57-(9=2)r1c2-(2)r9c2=(589)r9c289-(9)r3c9=(71)r3c59-(1)r1c5 => r8c2 <> 2
ALS - Ring: (1)r1c5=(79)r1c57-(9)r9c7=(263)b9p457-(3)r7c9=(5689)r2579c9-(9)r3c9=(71)r3c59-(1)r1c5 => r47c9,r8c12 <> 6
ALS - Ring: (1)r1c5=(792)r1c257-(2)r9c2=(589)r9c289-(9=7)r3c9-(7=1)r3c5-(1)r1c5 => r8c2 <> 2
ALS - Ring: (1=7)r1c5-(7)r1c7=(92)r1c27-(2)r9c2=(589)r9c289-(9)r3c9=(71)r3c59-(1)r1c5 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(672)r148c7-(2=9)r9c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(672)r148c7-(2)r9c7=(97)r19c7-(7)r1c5=(12)r1c58-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(672)r148c7-(2)r9c7=(97)r19c7-(7)r3c9=(92)r3c19-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9=7)r1c7-(7)r4c7=(269)r489c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(76)r14c7-(6)r8c7=(29)r89c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9=2)r3c1-(2)r3c8=(179)r3c589-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r3c1=(127)r3c158-(7=9)r3c9-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(4563)b6p1268-(3)r8c8=(68)r28c8-(8)r9c8=(52)r9c28-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(4563)b6p1268-(3)r8c8=(685)r289c8-(5=2)r9c2-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(62)r48c7-(2=9)r9c7-(9)r1c7=(172)r1c578-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(62)r48c7-(2=9)r9c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7=6)r4c7-(6)r8c7=(29)r89c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(65)b6p16-(5)r7c9=(2369)b9p3457-(9)r9c9=(582)r9c289-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r3c9=(56893)r23579c9-(3)r8c8=(68)r28c8-(8)r9c8=(52)r9c28-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r3c9=(56893)r23579c9-(3)r8c8=(685)r289c8-(5=2)r9c2-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7=9)r3c9-(9)r9c9=(285)r9c289-(5)r9c2=(92)r19c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7=9)r3c9-(9)r9c9=(85)r9c89-(5)r9c2=(92)r19c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(63)r28c8-(3)r7c9=(5689)r2579c9-(9)r9c7=(52)r9c27-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(3465)r2468c8-(5=6)r5c9-(6)r4c7=(792)r149c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(3465)r2468c8-(5)r5c9=(67)b6p16-(7)r1c7=(92)r19c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(85)r9c28-(5)r9c8=(683)r289c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=5)r9c2-(5)r7c12=(163)r7c124-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r9c2 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(796)r149c7-(6)b6p26=(453)b6p268-(3=6)r8c8-(6)r8c7=(92)r89c7-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(697)r149c7-(7)r4c7=(4563)b6p1268-(3=6)r8c8-(6)r8c7=(92)r89c7-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(697)r149c7-(7)r4c7=(65)b6p16-(5)r7c9=(36)b9p35-(6)r8c7=(92)r89c7-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(79)r19c7-(9)r1c7=(67)r14c7-(7)r4c7=(65)b6p16-(5)r7c9=(3692)b9p3457-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(97)r19c7-(7=6)r4c7-(6)b6p26=(453)b6p268-(3)r8c8=(692)b9p457-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (3)r46c8=(456)b6p268-(6=7)r4c7-(7=9)r1c7-(9)r9c7=(263)b9p457-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r46c8=(456)b6p268-(6=7)r4c7-(7)r1c7=(296)r189c7-(6=3)r8c8-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r46c8=(456)b6p268-(6)r4c7=(79)r14c7-(9)r9c7=(26)r89c7-(6=3)r8c8-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r46c8=(4576)b6p1268-(6)r4c7=(79)r14c7-(9)r9c7=(26)r89c7-(6=3)r8c8-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(56897)r23579c9-(7=9)r1c7-(9)r1c2=(25)r19c2-(5)r9c8=(683)r289c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(25)r9c27-(5)r9c8=(68)r29c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(2365)b9p3457-(5)r9c8=(86)r29c8-(6=3)r8c8-(3)r7c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(2365)b9p3457-(5=8)r9c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(267)r489c7-(7)r1c7=(296)r189c7-(6=3)r8c8-(3)r7c9 