Structures within nodes (Extreme #110)

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Structures within nodes (Extreme #110)

Postby Luke » Mon Jan 05, 2009 5:46 am

When DonM posted his Sue de Coq articles I began to understand the concept of structures as nodes within AIC's and nice loops. I noticed how many of the solutions to the toughest puzzles included groups, hidden doubles, hidden triples, ALS, etc. Solvers like aran, ttt, and others get wildly creative with these structures and it now seems clear to me that's where the real power lies when looking at loops and chains.

Here's a puzzle I've been stuck on for weeks and I finally made a placement using such a technique. It's Extreme #110 from late October:
Code: Select all
2..5.1..7.8.....6...9.....28.69.3......1.4......6.27.53.....6...1.....2.5..2.8..9

 *-----------------------------------------------------------*
 | 2     346  #34    | 5     3469  1     | 3489  3489  7     |
 | 147   8    *1457  | 347   2     79    |*1459  6     134   |
 | 1467  3457  9     | 8     34    67    | 1345 *1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   2357  | 1     57    4     | 389   389   6     |
 | 149   349  #134   | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     2479  2478  | 47    149   579   | 6    *1457  148   |
 | 4679  1     478   | 347   49    5679  | 45    2     348   |
 | 5     467  #47    | 2     1346  8     | 134  *1347  9     |
 *-----------------------------------------------------------*

The cells marked with [#] comprise a “hidden triple" on [134] and the rest is an AIC.

134r169c3=7r9c3-7r9c8=(7-5)r7c8=5r3c8-5r2c7=5r2c3 => <14>r2c3. r6c3=1 follows.

I'm trying to find more, so if anyone wants to help me expand my horizons with this puzzle I'd be grateful!
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Re: Structures within nodes

Postby aran » Mon Jan 05, 2009 6:34 am

Luke451 wrote:When DonM posted his Sue de Coq articles I began to understand the concept of structures as nodes within AIC's and nice loops. I noticed how many of the solutions to the toughest puzzles included groups, hidden doubles, hidden triples, ALS, etc. Solvers like aran, ttt, and others get wildly creative with these structures and it now seems clear to me that's where the real power lies when looking at loops and chains.

Here's a puzzle I've been stuck on for weeks and I finally made a placement using such a technique. It's Extreme #110 from late October:
Code: Select all
2..5.1..7.8.....6...9.....28.69.3......1.4......6.27.53.....6...1.....2.5..2.8..9

 *-----------------------------------------------------------*
 | 2     346  #34    | 5     3469  1     | 3489  3489  7     |
 | 147   8    *1457  | 347   2     79    |*1459  6     134   |
 | 1467  3457  9     | 8     34    67    | 1345 *1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   2357  | 1     57    4     | 389   389   6     |
 | 149   349  #134   | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     2479  2478  | 47    149   579   | 6    *1457  148   |
 | 4679  1     478   | 347   49    5679  | 45    2     348   |
 | 5     467  #47    | 2     1346  8     | 134  *1347  9     |
 *-----------------------------------------------------------*

The cells marked with [#] comprise a “hidden triple" on [134] and the rest is an AIC.

134r169c3=7r9c3-7r9c8=(7-5)r7c8=5r3c8-5r2c7=5r2c3 => <14>r2c3. r6c3=1 follows.

I'm trying to find more, so if anyone wants to help me expand my horizons with this puzzle I'd be grateful!

Luke
A couple of moves to further the quest:)
1. 47r9c23=6r9c2-6r1c2=34r1c23-34r3c2
A=57r34c2 : =><7>r7c2
B (using deadly rectangle considerations)=89r1c78-(8+9)r5c78=3r5c7/8-(3=9)r6c8-(9=34)r6c2 (=>pair34 r16c2) : =><4>r7c2
2. 7r7c8=7r9c8-(7=4)r9c3-(47=6)r9c2-6r1c2=34r1c23-34r1c578=89r1c78-(9=6)r1c5-(6=7)r3c6-(7=9)r2c6-(79=5)r7c6-5r7c8 : => <5> r7c8 => placement 5 r7c6, r3c8 etc
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Postby daj95376 » Mon Jan 05, 2009 7:05 am

Luke451: Your results remind me of a forcing net on cell [r9c3].

