## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

David P Bird, you've posted naked-pair-loops. Do you still intend to post a hidden-pair-loop? Hint: The hidden-pair-loop would use candidate values 1, 2 and 5 only.

David P Bird wrote:Woe is me! Yesterday I made a schoolboy error and missed half the strong inferences ... As no-one picked up on this ...

I picked up on it, rolled my eyes, and sighed.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

ronk wrote:David P Bird, you've posted naked-pair-loops. Do you still intend to post a hidden-pair-loop?

Thanks for this thought provoking comment. I've never questioned SK's description of his loop as being a hidden pair loop before as an AAHS in two cells contains no locked candidates and so describes any two peer cells. As I recall his description used AANSs rather than AAHSs as it uses fewer cells, but AFAIK no-one has picked up on the misnomer before.

What I've always considered as his breakthrough was to compose a twin AIC loop where two linking digits were used throughout with three possible ways the truths could be divided rather than two. That, more than anything else, is what defines the approach, and rather than calling them hidden pair loops I should perhaps call them AALS loops (so either naked or hidden set notations can be used, whichever is more convenient).

ronk wrote:
David P Bird wrote:Woe is me! Yesterday I made a schoolboy error and missed half the strong inferences ... As no-one picked up on this ...

I picked up on it, rolled my eyes, and sighed.

That's strange, you usually pounce on my mistakes, something which I've come to rely on.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

David P Bird wrote:
ronk wrote:David P Bird, you've posted naked-pair-loops. Do you still intend to post a hidden-pair-loop?

Thanks for this thought provoking comment. I've never questioned SK's description of his loop as being a hidden pair loop before as an AAHS in two cells contains no locked candidates and so describes any two peer cells. As I recall his description used AANSs rather than AAHSs as it uses fewer cells, but AFAIK no-one has picked up on the misnomer before.

I can't believe that you believe Steve Kurzhals would make such a mistake. See coloin's first post here. coloin actually quoted my post on Eureka! in which I quoted Steve's original hpl expression for the Easter Monster. I "authored" the A, B ... K, L labeling for the hpl cell pairs and the AALS comment as quoted by coloin.

ronk wrote:
Code: Select all
` 1      A478     34578   | 3567    3689    5678    | 3489   I369     2L238     9      L378     | 4      K12368  K12678   |J138     5      J368 23458  A248     6       | 1235    12389   1258    | 7      I139     3489-------------------------+-------------------------+----------------------- 2468    5       1478    | 9       1246    3       | 128    H1267    678 234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689 2369   B1267    1379    | 8       5       126     | 1239    4       3679-------------------------+-------------------------+----------------------- 7      C148     14589   | 1235    12348   12458   | 6      G239     3459D456     3      D145     |E12567  E1246    9       |F245     8      F457 45689  C468     2       | 3567    3468    45678   | 3459   G379     1`

Steve Kurzhals wrote:(27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-
(27)r79c8=(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 -
loop

Note that nodes marked A, C, D, F, G, I, J and L are all AALSs.

David, when you find yourself in a hole, it's time to stop digging.

[edit: Made it clear that Steve Kurzhals authored the chain, not me.]
Last edited by ronk on Tue Aug 18, 2015 10:06 pm, edited 1 time in total.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

Code: Select all
`     1      A478     34578   | 3567    3689    5678    | 3489   I369     2    L238     9      L378     | 4      K12368  K12678   |J138     5      J368     23458  A248     6       | 1235    12389   1258    | 7      I139     3489    -------------------------+-------------------------+-----------------------     2468    5       1478    | 9       1246    3       | 128    H1267    678     234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689     2369   B1267    1379    | 8       5       126     | 1239    4       3679    -------------------------+-------------------------+-----------------------     7      C148     14589   | 1235    12348   12458   | 6      G239     3459    D456     3      D145     |E12567  E1246    9       |F245     8      F457     45689  C468     2       | 3567    3468    45678   | 3459   G379     1    (27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-    (27)r79c8=(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 -    loop    Note that nodes marked A, C, D, F, G, I, J and L are all AALSs.`

At least I am very happy to get the original post from Steve Kurzhals.

It is exactly what I had in mind.

My own version is just a shorter loop using 8 AAHS/AALS instead of 16 AALS (a pattern of 2 cells 4 digits if both AALS and AAHS)

I'll dig in the full tagging thread to see when I did that simplification, but as I already worked on the "virus chains" and Easter Monster, I am sure it came very fast. and I would be very surprised if Steve Kurzhals had anything to object to that simplification

EDIT just for history, it has not been to hard to find back the relevant post

Post by champagne » Mon Oct 29, 2007 9:53 am in the full tagging thread

full tagging

I think Mike Barker, after I published my first version of an Easter Monster solution has been kind enough to give me a link to a post where steve Kurzhals solution was discussed
champagne
2017 Supporter

Posts: 6682
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

champagne wrote:
Steve Kurzhals wrote:(27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-
(27)r79c8=(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 -
loop

At least I am very happy to get the original post from Steve Kurzhals.

