## Nice loop question (Extreme 100)

Post the puzzle or solving technique that's causing you trouble and someone will help

### Nice loop question (Extreme 100)

Is this a nice loop? (I've been restudying the rules of propagation because they didn't sink in the first few times.)
Code: Select all
` Extreme 100  *-----------* |1..|..9|...| |...|4.5|.2.| |9.6|2..|7.5| |---+---+---| |...|.5.|8.9| |...|...|...| |7.3|.8.|...| |---+---+---| |5.8|..2|1.4| |.9.|5.1|...| |...|8..|..3| *-----------* *-----------------------------------------------------------------------------* | 1       2       5       | 367     367     9       | 346     3468    68      | | 38      38      7       | 4       16      5       | 9       2       16      | | 9       4       6       | 2       13      8       | 7       13      5       | |-------------------------+-------------------------+-------------------------| | 246     16      124     | 167     5       3467    | 8       13467   9       | | 468     1568    9       | 167     2       3467    | 3456    134567  167     | | 7       156     3       | 9       8       46      | 2456    1456    126     | |-------------------------+-------------------------+-------------------------| | 5       367     8       | 367     3679    2       | 1       679     4       | | 2346    9       24      | 5       3467    1       | 26      78      2678    | | 246     167     14      | 8       49      67      | 25      579     3       | *-----------------------------------------------------------------------------*`

r9c8=5=r9c7=2=r8c79=4=r8c3-4-r8c5=4=r9c5=9=r9c8 =>r9c8<>7.
(Also practicing Eureka:) (5)r9c8=(5-2)r9c7=(2)r8c79-(2=4)r8c3-(4)r8c5=(4-9)r9c5=(9)r9c8 =><>(7)r9c8.
(Feel free to correct my notation if this is presented out of norm.)

My notes say I can also zap "all remaining candidates in the houses providing weak links." So also, <> (24)r8c1, right?

BTW, I think there's a SdQ that does all this for those who are interested.

Luke
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### Re: Nice loop question (Extreme 100)

Luke451 wrote:Is this a nice loop? (I've been restudying the rules of propagation because they didn't sink in the first few times.)

r9c8=5=r9c7=2=r8c79=4=r8c3-4-r8c5=4=r9c5=9=r9c8 =>r9c8<>7.
(Also practicing Eureka:) (5)r9c8=(5-2)r9c7=(2)r8c79-(2=4)r8c3-(4)r8c5=(4-9)r9c5=(9)r9c8 =><>(7)r9c8.
(Feel free to correct my notation if this is presented out of norm.)

My notes say I can also zap "all remaining candidates in the houses providing weak links." So also, <> (24)r8c1, right?

Yes, and nice move…
All week links becomes strong links => r9c8<>7, r8c1<>24 and note that it’s also r9c78<>6 that you eliminated on your grid.

ttt
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### Re: Nice loop question (Extreme 100)

ttt wrote:All week links becomes strong links => r9c8<>7, r8c1<>24 and note that it’s also r9c78<>6 that you eliminated on your grid.ttt

<Getting out notebook> "If a nice loop is completed all weak links become strong links." That's a good way to think of it. I don't know what you mean by the last part, though, "...it’s also r9c78<>6..."

Luke
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A variant with the same eliminations but without group nodes:

Continuous Nice Loop r9c8 =5= r9c7 =2= r9c1 -2- r8c3 -4- r8c5 =4= r9c5 =9= r9c8 => r8c1<>24, r9c8<>7

The Sue de Coq:

Sue de Coq: r9c123 - {12467} (r9c6 - {67}, r8c3 - {24}) => r8c1<>24, r9c8<>7
hobiwan
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### Re: Nice loop question (Extreme 100)

Luke451 wrote:I don't know what you mean by the last part, though, "...it’s also r9c78<>6..."

Original puzzle after SSTS:
Code: Select all
`*-----------------------------------------------------------------------------* | 1       2       5       | 367     367     9       | 346     3468    68      | | 38      38      7       | 4       16      5       | 9       2       16      | | 9       4       6       | 2       13      8       | 7       13      5       | |-------------------------+-------------------------+-------------------------| | 246     16      124     | 167     5       3467    | 8       13467   9       | | 468     1568    9       | 167     2       3467    | 3456    134567  167     | | 7       156     3       | 9       8       46      | 2456    1456    126     | |-------------------------+-------------------------+-------------------------| | 5       367     8       | 367     3679    2       | 1       679     4       | | 2346    9       24      | 5       3467    1       | 26      678     2678    | | 246     167     124     | 8       4[67]9  67      | 25[6]   5[6]79  3       | *-----------------------------------------------------------------------------*`
I meant, on original puzzle after SSTS: 6’s at r9c78 are still on grid then you eliminated them before your move above.

ttt
ttt

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Thanks, ttt. Yes, I've been chipping away at this for a while now. It's one of the puzzles in my "stuck file." I've been digging them all out lately and having another go as I learn new things. Now my neighbors are getting annoyed by the constant chipping noise.

