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gsf # 176 # 108
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Pat

Joined: 23 Feb 2010
Posts: 207

Posted: Fri Jun 08, 2012 8:35 am Post subject: gsf # 176 # 108

..7...1...6...3.5.5.....9.4.....9.8.....8.....9.7.1...4.9.....5.8.2...4...1...7..

[ play ]

Code:

. . 7 | . . . | 1 . .
. 6 . | . . 3 | . 5 .
5 . . | . . . | 9 . 4
-------+-------+------
. . . | . . 9 | . 8 .
. . . | . 8 . | . . .
. 9 . | 7 . 1 | . . .
-------+-------+------
4 . 9 | . . . | . . 5
. 8 . | 2 . . | . 4 .
. . 1 | . . . | 7 . .

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Fri Jun 08, 2012 12:52 pm Post subject:

Good puzzle Very Happy

After a hidden pair in row 8 there is a SDC that reduces it to one naked pair and singles.

Code:

*-----------------------------------------------------------------------------*
| 2389 234 7 | 45689 24569 24568 | 1 236 2368 |
| 1289 6 248 | 1489 12479 3 | 28 5 28-7 |
| 5 123 238 | 168 1267 2678 | 9 2367 4 |
|-------------------------+-------------------------+-------------------------|
| 12367 123457 23456 | 3456 23456 9 |b23456 8 c12367 |
| 12367 123457 23456 | 3456 8 2456 |b23456 19-2367 c123679 |
| 2368 9 234568 | 7 23456 1 |b23456 b236 c236 |
|-------------------------+-------------------------+-------------------------|
| 4 237 9 | 1368 1367 678 | 2368 1236 5 |
| 367 8 356 | 2 19 567 | 36 4 a19 |
| 236 235 1 | 345689 34569 4568 | 7 2369 23689 |
*-----------------------------------------------------------------------------*
Sue De Coq
(19)r8c9, (23456)r6c78,r45c7, (123679)r456c9 => r5c8<>2367, r2c9<>7

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Fri Jun 08, 2012 1:28 pm Post subject:

Excellent SdC I do not normally look for such big, involved SdCs but this one is definitely a winner. Although it is not needed to complete the puzzle, I believe that you could also delete (9) from r9c9. Ted

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Fri Jun 08, 2012 1:39 pm Post subject:

Instead of a hidden pair in r8c59, I found the naked quad in r81367. However it was not until I reviewed the great SdQ that I found the naked 5-cell pattern in b6: r456c7\|r6c89, which also corresponds to the naked triple in r4c9\|r5c89. I just do not normally check for such "big" patterns. Ted

ronk

Joined: 07 May 2006
Posts: 398

Posted: Fri Jun 08, 2012 2:11 pm Post subject:

arkietech wrote:

Good puzzle Very Happy

After a hidden pair in row 8 there is a SDC that reduces it to one naked pair and singles.

Code:

This SDC may also be viewed as an m-ring: (1=9)r8c9 - (9)r5c9 = (9-1)r5c8 = (1)r45c9 - continuous loop

Last edited by ronk on Fri Jun 15, 2012 10:22 pm; edited 1 time in total

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Fri Jun 08, 2012 2:35 pm Post subject:

tlanglet wrote:

I believe that you could also delete (9) from r9c9.

Thanks

Pat

Joined: 23 Feb 2010
Posts: 207

Posted: Sun Jun 10, 2012 7:17 am Post subject:

tlanglet wrote:

Instead of a hidden pair in r8, I found the naked quad.

---I found the naked 5-cell in b6, which also corresponds to the triple in r4c9+r5c89

yes, r8 and b6 are the first 2 moves in my solution-path;
what's the 3rd move ?

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Sun Jun 10, 2012 12:10 pm Post subject:

Pat wrote:

however, it only needs "basic" moves -- did nobody try that ?
what's the 3rd move ?

Of course. But that is not any fun. Very Happy

The hidden triple in box 6 uncovers another triple in col 8 and leads to spotting the SDC.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Jun 10, 2012 4:31 pm Post subject:

arkietech wrote:

Of course. But that is not any fun. Very Happy

I do these on paper with no pencil marks.

I stared at it for about a day to see the pair 19 in R8. Then, another day to see the triple 179 in B6. Then, a pair 28 in B3 and you are done.

Pat, thank you.

And, by the way, I much more enjoy doing this site's Hard puzzles (with no pencil marks) than the usual Very Hard one-step XY-wing puzzles.