Code: Select all
 +--------------------------------------------------------------------+
 |  2      346    34    |  5      3469   1     |  3489   3489   7     |
 |  147    8      1457  |  347    2      79    |  1459   6      134   |
 |  1467   3457   9     |  8      34     67    |  1345   1345   2     |
 |----------------------+----------------------+----------------------|
 |  8      57     6     |  9      57     3     |  2      14     14    |
 |  79     239    2357  |  1      57     4     |  389    389    6     |
 |  149    349    134   |  6      8      2     |  7      39     5     |
 |----------------------+----------------------+----------------------|
 |  3      2479   2478  |  47     149    579   |  6      1457   148   |
 |  4679   1      478   |  347    49     5679  |  45     2      348   |
 |  5      467    47    |  2      1346   8     |  134    1347   9     |
 +--------------------------------------------------------------------+

Code: Select all
 [r9c3]=4 ([r6c3]<>4) [r1c2]=3 [r6c3]=1
 *-----------------------------------------------------------*
 | 2     46   *3     | 5     469   1     | 489   489   7     |
 | 147   8     57    | 347   2     79    | 1459  6     134   |
 | 1467  457   9     | 8     34    67    | 1345  1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   257   | 1     57    4     | 389   389   6     |
 | 49    349  *1     | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     279   278   | 47    149   579   | 6     1457  148   |
 | 679   1     78    | 347   49    5679  | 45    2     348   |
 | 5     67   #4     | 2     136   8     | 13    137   9     |
 *-----------------------------------------------------------*

Code: Select all
 [r9c3]=7 [r7c8]=7 [r3c8]=5 [r2c3]=5 [r6c3]=1
 *-----------------------------------------------------------*
 | 2     346   34    | 5     3469  1     | 3489  3489  7     |
 | 147   8    *5     | 347   2     79    | 149   6     134   |
 | 1467  347   9     | 8     34    67    | 134  *5     2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   23    | 1     57    4     | 389   389   6     |
 | 49    349  *1     | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     249   248   | 4     149   59    | 6    *7     148   |
 | 469   1     48    | 347   49    5679  | 45    2     348   |
 | 5     46   #7     | 2     1346  8     | 134   134   9     |
 *-----------------------------------------------------------*
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Re: Structures within nodes

Postby Luke » Mon Jan 05, 2009 7:35 am

aran wrote:
Code: Select all
2..5.1..7.8.....6...9.....28.69.3......1.4......6.27.53.....6...1.....2.5..2.8..9

 *-----------------------------------------------------------*
 | 2     346  #34    | 5     3469  1     | 3489  3489  7     |
 | 147   8    *1457  | 347   2     79    |*1459  6     134   |
 | 1467  3457  9     | 8     34    67    | 1345 *1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   2357  | 1     57    4     | 389   389   6     |
 | 149   349  #134   | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     2479  2478  | 47    149   579   | 6    *1457  148   |
 | 4679  1     478   | 347   49    5679  | 45    2     348   |
 | 5     467  #47    | 2     1346  8     | 134  *1347  9     |
 *-----------------------------------------------------------*

A couple of moves to further the quest:)
1. 47r9c23=6r9c2-6r1c2=34r1c23-34r3c2
A=57r34c2 : =><7>r7c2
B (using deadly rectangle considerations)=89r1c78-(8+9)r5c78=3r5c7/8-(3=9)r6c8-(9=34)r6c2 (=>pair34 r16c2) : =><4>r7c2
2. 7r7c8=7r9c8-(7=4)r9c3-(47=6)r9c2-6r1c2=34r1c23-34r1c578=89r1c78-(9=6)r1c5-(6=7)r3c6-(7=9)r2c6-(79=5)r7c6-5r7c8 : => <5> r7c8 => placement 5 r7c6, r3c8 etc

re 1A. Very cool. I looked at that but went the wrong way with the [34]: I went into r1c5 and hit a dead end.