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(285)r9c278-(5)r9c8=(86)r29c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(568)r257c9-(8)r2c8=(3465)r2468c8-(5)r9c8=(86)r29c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(568)r257c9-(8)r9c9=(295)r9c279-(5)r9c8=(86)r29c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(568)r257c9-(8)r9c9=(295)r9c279-(5=8)r9c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r4c9=(76)r4c79-(6=5)r5c9-(5)r6c8=(3468)r2468c8-(8)r2c9=(563)r257c9-(3)r4c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (5=6)r5c9-(6=7)r4c7-(7)r4c9=(3568)r2457c9-(8)r2c8=(3465)r2468c8-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5=6)r5c9-(6)r4c7=(79)r14c7-(9)r9c7=(258)r9c278-(8)r2c8=(3465)r2468c8-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5)r5c9=(67)b6p16-(7=9)r1c7-(9)r9c7=(258)r9c278-(8)r2c8=(3465)r2468c8-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (5)r5c9=(76)b6p16-(6)r4c7=(97)r14c7-(7)r1c7=(296)r189c7-(6)b9p35=(35)b9p35-(5)r5c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (1)r3c5=(79)r3c59-(9)r9c9=(582)r9c289-(2=9)r1c2-(9)r3c1=(271)r3c158-(1)r3c5 => r8c2 <> 2
ALS - Ring: (1)r3c5=(79)r3c59-(9)r9c9=(85)r9c89-(5)r9c2=(29)r19c2-(9)r3c1=(21)r3c18-(1)r3c5 => r8c2 <> 2
ALS - Ring: (1)r3c5=(79)r3c59-(9)r9c9=(285)r9c289-(5)r9c2=(29)r19c2-(9)r3c1=(21)r3c18-(1)r3c5 => r8c2 <> 2
ALS - Ring: (2)r8c7=(365)b9p345-(5)r9c8=(683)r289c8-(3)r7c9=(5689)r2579c9-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(563)b9p345-(3)r7c9=(56897)r23579c9-(7=9)r1c7-(9=2)r9c7-(2)r8c7 => r47c9 <> 6
ALS - Ring: (2)r8c7=(563)b9p345-(3)r7c9=(5689)r2579c9-(9=7)r3c9-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9 <> 6
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(673)b6p136-(3)r7c9=(5689)r2579c9-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(67)b6p16-(7)r1c7=(296)r189c7-(6)r4c7=(792)r149c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r5c9=(67)b6p16-(7)r4c9=(35689)r24579c9-(9=2)r9c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(365)b9p345-(5)r59c9=(689)r259c9-(9=7)r3c9-(7)r1c7=(92)r19c7-(2)r8c7 => r47c9 <> 6
ALS - Ring: (2)r8c7=(365)b9p345-(5)r59c9=(6897)r2359c9-(7=9)r1c7-(9=2)r9c7-(2)r8c7 => r47c9 <> 6
ALS - Ring: (2)r8c7=(3568)b9p3458-(8)r2c8=(63)r28c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(3568)b9p3458-(8)r2c8=(63)r28c8-(3)r7c9=(5689)r2579c9-(9)r9c7=(62)r89c7-(2)r8c7 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (2=6)r8c7-(6)r4c7=(79)r14c7-(9)r1c2=(25)r19c2-(5)r9c89=(892)r9c789-(2)r8c7 => r8c2 <> 2
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9)r9c7=(25)r9c27-(5)r9c89=(892)r9c789-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9)r9c7=(267)r489c7-(7)r1c7=(692)r189c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r7c9=(5689)r2579c9-(9)r9c7=(276)r489c7-(6)r4c7=(792)r149c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6)r4c7=(97)r14c7-(7)r1c7=(692)r189c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(456)b6p268-(6)r4c7=(279)r149c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4576)b6p1268-(6)r4c7=(97)r14c7-(7)r1c7=(692)r189c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(63)r8c78-(3)r46c8=(4576)b6p1268-(6)r4c7=(279)r149c7-(9)r9c7=(62)r89c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r8c7=(679)r148c7-(9)r1c2=(52)r19c2-(2)r9c2=(589)r9c289-(9=2)r9c7-(2)r8c7 => r8c2 <> 2