I’m interested in how you and the experts would proceed from here.
Code: Select all
` *-----------------------------------------------------------------------------* | 1       2       5       | 367     367     9       | 346     3468    68      | | 38      38      7       | 4       16      5       | 9       2       16      | | 9       4       6       | 2       13      8       | 7       13      5       | |-------------------------+-------------------------+-------------------------| | 246     16      124     | 167     5       3467    | 8       13467   9       | | 468     1568    9       | 167     2       3467    | 3456    134567  167     | | 7       156     3       | 9       8       46      | 2456    1456    126     | |-------------------------+-------------------------+-------------------------| | 5       367     8       | 367     3679    2       | 1       679     4       | | 36      9       24      | 5       3467    1       | 26      78      2678    | | 246     167     14      | 8       49      67      | 25      59      3       | *-----------------------------------------------------------------------------* `

Luke
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Luke451 wrote:I’m interested in how you and the experts would proceed from here.

I solved it here (Aug. 24/08). Hope, it’s useful for you.

ttt
ttt

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Luke451 wrote:Thanks, ttt. Yes, I've been chipping away at this for a while now. It's one of the puzzles in my "stuck file." I've been digging them all out lately and having another go as I learn new things. Now my neighbors are getting annoyed by the constant chipping noise.

I’m interested in how you and the experts would proceed from here.
Code: Select all
` *-----------------------------------------------------------------------------* | 1       2       5       | 367     367     9       | 346     3468    68      | | 38      38      7       | 4       16      5       | 9       2       16      | | 9       4       6       | 2       13      8       | 7       13      5       | |-------------------------+-------------------------+-------------------------| | 246     16      124     | 167     5       3467    | 8       13467   9       | | 468     1568    9       | 167     2       3467    | 3456    134567  167     | | 7       156     3       | 9       8       46      | 2456    1456    126     | |-------------------------+-------------------------+-------------------------| | 5       367     8       | 367     3679    2       | 1       679     4       | | 36      9       24      | 5       3467    1       | 26      78      2678    | | 246     167     14      | 8       49      67      | 25      59      3       | *-----------------------------------------------------------------------------* `

From the above position, this might take you further on your journey :
1.5r6c2=(5-8)r5c2=(8-3)r2c2=3r2c1-(3=6)r8c1-(6=2)r8c7-(2=5)r9c7 : => <5>r6c7
2.26r68c7=4r6c7-(4=6)r6c6-(6=7)r9c6-(7=16)r49c2-(16=5)r6c2-(456=1)r6c8-(1=3)r3c8-(34=6)r1c7-(6=2)r8c7 :=> <2>=5r9c7. Then 7 other resulting placements, and related eliminations.
aran

Posts: 334
Joined: 02 March 2007

I'm trying to use this as a continuous nice loop on 4, but I'm unsure if the use of the groups in row 1 is proper.
Code: Select all
`Ruud's Nightmare, 1/05/08  *-----------------------------------------------------------------------------* |*346     1      *345     | 2368    28      7       | 26     *49     *459     | |*456     8       2       | 1569   *45      1569    | 16      7       3       | | 9       35      7       | 12356  *245     12356   | 126     8      *45      | |-------------------------+-------------------------+-------------------------| | 34      239     6       | 278     1       48      | 5       29      79      | | 1245    7       45      | 256     9       2456    | 8       3       12      | | 15      259     8       | 257     3       25      | 4       6       1279    | |-------------------------+-------------------------+-------------------------| | 57      4       1359    | 123589  258     23589   | 37      12      6       | | 8       6       135     | 1235    7       1235    | 9       124    -42      | | 27      23      19      | 4       6       19      | 37      5       8       | *-----------------------------------------------------------------------------*`

[4]: -[r2c5]=[r2c1]-[r1c13]=[r1c89]-[r3c9]=[r3c5]-[r2c5]=continuous => r8c9<>4. Grateful for any help.

Luke
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Luke451 wrote:I'm trying to use this as a continuous nice loop on 4, but I'm unsure if the use of the groups in row 1 is proper.

[4]: -[r2c5]=[r2c1]-[r1c13]= [r1c89]-[r3c9] =[r3c5]-[r2c5]=continuous => r8c9<>4

Although the continuous loop is correct, the elimination is not.

All weak links of a continuous loop are converted to conjugate links. However, an elimination candidate must see all candidates of the weak link. In your example, r8c9 does not see r1c8.
ronk
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Got it, thanks. I knew something smelled fishy.....

Luke
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Here's the nice loop mystery I'm trying to unravel for this week...