re1B: This is what I'm talkin' about. I've never used a UR like this! That said, I get lost at the end. Here's how I'm reading it: if the [89]'s are both in box 3 they can't both be in box 6 or there'd be a deadly pattern. So if it isn't [89] in box 6 it must be [3], putting [9] into r6c8 and removing [9] from r6c12. I don't follow from there.
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Re: Structures within nodes

Postby aran » Mon Jan 05, 2009 10:49 am

Luke451 wrote:
aran wrote:
Code: Select all
2..5.1..7.8.....6...9.....28.69.3......1.4......6.27.53.....6...1.....2.5..2.8..9

 *-----------------------------------------------------------*
 | 2     346  #34    | 5     3469  1     | 3489  3489  7     |
 | 147   8    *1457  | 347   2     79    |*1459  6     134   |
 | 1467  3457  9     | 8     34    67    | 1345 *1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   2357  | 1     57    4     | 389   389   6     |
 | 149   349  #134   | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     2479  2478  | 47    149   579   | 6    *1457  148   |
 | 4679  1     478   | 347   49    5679  | 45    2     348   |
 | 5     467  #47    | 2     1346  8     | 134  *1347  9     |
 *-----------------------------------------------------------*

A couple of moves to further the quest:)
1. 47r9c23=6r9c2-6r1c2=34r1c23-34r3c2
A=57r34c2 : =><7>r7c2
B (using deadly rectangle considerations)=89r1c78-(8+9)r5c78=3r5c7/8-(3=9)r6c8-(9=34)r6c2 (=>pair34 r16c2) : =><4>r7c2
2. 7r7c8=7r9c8-(7=4)r9c3-(47=6)r9c2-6r1c2=34r1c23-34r1c578=89r1c78-(9=6)r1c5-(6=7)r3c6-(7=9)r2c6-(79=5)r7c6-5r7c8 : => <5> r7c8 => placement 5 r7c6, r3c8 etc

re 1A. Very cool. I looked at that but went the wrong way with the [34]: I went into r1c5 and hit a dead end.

re1B: This is what I'm talkin' about. I've never used a UR like this! That said, I get lost at the end. Here's how I'm reading it: if the [89]'s are both in box 3 they can't both be in box 6 or there'd be a deadly pattern. So if it isn't [89] in box 6 it must be [3], putting [9] into r6c8 and removing [9] from r6c12. I don't follow from there.


You're as good as there. 9 removed from r6c2 leaves 34 which combines with 34 in r1c2 (as generated early on in the chain) to form the pair 34 in column 2 : so either 47r9c23 is true or the 34 pair is true (or both to be strictly correct) and whichever the elimination <4>r7c2 follows.
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Re: Structures within nodes

Postby Luke » Mon Jan 05, 2009 11:50 am

aran wrote:9 removed from r6c2 leaves 34 which combines with 34 in r1c2 (as generated early on in the chain) to form the pair 34 in column 2 : so either 47r9c23 is true or the 34 pair is true (or both to be strictly correct) and whichever the elimination <4>r7c2 follows.

Ok, claro que si. When =6r9c2 was established at the start, r1c2 became [34]. I inconveniently forgot that when I got to the end and looked at my PM with the [6] still up there. I gotta pay more attention....

Anyway, I appreciate the UR example very much. I'm beginning to see there is no limit as to what can be used in an AIC...and that I'm late to the party again.

Here's another just for (my) practice:
346r1c235=9r1c5-(9=4)r8c5-(4=3)r3c5-3r2c4=3r2c9 =><3>r1c78.
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Re: Structures within nodes

Postby ttt » Mon Jan 05, 2009 4:46 pm

Luke451 wrote:Here's a puzzle I've been stuck on for weeks and I finally made a placement using such a technique. It's Extreme #110 from late October:
Code: Select all
2..5.1..7.8.....6...9.....28.69.3......1.4......6.27.53.....6...1.....2.5..2.8..9

 *-----------------------------------------------------------*
 | 2     346  #34    | 5     3469  1     | 3489  3489  7     |
 | 147   8    *1457  | 347   2     79    |*1459  6     134   |
 | 1467  3457  9     | 8     34    67    | 1345 *1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   2357  | 1     57    4     | 389   389   6     |
 | 149   349  #134   | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     2479  2478  | 47    149   579   | 6    *1457  148   |
 | 4679  1     478   | 347   49    5679  | 45    2     348   |
 | 5     467  #47    | 2     1346  8     | 134  *1347  9     |
 *-----------------------------------------------------------*

The cells marked with [#] comprise a “hidden triple" on [134] and the rest is an AIC.