ALS - Ring: (2)r8c7=(679)r148c7-(9)r1c2=(25)r19c2-(5)r9c89=(89)r9c89-(9=2)r9c7-(2)r8c7 => r8c2 <> 2
ALS - Ring: (2)r8c7=(679)r148c7-(9)r9c7=(2365)b9p3457-(5=6)r5c9-(6)r4c7=(792)r149c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(679)r148c7-(9)r9c7=(2365)b9p3457-(5)r5c9=(67)b6p16-(7)r1c7=(92)r19c7-(2)r8c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r8c7=(67)r48c7-(7=9)r1c7-(9)r1c2=(25)r19c2-(5)r9c89=(892)r9c789-(2)r8c7 => r8c2 <> 2
ALS - Ring: (1)r1c5=(79)r1c57-(9)r1c2=(52)r19c2-(2)r9c2=(589)r9c289-(9)r3c9=(71)r3c59-(1)r1c5 => r8c2 <> 2
ALS - Ring: (1)r1c5=(79)r1c57-(9)r1c2=(25)r19c2-(5)r9c89=(89)r9c89-(9)r3c9=(71)r3c59-(1)r1c5 => r8c2 <> 2
ALS - Ring: (1)r1c5=(79)r1c57-(9)r9c7=(263)b9p457-(3)r7c9=(56789)r23579c9-(9)r3c9=(71)r3c59-(1)r1c5 => r47c9,r8c12 <> 6
ALS - Ring: (1)r1c5=(79)r1c57-(9)r9c7=(2365)b9p3457-(5)r5c9=(67)b6p16-(7)r1c7=(291)r1c278-(1)r1c5 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (1)r1c5=(97)r1c57-(7)r1c7=(92)r1c27-(2)r9c2=(589)r9c289-(9)r3c9=(71)r3c59-(1)r1c5 => r8c2 <> 2
ALS - Ring: (1)r1c5=(792)r1c257-(2=5)r9c2-(5)r9c89=(89)r9c89-(9)r3c9=(71)r3c59-(1)r1c5 => r8c2 <> 2
ALS - Ring: (1)r3c8=(29)r3c18-(9=2)r1c2-(2)r9c2=(589)r9c289-(9)r3c9=(271)r3c589-(1)r3c8 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(672)r148c7-(2)r9c7=(895)r9c789-(5=2)r9c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(276)r148c7-(6)r8c7=(29)r89c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(276)r148c7-(6)r8c7=(297)r189c7-(7)r1c5=(12)r1c58-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(276)r148c7-(6)r8c7=(297)r189c7-(7)r3c9=(92)r3c19-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(76)r14c7-(6)r8c7=(2895)b9p4789-(5=2)r9c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2=9)r1c2-(9)r1c7=(67)r14c7-(7)r4c7=(269)r489c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(79)r1c27-(9)r1c7=(672)r148c7-(2=9)r9c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(79)r1c27-(9)r1c7=(76)r14c7-(6)r8c7=(29)r89c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(4563)b6p1268-(3)r8c8=(269)b9p457-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2, 6; r47c9,r8c1 <> 6
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(4563)b6p1268-(3)r8c8=(685)r289c8-(5)r9c2=(92)r19c2-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(4563)b6p1268-(3)r8c8=(568)r289c8-(8)r9c8=(52)r9c28-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(62)r48c7-(2)r9c7=(895)r9c789-(5=2)r9c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(26)r48c7-(6)r8c7=(29)r89c7-(9)r1c7=(172)r1c578-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(26)r48c7-(6)r8c7=(29)r89c7-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7=6)r4c7-(6)r8c7=(2895)b9p4789-(5=2)r9c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(269)r489c7-(9)r9c9=(85)r9c89-(5=2)r9c2-(2)r1c2 => r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(65)b6p16-(5)r79c9=(23698)b9p34579-(8)r9c8=(52)r9c28-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r4c7=(65)b6p16-(5)r7c9=(2369)b9p3457-(9)r1c7=(172)r1c578-(2)r1c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r1c2=(97)r1c27-(7)r3c9=(56893)r23579c9-(3)r8c8=(269)b9p457-(9)r9c9=(582)r9c289-(2)r1c2 => r8c2 <> 2, 6; r47c9,r8c1 <> 6