Keith

Last edited by keith on Sun Jun 10, 2012 4:41 pm; edited 1 time in total

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Sun Jun 10, 2012 4:39 pm Post subject:

keith wrote:

arkietech wrote:

Of course. But that is not any fun. Very Happy

Correction: unless done without pencil marks Exclamation

aran

Joined: 19 Apr 2010
Posts: 70

Posted: Wed Jun 13, 2012 5:29 pm Post subject:

ronk wrote:

This is probably ancient news, but I think all SDCs are also HSR (hub, spoke, rim) patterns, a pattern rarely used any more.

HSR imo suffered from lack of clear definition, and ended up being neither a clear concept nor a clear pattern.
SDC is at any rate a specific example of DL-ALS.
And suffers from a cumbersome definition (bivalue in a box, ALS in a row intersecting the box with the bivalue candidates also occurring in the ALS but not outside the box-line intersection, in which case any outside candidate, not being a bivalue candidate, seeing all occurences in the ALS....etc) mainly because it is not seen as a specific case of DL-ALS.
DL-ALS being a powerful concept with a clear and simple definition.

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Wed Jun 13, 2012 6:45 pm Post subject:

aran wrote:

HSR means Hub Spoke Rim.
What does the DL of DL-ALS mean? Are they the same thing?
Can you give an example of where a DL-ALS would not be an SDC? Confused

I assume the bivalue is the hub, and the line(row/col) is the spoke. What is the rim?

DonM

Joined: 15 Sep 2009
Posts: 51

Posted: Wed Jun 13, 2012 10:00 pm Post subject:

aran wrote:

ronk wrote:

This is probably ancient news, but I think all SDCs are also HSR (hub, spoke, rim) patterns, a pattern rarely used any more.

HSR imo suffered from lack of clear definition, and ended up being neither a clear concept nor a clear pattern.

Hi Aran! I agree and I don't see the connection with SDCs, but that's probably because I never delved into HSR as a pattern to look for.

Quote:

SDC is at any rate a specific example of DL-ALS.
And suffers from a cumbersome definition (bivalue in a box, ALS in a row intersecting the box with the bivalue candidates also occurring in the ALS but not outside the box-line intersection, in which case any outside candidate, not being a bivalue candidate, seeing all occurences in the ALS....etc) mainly because it is not seen as a specific case of DL-ALS.
DL-ALS being a powerful concept with a clear and simple definition.

Yes, the SDC definition can be combersome and confusing as compared to DL-ALS, but even so and ironically (as I've mentioned in the past) once the SDC pattern concept is understood, IMO it is much easier to find than looking for a corresponding DL-ALS pattern. It's pretty rare to see a manual solution that describes a DL-ALS.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Thu Jun 14, 2012 9:22 am Post subject:

arkietech wrote:

aran wrote:

HSR means Hub Spoke Rim.
What does the DL of DL-ALS mean? Are they the same thing?
Can you give an example of where a DL-ALS would not be an SDC? Confused

I assume the bivalue is the hub, and the line(row/col) is the spoke. What is the rim?

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=26009&sid=52db1fef6fe172ec93871735298d3469#26009
Keith

aran

Joined: 19 Apr 2010
Posts: 70

Posted: Thu Jun 14, 2012 11:26 am Post subject:

arkietech wrote:

What does the DL of DL-ALS mean? Are they the same thing?
Can you give an example of where a DL-ALS would not be an SDC? Confused

I assume the bivalue is the hub, and the line(row/col) is the spoke. What is the rim?

DL means doubly-linked or as preferred by some dual-linked.
The concept HSR lacks as mentioned imo clear definition by which I mean clear definition of Hub, of Spoke, of Rim, and very importantly where and why fall the eliminations.

Example of non-SDC DL-ALS (taken from post by ronk, as followed up by Allan Barker [http://forum.enjoysudoku.com/almost-locked-sets-xz-rule-doubly-linked-t3979.html]

Code:

+---------------------------------------------------------------------------------------+
| 458 1 9 | 258 458 6 | 3 2478 247 |
| 458 7 2 | 589 34589 34589 | 168 14689 469 |
| 348 348 6 | 289 1 7 | 28 2489 5 |
+---------------------------------------------------------------------------------------+
| 1 245 457 | 3 5678 258 | 9 2467 2467 |
| 2347 23459 457 | 15679 5679 1259 | 2567 23467 8 |
| 6 2359 8 | 4 579 259 | 257 237 1 |
+---------------------------------------------------------------------------------------+
| 2478 6 457 | 5789 345789 34589 | 1278 12789 2379 |
| 478 458 1 | 56789 2 34589 | 678 6789 3679 |
| 9 28 3 | 1678 678 18 | 4 5 267 |
+---------------------------------------------------------------------------------------+