134r169c3=7r9c3-7r9c8=(7-5)r7c8=5r3c8-5r2c7=5r2c3 => <14>r2c3. r6c3=1 follows.

I'm trying to find more, so if anyone wants to help me expand my horizons with this puzzle I'd be grateful!


Based on aran's step2, I found (using Eureka/AIC notation):

01: (7)r7c8=(7)r9c8-(hp47=6)r9c23-(6)r1c2=(6)r3c1-(6=7)r3c6-(hp79=5)r27c6 => r7c8<>5, some singles
02: (7)r3c12=(7-1)r2c1=(1-6)r3c1=(6)r3c6 => r3c6<>7, some singles and SSTS to the end

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Postby Luke » Mon Jan 05, 2009 4:49 pm

Code: Select all
 *-----------------------------------------------------------*
 | 2     346   34    | 5     3469  1     | 3489  3489  7     |
 | 147   8     1457  | 347   2     79    | 1459  6     134   |
 | 1467  3457  9     | 8     34    67    | 1345  1345  2     |
 |-------------------+-------------------+-------------------|
 | 8     57    6     | 9     57    3     | 2     14    14    |
 | 79    239   2357  | 1     57    4     | 389   389   6     |
 | 149   349   134   | 6     8     2     | 7     39    5     |
 |-------------------+-------------------+-------------------|
 | 3     2479  2478  | 47    149   579   | 6     1457  148   |
 | 4679  1     478   | 347   49    5679  | 45    2     348   |
 | 5     467   47    | 2     1346  8     | 134   1347  9     |
 *-----------------------------------------------------------*

aran wrote:
2. 7r7c8=7r9c8-(7=4)r9c3-(47=6)r9c2-6r1c2=34r1c23-34r1c578=89r1c78-(9=6)r1c5-(6=7)r3c6-(7=9)r2c6-(79=5)r7c6-5r7c8 : => <5> r7c8 => placement 5 r7c6, r3c8 etc

Weak links like these are not widely used but seem very effective. Yet another way to advance a chain. Thanks for the enlightenment. I've never seen them suggested by any web site, tutorial or solver/analyzer.

I see ttt has offered a shorthand for the same link. More grist for the mill, thanks! And ttt, that being your 100th post here, please see the mods for your cake.:D
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Postby ronk » Mon Jan 05, 2009 6:03 pm

Luke451 wrote:
aran wrote:2. 7r7c8=7r9c8-(7=4)r9c3-(47=6)r9c2-6r1c2=34r1c23-34r1c578=89r1c78-(9=6)r1c5-(6=7)r3c6-(7=9)r2c6-(79=5)r7c6-5r7c8 : => <5> r7c8 => placement 5 r7c6, r3c8 etc

Weak links like these are not widely used but seem very effective.

r7c8 =7= r9c8 -7- als:r9c23 -6- r1c2 =6= r1c5 -6- als:r237c6 -5- r7c8 ==> r7c8<>5
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Postby ttt » Mon Jan 05, 2009 8:54 pm

Luke451 wrote:And ttt, that being your 100th post here, please see the mods for your cake.:D

Of cause, thanks for noticing that:) and now: 101:D

BTW, this puzzle solved here (date: Nov.02/08) that I used AUR’s path.