ALS - Ring: (2)r1c2=(97)r1c27-(7)r3c9=(56893)r23579c9-(3)r8c8=(685)r289c8-(5)r9c2=(92)r19c2-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r3c9=(56893)r23579c9-(3)r8c8=(568)r289c8-(8)r9c8=(52)r9c28-(2)r1c2 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (2)r1c2=(97)r1c27-(7)r3c9=(56893)r23579c9-(3)r7c14=(165)r7c124-(5=2)r9c2-(2)r1c2 => r8c2 <> 2, 6; r47c9,r8c1 <> 6
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(63)r28c8-(3)r46c8=(4567)b6p1268-(7)r1c7=(92)r19c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(63)r28c8-(3)r7c9=(56897)r23579c9-(7)r1c7=(92)r19c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(58)r9c28-(8)r2c8=(3465)r2468c8-(5)r5c9=(76)b6p16-(6)r4c7=(792)r149c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(85)r9c28-(5)r9c8=(683)r289c8-(3)r7c9=(5689)r2579c9-(9)r9c7=(52)r9c27-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(589)r9c289-(9=7)r3c9-(7)r3c5=(129)r3c158-(9)r1c2=(52)r19c2-(2)r9c2 => r8c2 <> 2
ALS - Ring: (2)r9c2=(589)r9c289-(9)r9c7=(26)r89c7-(6)r4c7=(79)r14c7-(9)r1c2=(52)r19c2-(2)r9c2 => r8c2 <> 2
ALS - Ring: (2)r9c2=(589)r9c289-(9)r9c7=(2365)b9p3457-(5=6)r5c9-(6)r4c7=(792)r149c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(589)r9c289-(9)r9c7=(2365)b9p3457-(5)r5c9=(67)b6p16-(7)r1c7=(92)r19c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c2=(589)r9c289-(9)r9c7=(267)r489c7-(7=9)r1c7-(9)r1c2=(52)r19c2-(2)r9c2 => r8c2 <> 2
ALS - Ring: (2=5)r9c2-(5)r9c89=(26893)b9p45789-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r9c2 => r47c9,r8c12 <> 6
ALS - Ring: (2=5)r9c2-(5)r9c8=(683)r289c8-(3)r7c9=(56897)r23579c9-(7)r1c7=(92)r19c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=5)r9c2-(5)r9c8=(683)r289c8-(3)r46c8=(4567)b6p1268-(7)r1c7=(92)r19c7-(2)r9c2 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(796)r149c7-(6=5)r5c9-(5)r6c8=(3468)r2468c8-(8)r9c8=(592)r9c278-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2)r9c7=(79)r19c7-(9)r1c7=(76)r14c7-(6)b6p26=(453)b6p268-(3)r8c8=(692)b9p457-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(79)r19c7-(9)r1c7=(67)r14c7-(7)r4c7=(4563)b6p1268-(3)r8c8=(692)b9p457-(2)r9c7 => r47c9,r8c12 <> 6
ALS - Ring: (2)r9c7=(97)r19c7-(7)r4c7=(65)b6p16-(5)r6c8=(3468)r2468c8-(8)r9c8=(592)r9c278-(2)r9c7 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=9)r3c1-(9)r1c2=(52)r19c2-(2)r9c2=(589)r9c289-(9)r3c9=(172)r3c589-(2)r3c1 => r8c2 <> 2
ALS - Ring: (2=9)r3c1-(9)r1c2=(25)r19c2-(5)r9c89=(89)r9c89-(9)r3c9=(172)r3c589-(2)r3c1 => r8c2 <> 2
ALS - Ring: (3)r46c8=(456)b6p268-(6)r4c7=(97)r14c7-(7)r1c7=(296)r189c7-(6=3)r8c8-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r46c8=(4567)b6p1268-(7=9)r1c7-(9)r1c2=(25)r19c2-(5)r9c8=(683)r289c8-(3)r46c8 => r4c89 <> 6; r9c9 <> 5; r8c2 <> 2
ALS - Ring: (3)r46c8=(4576)b6p1268-(6)r4c7=(97)r14c7-(7)r1c7=(296)r189c7-(6=3)r8c8-(3)r46c8 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(56897)r23579c9-(7)r4c9=(3568)r2457c9-(8=6)r2c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(56897)r23579c9-(7=9)r1c7-(9)r9c7=(25)r9c27-(5)r9c8=(683)r289c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(56897)r23579c9-(7=9)r1c7-(9)r9c7=(258)r9c278-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(56)r57c9-(6=8)r2c9-(8)r2c8=(3465)r2468c8-(5)r9c8=(683)r289c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(56)r57c9-(6=8)r2c9-(8)r9c9=(295)r9c279-(5)r9c8=(683)r289c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9=7)r3c9-(7)r4c9=(3568)r2457c9-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9=7)r3c9-(7=9)r1c7-(9)r9c7=(2563)b9p3457-(3)r7c9 => r47c9 <> 6