It is exactly what I had in mind.

Didn't know you were even interested in hidden-pair-loop expressions, but since you are, perhaps you would assist David P Bird with the one for the recent puzzle from a French forum.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

ronk wrote:Didn't know you were even interested in hidden-pair-loop expressions, but since you are, perhaps you would assist David P Bird with the one for the recent puzzle from a French forum.

I am interested in the simplest logic coming to the same eliminations as steve's loop.

The loop based on the 8 AAHS/AALS Is working pretty well and has been given by several players b(including me). No need to do more
champagne
2017 Supporter

Posts: 6682
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

champagne wrote:
Code: Select all
`     1      A478     34578   | 3567    3689    5678    | 3489   I369     2    L238     9      L378     | 4      K12368  K12678   |J138     5      J368     23458  A248     6       | 1235    12389   1258    | 7      I139     3489    -------------------------+-------------------------+-----------------------     2468    5       1478    | 9       1246    3       | 128    H1267    678     234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689     2369   B1267    1379    | 8       5       126     | 1239    4       3679    -------------------------+-------------------------+-----------------------     7      C148     14589   | 1235    12348   12458   | 6      G239     3459    D456     3      D145     |E12567  E1246    9       |F245     8      F457     45689  C468     2       | 3567    3468    45678   | 3459   G379     1    (27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-    (27)r79c8=(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 -    loop    Note that nodes marked A, C, D, F, G, I, J and L are all AALSs.`

At least I am very happy to get the original post from Steve Kurzhals.

Okay, so do we now give a name to this loop for Easter Monster (and the French puzzle)?

Code: Select all
`1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1 +--------------------------------------------------------------------------------+ | *1      A48+7    34578   |  3567    3689    5678    |  3489   I39+6   *2       | | L38+2    9      L38+7    |  4       12368   12678   | J38+1    5      J38+6    | |  23458  A48+2   *6       |  1235    12389   1258    | *7      I39+1    3489    | |--------------------------+--------------------------+--------------------------| |  2468    5       1478    |  9       1246    3       |  128     1267    678     | |  234689  12468   13489   |  126     7       1246    |  123589  12369   35689   | |  2369    1267    1379    |  8       5       126     |  1239    4       3679    | |--------------------------+--------------------------+--------------------------| | *7      C48+1    14589   |  1235    12348   12458   | *6      G39+2    3459    | | D45+6    3      D45+1    |  12567   1246    9       | F45+2    8      F45+7    | |  45689  C48+6   *2       |  3567    3468    45678   |  3459   G39+7   *1       | +--------------------------------------------------------------------------------+ # 179 eliminations remain A(27=48)r13c2 - C(48=16)r79c2 - D(16=45)r8c13 - F(45=27)r8c79 - G(27=39)r79c8 - I(39=16)r13c8 - J(16=38)r2c79 - L(38=27)r2c13 - loop  =>  r2c5<>38; r5c2<>48; r5c8<>39;  r7c3<>1; r3c1<>2; r8c5<>4; r8c4<>5; r9c1<>6; r1c3<>7; r2c6<>8`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:
champagne wrote:
Code: Select all
`     1      A478     34578   | 3567    3689    5678    | 3489   I369     2    L238     9      L378     | 4      K12368  K12678   |J138     5      J368     23458  A248     6       | 1235    12389   1258    | 7      I139     3489    -------------------------+-------------------------+-----------------------     2468    5       1478    | 9       1246    3       | 128    H1267    678     234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689     2369   B1267    1379    | 8       5       126     | 1239    4       3679    -------------------------+-------------------------+-----------------------[b][/b]     7      C148     14589   | 1235    12348   12458   | 6      G239     3459    D456     3      D145     |E12567  E1246    9       |F245     8      F457     45689  C468     2       | 3567    3468    45678   | 3459   G379     1    (27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-    (27)r79c8=(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 -    loop    Note that nodes marked A, C, D, F, G, I, J and L are all AALSs.`
At least I am very happy to get the original post from Steve Kurzhals.

The only part that champagne authored is the last sentence.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

ronk wrote:The only part that champagne authored is the last sentence.

I'm aware of that ... and that's why I included his comment.

I only referenced his post in order to contrast the SK-Loop logic to a shorter loop.

The important part of my post still remains to be answered.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:Okay, so do we now give a name to this loop for Easter Monster (and the French puzzle)?