ALS1 = 2589r123c4
ALS2 = 156789r789c4+r9c56
double links on 5 and 9
ie just to be clear : 5ALS1-5ALS2 and 9ALS1-9ALS2

write as {2859} {591678} ie highlighting the double-links and having them face each other
then one can immediately write-out all the eliminations almost without thinking (hence to my mind the beauty of this structure : simple logic, powerful, eliminations facile)
starting with ALS1
any peer of 2 : none
any peer of 8 : <8>r1c5 <8>r2c5 <8>r2c6 <8>r7c4 <8>r8c4 <8>r9c4
moving on to ALS2
any peer of 1 : none
any peer of 6 : none
any peer of 7 : <7>r7c5
any peer of 8 : <8>r7c5 <8>r7c6 <8>r8c6
moving on to the double-links
any peer of BOTH 5s : <5>r5c4
any peer of BOTH 9s : <9>r5c4

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Thu Jun 14, 2012 11:51 am Post subject:

aran wrote:

write as {2859} {591678} ie highlighting the double-links and having them face each other
then one can immediately write-out all the eliminations almost without thinking (hence to my mind the beauty of this structure : simple logic, powerful, eliminations facile)

Thanks

Most helpful and POWERFUL.

ronk

Joined: 07 May 2006
Posts: 398

Posted: Thu Jun 14, 2012 1:50 pm Post subject:

[edit: deleted] Last edited by ronk on Fri Jun 15, 2012 10:25 pm; edited 2 times in total

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Jun 15, 2012 3:51 am Post subject:

My solver doesn't handle DL-ALS. However,, it did manage to find most of the DL-ALS eliminations; but through different ALS sets.

Note: my solver doesn't (necessarily) find all eliminations when an ALS loop is involved.

Code:

+--------------------------------------------------------------------------------+
| 458 1 9 | 258 458 6 | 3 2478 247 |
| 458 7 2 | 589 34589 34589 | 168 14689 469 |
| 348 348 6 | 289 1 7 | 28 2489 5 |
|--------------------------+--------------------------+--------------------------|
| 1 245 457 | 3 5678 258 | 9 2467 2467 |
| 2347 23459 457 | 15679 5679 1259 | 2567 23467 8 |
| 6 2359 8 | 4 579 259 | 257 237 1 |
|--------------------------+--------------------------+--------------------------|
| 2478 6 457 | 5789 345789 34589 | 1278 12789 2379 |
| 478 458 1 | 56789 2 34589 | 678 6789 3679 |
| 9 28 3 | 1678 678 18 | 4 5 267 |
+--------------------------------------------------------------------------------+
# 149 eliminations remain

(6789=5) r4569c5 - (5=ALS=9)r4569c6 - (9=5678)r4569c5 => r7c5<>78; r12c5<>8
(1289=5) r4569c6 - (5=ALS=9)r4569c5 - (9=1258)r4569c6 => r278c6<>8
(5=ALS=9)r4569c5 - (9=ALS=5)r4569c6 - loop => r5c4<>59
(168=7) r9c456 - (7=2589) r1237c4 => r8c4<>8

aran

Joined: 19 Apr 2010
Posts: 70

Posted: Fri Jun 15, 2012 12:32 pm Post subject:

ronk wrote:

Code:

+---------------------------------------------------------------------------------------+
| 458 1 9 | 258 458 6 | 3 2478 247 |
| 458 7 2 | 589 34589 34589 | 168 14689 469 |
| 348 348 6 | 289 1 7 | 28 2489 5 |
+---------------------------------------------------------------------------------------+
| 1 245 457 | 3 5678 258 | 9 2467 2467 |
| 2347 23459 457 |H15679 5679 1259 | 2567 23467 8 |
| 6 2359 8 | 4 579 259 | 257 237 1 |
+---------------------------------------------------------------------------------------+
| 2478 6 457 | 5789 345789 34589 | 1278 12789 2379 |
| 478 458 1 | 56789 2 34589 | 678 6789 3679 |
| 9 28 3 | 1678 R678 R18 | 4 5 267 |
+---------------------------------------------------------------------------------------+

Consider the AHS complement in c4 instead, i.e., 167c4, and you have an HSR. The AALS r9c56 is the rim, where three of the four digits each see a strong link terminating in one cell r5c4, which is the hub. Whichever two digits are ultimately true in the rim, one of them must be true in the hub. Each inference path from the rim to the hub is considered a spoke.