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r3c9=(35678)r23457c9-(8=6)r2c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(23568)b9p34578-(8=6)r2c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(25)r9c27-(5)r9c89=(2896)b9p4789-(6=3)r8c8-(3)r7c9 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(26)r89c7-(6)b9p35=(358)b9p358-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(26)r89c7-(6)b9p35=(35)b9p35-(5)r9c8=(683)r289c8-(3)r7c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(2365)b9p3457-(5)r9c8=(68)r29c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(2365)b9p3457-(5)r5c9=(68)r25c9-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5689)r2579c9-(9)r9c7=(285)r9c278-(5)r9c8=(68)r29c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5698)r2579c9-(8)r9c9=(295)r9c279-(5)r9c8=(86)r29c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(5698)r2579c9-(8)r9c9=(295)r9c279-(5=8)r9c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(568)r257c9-(8=6)r2c8-(6)r48c8=(345)r468c8-(5)r9c8=(683)r289c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r7c9=(568)r257c9-(8)r9c9=(295)r9c279-(5)r9c8=(68)r29c8-(8)r2c8=(63)r28c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r4c9=(675)b6p136-(5)r7c9=(36)b9p35-(6)r8c7=(29)r89c7-(9)r9c9=(5683)r2579c9-(3)r4c9 => r4c89,r7c9 <> 6; r9c9 <> 5
ALS - Ring: (3)r4c9=(675)b6p136-(5)r6c8=(346)r468c8-(6=8)r2c8-(8)r2c9=(563)r257c9-(3)r4c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r4c9=(675)b6p136-(5)r6c8=(3468)r2468c8-(8=6)r2c9-(6)r57c9=(53)r57c9-(3)r4c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (3)r4c9=(675)b6p136-(5)r6c8=(3468)r2468c8-(8=6)r2c9-(6)r57c9=(53)r57c9-(3)r4c9 => r4c89 <> 6; r9c9 <> 5
ALS - Ring: (2=6)r8c7-(6=3)r8c8-(3)r7c9=(5689)r2579c9-(9=2)r9c7-(2)r8c7 => r47c9,r8c12 <> 6
ALS - Ring: (3)r7c9=(56)r57c9-(6=8)r2c9-(8=6)r2c8-(6=3)r8c8-(3)r7c9 => r4c89 <> 6; r9c9 <> 5
... truncated list
Some do, some teach, the rest look it up.
stormdoku
stormdoku
-
StrmCkr - Posts: 1475
- Joined: 05 September 2006
Re: ALS Loops/Rings
by Wepwawet » Sat Oct 11, 2025 5:51 am
StrmCkr wrote:note: all the following examples are from a max BFS of 8.
- Code: Select all
.--------------.-------------.---------------.
| 6 28 34 | 34 12 5 | 18 7 9 |
| 12 358 9 | 34 12 7 | 6 3458 45 |
| 17 35 347 | 6 9 8 | 135 345 2 |
:--------------+-------------+---------------:
| 8 7 6 | 9 4 1 | 25 25 3 |
| 3 1 2 | 7 5 6 | 4 9 8 |
| 4 9 5 | 2 8 3 | 7 1 6 |
:--------------+-------------+---------------:
| 9 236 37 | 5 367 24 | 38 3468 1 |
| 27 236 8 | 1 367 24 | 9 3456 45 |
| 5 4 1 | 8 36 9 | 23 236 7 |
'--------------'-------------'---------------'
{3 RCC} Ring Rule examples:
ALS - XY: A=r17c7 {138}, B=r7c3 {37}, C=r3c2378 {13457}, X:(AB =3), (BC =7), (CA =1) => r7c258 <> 3 ...
ALS - Ring: (1)r2c1=(234587)b1p234589-(7)r3c1=(1354)r3c1278-(4)r7c8=(36782)r7c23578-(2)r1c2=(345781)b1p235789-(1)r2c1 => r28c8 <> 4; r3c3 <> 3; r8c2 <> 2
Thanks for you examples, much to reflect on. This seems to suggest that the existence of ALS Rings in puzzles are not that uncommon, but, they are rarely encountered after other solving algorithms have been applied (having said that, I did find an 8 node ring the other day that did not succumb to the usual solving process).
Wept
-
Wepwawet - Posts: 35
- Joined: 19 November 2019
Re: ALS Loops/Rings
by StrmCkr » Tue Oct 14, 2025 8:47 am
this happens to pretty much every move depending on hierarchy if they are seen or not seen.they are rarely encountered after other solving algorithms have been applied
Some do, some teach, the rest look it up.
stormdoku
stormdoku
-
StrmCkr - Posts: 1475
- Joined: 05 September 2006
12 posts
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