Generically, it's a naked-pair-loop. If there exists a complementary hidden-pair-loop as for Easter Monster, then it's also an sk-loop. If not, it's a 0-rank almost sk-loop.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

Why should the french puzzle disqualify as containing an sk-loop because it contains an hidden triple loop instead of an hidden pair loop ?
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: Exotic patterns a resume

I think Steve Kurzhals would strongly disagree to learn that the "french puzzle" is not qualified for a "sk loop"

But If i follow daj95376 after the permanent deny from ronk, we should have to conclude that we have a pattern super setting the sk loop .

IMO that the improvement is so small (and not clearly established as said JC Van Hay) that it would not be fair to go in that direction, but if keeping the same name is source of trouble, we have to take another name and withdraw the use of the sub setting pattern name (sk loop).
champagne
2017 Supporter

Posts: 6682
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

JC Van Hay wrote:Why should the french puzzle disqualify as containing an sk-loop because it contains an hidden triple loop instead of an hidden pair loop ?

The hidden pair loop has a describable pattern, which is much different than in the French puzzle. That no one has attempted to describe the latter pattern or successfully written the AIC for the hidden-whatever-loop is revealing IMO. BTW hidden-triple-loop would not be accurate IMO.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

The way things are going, It's time to create a new name for the pattern I described in the definition

I suggest "V loop" (as of virus chain loop).

I am off for a little more than one week, but I'll adjust the text as soon as I am back.

Consequently, I'll withdraw the "sk loop" qualifier which is too restrictive in ronk's understanding
champagne
2017 Supporter

Posts: 6682
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

ronk wrote:
JC Van Hay wrote:Why should the french puzzle disqualify as containing an sk-loop because it contains an hidden triple loop instead of an hidden pair loop ?

The hidden pair loop has a describable pattern, which is much different than in the French puzzle. That no one has attempted to describe the latter pattern or successfully written the AIC for the hidden-whatever-loop is revealing IMO. BTW hidden-triple-loop would not be accurate IMO.

A hidden triple loop in the condensed form of the AIC and a hidden single loop otherwise

Code: Select all
`The hidden pair loop in Easter Monster+--------------------------+------------------------------+-------------------------+| 1       48(7)     3458-7 | 3567      3689      5678     | 3489    39(6)     2     || 38(2)   9         38(7)  | 4         -38(126)  -8(1267) | 38(1)   5         38(6) || 3458-2  48(2)     6      | 1235      12389     1258     | 7       39(1)     3489  |+--------------------------+------------------------------+-------------------------+| 2468    5         1478   | 9         1246      3        | 128     (1267)    678   || 234689  -48(126)  13489  | 126       7         1246     | 123589  -39(126)  35689 || 2369    (1267)    1379   | 8         5         126      | 1239    4         3679  |+--------------------------+------------------------------+-------------------------+| 7       48(1)     4589-1 | 1235      12348     12458    | 6       39(2)     3459  || 45(6)   3         45(1)  | -5(1267)  -4(126)   9        | 45(2)   8         45(7) || 4589-6  48(6)     2      | 3567      3468      45678    | 3459    39(7)     1     |+--------------------------+------------------------------+-------------------------+|V27r2c13=(27-16)r2c56=16(r2c79-r13c8)=(16-27)r45c8=27(r79c8-r8c79)=(27-16)r8c45=16(r8c13-r79c2)=(16-27)r56c2=27r13c2 @25r3c13=(2 -15)r3c4 =15(r3c79-r12c8)=             15(r89c8-r7c79)=(5 -12)r7c6 =12(r7c13-r89c2)=(1 - 5)r4 c2=25r12c2 @^|The hidden single loop in the french puzzle+------------------------+-----------------------+-------------------------+| 468-25  48(25)  469-2  | 1256   12569  3       | 4789-15  4(15)  4789-15 || 1       48(5)   3469   | 56     569    7       | 2        34(5)  489-5   || 3(25)   7       39(2)  | (125)  8      4       | 39(15)   6      9(15)   |+------------------------+-----------------------+-------------------------+| 457     -4(15)  8      | 1256   12567  1256    | 145      9      3       || 25      6       12     | 3      4      9       | 158      7      158     || 9       3       147    | 8      157    15      | 6        2      145     |+------------------------+-----------------------+-------------------------+| 46(2)   9       46(12) | 7      3      -6(125) | 4(15)    8      46(15)  || 34678   48(1)   5      | 9      16     168     | 347-1    34(1)  2       || 3678-2  8(12)   367-12 | 4      1256   12568   | 379-15   3(15)  679-15  |+------------------------+-----------------------+-------------------------+`
JC Van Hay

Posts: 719
Joined: 22 May 2010

PreviousNext