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Postby Luke » Tue Jan 06, 2009 4:51 am

ronk wrote:r7c8 =7= r9c8 -7- als:r9c23 -6- r1c2 =6= r1c5 -6- als:r237c6 -5- r7c8 ==> r7c8<>5

Nice. Not only is that a link or two shorter, but now I have an inkling as to how to present these in NL notation next time. I also think I understand better why the highlighted links work. I.e., as in the the first one, the [47] itself is an almost locked set that can be used as a link in the chain. I've seen these before in the forum, but I'm just now starting to get a handle on them.

ttt, I figured this puzzle had been parsed out elsewhere, as are all the Extremes these days. I simply hijacked this one for my own purposes.
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Postby DonM » Tue Jan 06, 2009 6:04 am

Code: Select all
SSTS:
*--------------------------------------------------------------------*
 | 2      346    34     | 5      3469   1      | 3489   3489   7      |
 | 147    8      1457   | 347    2      79     | 1459   6      134    |
 | 1467   3457   9      | 8      34     67     | 1345   1345   2      |
 |----------------------+----------------------+----------------------|
 | 8      57     6      | 9      57     3      | 2      14     14     |
 | 79     23579  2357   | 1      57     4      | 389    389    6      |
 | 149    349    134    | 6      8      2      | 7      39     5      |
 |----------------------+----------------------+----------------------|
 | 3      2479   2478   | 47     149    579    | 6      1457   148    |
 | 4679   1      478    | 347    49     5679   | 45     2      348    |
 | 5      467    47     | 2      1346   8      | 134    1347   9      |
 *--------------------------------------------------------------------*


From the SSTS position, this was my opening move as posted back in October (FWIW: With the Extremes, on Eureka, we typically start from the SSTS position.)

(6)r8c6 = r8c1 - als(6=47)r9c23 - (7)r9c8 = (7-5)r7c8 = (5)r7c6 => r8c6<>5 -> r7c6=5, r8c7=5, r2c3=5, r3c8=5
->type 1 UR(5,7)r45c25 ->r5c2<>5,7 -> r4c2=5, r5c5=5, r4c5=7, r6c3=1
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Postby Luke » Thu Jan 08, 2009 6:06 am

Acronym questions have come up as I study all this. On the left is the acronym, the right what I think it means:

Code: Select all
np     naked pair
nt     naked triple
hp     hidden pair
ht     hidden triple
AHT    almost hidden triple
AHS    almost hidden set
sis    ??
xw     ??
fxw    ??

It appears that the majority of the "structures" in AICs fall into the general category of almost locked sets of various sizes. The basic logic in all of them is that either the set is true or the extra candidate is. So far, the techniques I've seen "almosted" in chains are als, URs, and Sue de Coqs. Theoretically, I guess that any almost structure can be used in the quest for the next strong link. For example, it figures that finned fish could be seen as "almost x-wings" or "almost swordfish" in an AIC.
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Postby DonM » Thu Jan 08, 2009 7:33 am

Luke451 wrote:Acronym questions have come up as I study all this. On the left is the acronym, the right what I think it means:

Code: Select all
np     naked pair
nt     naked triple
hp     hidden pair
ht     hidden triple
AHT    almost hidden triple
AHS    almost hidden set
sis    ??
xw     ??
fxw    ??

It appears that the majority of the "structures" in AICs fall into the general category of almost locked sets of various sizes. The basic logic in all of them is that either the set is true or the extra candidate is. So far, the techniques I've seen "almosted" in chains are als, URs, and Sue de Coqs. Theoretically, I guess that any almost structure can be used in the quest for the next strong link. For example, it figures that finned fish could be seen as "almost x-wings" or "almost swordfish" in an AIC.


sis = strong inference set (as first popularized by Steve K, I believe).
xw = x-wing
fxw = finned x-wing
:)
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Postby Luke » Thu Jan 08, 2009 4:39 pm

Thanks, Don. The latter two seem so obvious now, but I was side-tracked into the notion that somehow they related to some variation like als-xz. Now I’ll have to delve into what “sis” is all about.

I’d like to say I appreciate how patient and indulgent the SPF cadre is when helping folks like me catch up on topics in which they've long been conversant. I know it must make their eyes roll sometimes. Hopefully there are other intermediate players who got something out of this as well. I know this, though: in the last three days I’ve solved two of the puzzles in my “stuck pile” as a result of this. Very happy!
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