dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

gsf # 176 # 108
Goto page 1, 2  Next
 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles
View previous topic :: View next topic  
Author Message
Pat



Joined: 23 Feb 2010
Posts: 162

PostPosted: Fri Jun 08, 2012 8:35 am    Post subject: gsf # 176 # 108 Reply with quote


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

    [ play ]

      -- graded "too hard"
      but only needs "basic" moves
Code:

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

Back to top
View user's profile Send private message
arkietech



Joined: 31 Jul 2008
Posts: 1687
Location: Northwest Arkansas USA

PostPosted: Fri Jun 08, 2012 12:52 pm    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Jun 08, 2012 1:28 pm    Post subject: Reply with quote

Excellent SdC Very Happy

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
Back to top
View user's profile Send private message
tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Jun 08, 2012 1:39 pm    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Jun 08, 2012 2:11 pm    Post subject: Reply with quote

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:

 *-----------------------------------------------------------------------------*
 | 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

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
Back to top
View user's profile Send private message
arkietech



Joined: 31 Jul 2008
Posts: 1687
Location: Northwest Arkansas USA

PostPosted: Fri Jun 08, 2012 2:35 pm    Post subject: Reply with quote

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


Thanks Embarassed
Back to top
View user's profile Send private message
Pat



Joined: 23 Feb 2010
Posts: 162

PostPosted: Sun Jun 10, 2012 7:17 am    Post subject: Reply with quote


    glad to see you all had such fun with this puzzle

    however, it only needs "basic" moves -- did nobody try that ?

    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 ?
Back to top
View user's profile Send private message
arkietech



Joined: 31 Jul 2008
Posts: 1687
Location: Northwest Arkansas USA

PostPosted: Sun Jun 10, 2012 12:10 pm    Post subject: Reply with quote

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.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sun Jun 10, 2012 4:31 pm    Post subject: Reply with quote

arkietech wrote:
Of course. But that is not any fun. Very Happy
Evil or Very Mad
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
Back to top
View user's profile Send private message
arkietech



Joined: 31 Jul 2008
Posts: 1687
Location: Northwest Arkansas USA

PostPosted: Sun Jun 10, 2012 4:39 pm    Post subject: Reply with quote

keith wrote:
arkietech wrote:
Of course. But that is not any fun. Very Happy


Correction: unless done without pencil marks Exclamation
Back to top
View user's profile Send private message
aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Wed Jun 13, 2012 5:29 pm    Post subject: Reply with quote

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.
Back to top
View user's profile Send private message
arkietech



Joined: 31 Jul 2008
Posts: 1687
Location: Northwest Arkansas USA

PostPosted: Wed Jun 13, 2012 6:45 pm    Post subject: Reply with quote

aran wrote:
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.

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?
Back to top
View user's profile Send private message
DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Wed Jun 13, 2012 10:00 pm    Post subject: Reply with quote

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.
Back to top
View user's profile Send private message
keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 14, 2012 9:22 am    Post subject: Reply with quote

arkietech wrote:
aran wrote:
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.

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
Back to top
View user's profile Send private message
aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Thu Jun 14, 2012 11:26 am    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
arkietech



Joined: 31 Jul 2008
Posts: 1687
Location: Northwest Arkansas USA

PostPosted: Thu Jun 14, 2012 11:51 am    Post subject: Reply with quote

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 Very Happy Most helpful and POWERFUL.
Back to top
View user's profile Send private message
ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Thu Jun 14, 2012 1:50 pm    Post subject: Reply with quote

[edit: deleted]

Last edited by ronk on Fri Jun 15, 2012 10:25 pm; edited 2 times in total
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Jun 15, 2012 3:51 am    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Fri Jun 15, 2012 12:32 pm    Post subject: Reply with quote

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
Back to top
View user's profile Send private message
aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Sat Jun 16, 2012 1:43 pm    Post subject: Reply with quote

DonM wrote:

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.

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 !
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles All times are GMT
Goto page 1, 2  Next
Page 1 of 2

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group