I've been checking out hobiwan's new solver HoDoKu (one word review: fantastic!) The solver comes up with some moves that are challenging to me. I've been staring at this one for a long time:
Code: Select all
`HoDoKu Extreme 5308 *-----------------------------------------------------------------------------* | 6       147     1237    | 13      479     5       | 379     8       279     | | 23457   147     123578  | 13      4789    789     | 35679   579     2679    | | 357     9       3578    | 2       6       78      | 357     4       1       | |-------------------------+-------------------------+-------------------------| | 8       16      1269    | 7       5       29      | 19      3       4       | | 79      5       4       | 8       1       3       | 2       6       79      | | 279     3       127     | 4       29      6       | 8       179     5       | |-------------------------+-------------------------+-------------------------| | 1       8       5679    | 56      3       4       | 5679    2       679     | | 34579   467     35679   | 56      27      127     | 145679  1579    8       | | 457     2       567     | 9       78      178     | 14567   157     3       | *-----------------------------------------------------------------------------*`

HoDoKu offered the following loop for this position:
Grouped Discontinuous Nice Loop: r4c2-1-r4c7-9-ALS:r1237c7-6-r9c7=6=r9c3-6-r4c3=6=r4c2 => r4c2<>1

My problem is trying to determine what the "assumed" shortcuts are in NL notation. The only way I can figure how the ALS portion of the loop works is as follows:
There is a weak link between the 9 in r4c7 and the group of all three 9's in r1237c7. Then there is a strong link between the group of 9's and the "hidden set" of (3567) remaining in r1237c7. The weak link to 6 in r9c7 is legitimate because it can see all the 6's in the "hidden set." By that reasoning, one could also form weak links to any 3, 5, 6 or 7 in r89c7.
Maybe another way to write it would be:
(1)r4c2-(1=9)r4c7-group(9)r127c7=hidden set(3567)r1237c7-(6)r9c7=etc.
Am I on the right track on this one

Luke
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Luke451 wrote:I've been checking out hobiwan's new solver HoDoKu (one word review: fantastic!)

Thanks a lot!

Luke451 wrote:There is a weak link between the 9 in r4c7 and the group of all three 9's in r1237c7. Then there is a strong link between the group of 9's and the "hidden set" of (3567) remaining in r1237c7. The weak link to 6 in r9c7 is legitimate because it can see all the 6's in the "hidden set." By that reasoning, one could also form weak links to any 3, 5, 6 or 7 in r89c7.

Maybe another way to write it would be:
(1)r4c2-(1=9)r4c7-group(9)r127c7=hidden set(3567)r1237c7-(6)r9c7=etc.

Am I on the right track on this one

I never really got into hidden sets but I think your reasining is perfectly sound.

The way I look at this: If you eliminate one candidate from an ALS you turn the ALS into a locked set (this is the strong link: if candidate x is not true, the ALS has to be a locked set).

r4c7=9 -> r127c7<>9 (weak inference)
r127c7<>9 -> ALS:r1237c7 becomes a locked set (strong inference)
ALS:r1237c7 is locked set in {3567} -> r9c7<>6 (weak inference)
As you wrote the last link could be r7c89<>3567

While rereading this: "hidden set" is probably more appropriate than "locked set"
hobiwan
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Code: Select all
` +--------------------------------------------------------------------------------+ |  6       147     1237    |  13      479     5       |  379     8       279     | |  23457   147     123578  |  13      4789    789     |  35679   579     2679    | |  357     9       3578    |  2       6       78      |  357     4       1       | |--------------------------+--------------------------+--------------------------| |  8       16      1269    |  7       5       29      |  19      3       4       | |  79      5       4       |  8       1       3       |  2       6       79      | |  279     3       127     |  4       29      6       |  8       179     5       | |--------------------------+--------------------------+--------------------------| |  1       8       5679    |  56      3       4       |  5679    2       679     | |  34579   467     35679   |  56      27      127     |  145679  1579    8       | |  457     2       567     |  9       78      178     |  14567   157     3       | +--------------------------------------------------------------------------------+ # 105 eliminations remain`

Please forgive me for interrupting, but does the following work? (I don't know how to write it as a chain.)

Code: Select all
` [r4c2]=1 [r4c7]<>1 r89c7=14 [r9c7]<>6 [r9c3]=6 [r4c3]<>6 [r4c2]=6 => [r4c2]<>1`

Hobiwan: Why didn't you offer the finned Franken Jellyfish present? (ronk: I didn't check to see if they were Sashimi.)
daj95376
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daj95376 wrote:does the following work? (I don't know how to write it as a chain.)

Code: Select all
` [r4c2]=1 [r4c7]<>1 r89c7=14 [r9c7]<>6 [r9c3]=6 [r4c3]<>6 [r4c2]=6 => [r4c2]<>1`

Looks fine to me. HoDoKu cant handle AHS and therefore cant find that chain (and no idea how to write this in NL notation either).

daj95376 wrote:Hobiwan: Why didn't you offer the finned Franken Jellyfish present? (ronk: I didn't check to see if they were Sashimi.)

Finned Franken Jellyfish is disabled by default for performance reasons. But even if it was enabled it is after Grouped Nice Loops. If you enable it and move it before GNL you get as next steps:
Code: Select all
`Finned Franken Jellyfish: 7 r57b34 c1379 fr2c8 efr5c1 => r2c1<>7Finned Franken Jellyfish: 9 r157b5 c3579 fr4c6 fr5c1 => r4c3<>9Locked Candidates Type 1 (Pointing): 9 in b4 => r8c1<>9...`
hobiwan
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