With only three possibilities for the hub, r5c4=167. Weak links within the spokes become conjugate links for r7c5<>7, and the AALS becomes locked for r7c456, r8c46, r9c4<>8. Follow-on locked candidate moves cause r1c5, r2c56, r9c2<>8.

On HSR, the presentation serves I think to illustrate the point made at the conclusion of this post, which begins with a preamble :
the most general form for the logic behind DL-ALS, Nice Loops, Fish and others is Rank 0 logic.
This term being (very useful) jargon won't meaning anything to those not familiar with the concept, so a brief illustration may help, using as an example the familiar Swordfish eg 5c147r258 :
- there are exactly 3 truths in 5c147 (ie 5 must occur once in each column)
- there are exactly 3 truths in 5r258.(ie 5 must occur once in each row)
- what happens if any truth in 5r258 occurs outside of r2c147 r5c147 r8c147 ?
- eg suppose 5r2c9 is true : then none of 5r2c147 can be true.
- consequently the 3 truths in c147 are now restricted to rows 5 and 8 at r5c147 and r8c147.
- but there can be only 2 truths in rows 5 and 8. So impossible, contradiction.
- hence any candidate 5 in rows 258 outside of c147 must be false
(all of that is well-known, but it's to prepare the ground for the jargon).
Proceeding now to terminology :
Call the object (ie some set of cells and certain or all of their candidates) under consideration a structure (above : structure=swordfish)
Determine number of truths within the structure (above : 3 truths in 5c147). Call that the BASE SET of truths. Suppose it consists of N truths
Find a way to (minimally) cover those truths with some other set of truths (above : 3 truths in 5r258). That is, regardless of where the truths in the base lie, they also definitely lie in the cover. Call that the COVER SET of truths. Suppose it consists of M truths.
Then the RANK of the structure is defined as M-N ie the excess of cover over base.

With that in find, then :
- RANK 0 structures are in themselves pleasing objects
- AND anything which would reduce the number of truths in the cover set must be false (for there would be N truths "covered" by N-1 truths : impossible) : leading often to a large number of eliminations.
- which could be formulated informally as : anything in the cover outside of the base is false.

With all that in mind, the point is now this :
most rank 0 structures cannot be visualised in any simple way; they are constructed from the ground up, and usually any attempt to express them in AIC style would be madness leading to virtually unfollowable hugely-bracketed mega-indigestible chains as against the compelling simple logic of Rank 0.

There are certain exceptions to all that and most notably DL-ALS where the logic is clear, and easy (visualisation of the double links).
As against that, HSR is NOT imo an exception. In other words it is a form of Rank 0 which does not have an easy logic, and represents in its own way a minor example of the complexity of Rank 0 logic when NOT EXPRESSED IN BASE/COVER form.

Lastly, taking the HSR example to which ronk points :
it can be seen in the following way as a rank 0 structure :
base of 5 truths
1c4
6c4
7c4
cell r9c5
cell r9c6
ie there must be exactly 5 truths there
cover of 5 truths
cell r5c5
6b8
7b8
8b8
1r9 (or 1b8)
ie there must be 5 truths there, with all of the truths in the base being covered ie lie somewhere in the cover.

Consequently anything in the base outside the cover can be eliminated ie
cell r5c5 : <59>r5c5
6b8 : none
7b8 : <7>r7c5
8b8 : <8>r7c5 <8>r7c6 <8>r8c6 <8>r7c4 <8>r8c4 <8>r9c4
1r9 (or 1b8) : none

aran

Joined: 19 Apr 2010
Posts: 70

Posted: Sat Jun 16, 2012 1:43 pm Post subject:

DonM wrote:

Hi Don !
One way of perserving the pattern, whilst simplifying the definition would be to extend the range in a symmetrical way (see below).
Define an SDC quite simply as a DL-ALS in which one ALS is a bivalue.
Looking for the pattern would then involve taking a bivalue and seeing whether in its box, row or column it double-links to another ALS.
In this way, the historic name remains, the scope increased, symmetry emphasised and the definition simplified.

At present SDCs :
- begin in a box (bivalue double-linking in box to second ALS)
- end in a row or column (remaining cells of second ALS).
Just complete the symmetry and include those which
- begin in a row or column
- end in a box (note if beginning in a row or column, then by virtue of the double-links, the second ALS is necessarily in a box, so no other configuration is possible)

That would, as you say, require definition of DL-ALS, but then unlike any other advanced concept, DL-ALS could be explained to a novice in 10 minutes including a coffee break !

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