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 

Puzzle 10/09/08: C

 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Puzzles by daj
View previous topic :: View next topic  
Author Message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Sep 08, 2010 2:30 am    Post subject: Puzzle 10/09/08: C Reply with quote

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

Play this puzzle online at the Daily Sudoku site


Rating wrote:
Extreme/XY

Extreme as single-stepper; XY if other steps applied first.

Back to top
View user's profile Send private message
JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Wed Sep 08, 2010 9:10 am    Post subject: Reply with quote

Quote:
X Wing (4)C48/r37 : r37C567<>4
M Wing (47) : (47)R8C5 7R2 4C6 : (4)r8c5=(4)r4c6 : => r4c5<>4
Back to top
View user's profile Send private message
peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK

PostPosted: Wed Sep 08, 2010 6:21 pm    Post subject: Reply with quote

I played the same wing as JC initially..

I went back to find this one-step ALS move...
Quote:
AIC with ALS (4=9)r4c5 - ANQ(1467):(9)r3c5=(1467)r1c6|r2c56|r3c5 - (4)r3c4=r7c4 ; r8c5<>4
You could also see it as an (89)AHP but to me less clear...
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 703

PostPosted: Wed Sep 08, 2010 7:03 pm    Post subject: Reply with quote

This one stepper perhaps:

(4=9)r4c5-r4c6=(9-8)r3c6=(8-4)r3c4=r7c4; r8c5<>4

Worked on this before seeing Peter's - similar but without the ANQ
Back to top
View user's profile Send private message
JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Wed Sep 08, 2010 7:07 pm    Post subject: Reply with quote

Peter, congratulations Exclamation

Just a comment on your AIC.

From the "hub" cell R3C6 (2 spokes from 8 & 9), one can write :
    SIS[(8-4)r3c4=r7c4,(9-4)r4c6=r4c5] or 4-SIS AIC : 4C4 8R3 9C6 4R4 : (4)r7c4=(4)r4c5 : => r78c5<>4.
Thus a 4-SIS AIC (4 strong links and 3 weak links) with 4 strengths in location instead of a 6-SIS AIC (6 strong links and 5 weak links) with 5 cells and 1 strength in location , even though the grouping of cells leads to an apparent AIC with 3 SL and 2 WL.

Regards, JC
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 703

PostPosted: Wed Sep 08, 2010 8:16 pm    Post subject: Reply with quote

Prior to finding the AIC above, I was working on this puzzle looking at ALS and encountered an interesting ALS xz situation. It didn't lead to a one step move but was interesting (to me) nonetheless as personally, I had not seen this situation before: (Danny and Ronk probably have a stash of them)

We have a situation where the x and z or restricted common and common candidates can do each others job - that is to say, become interchangeable:

A={1,4,6,7,9}
B={1,6}
x = 1 or 6 (r23c5)
z = 1 or 6 (r23c5)

We can therefore eliminate both 1 and 6 from r2c6 and r3c46



Code:
+----------------------+----------------------+----------------------+
| 8      16     4      | 3      2      B16    | 5      7      9      |
| 9      16     2      | 5      A1467  47-16  | 146    3      8      |
| 5      7      3      |48-16   A1469 489-16  | 1246   14     12     |
+----------------------+----------------------+----------------------+
| 1      3      57     | 2      A49    49     | 8      6      57     |
| 2      9      567    | 1678   13567  135678 | 137    15     4      |
| 4      8      567    | 167    13567  13567  | 1237   9      12357  |
+----------------------+----------------------+----------------------+
| 6      2      8      | 147    13457  13457  | 9      145    1357   |
| 3      5      1      | 9      A47    2      | 47     8      6      |
| 7      4      9      | 16     8      1356   | 13     2      135    |
+----------------------+----------------------+----------------------+

No cigar but fun anyway!
Back to top
View user's profile Send private message
ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Wed Sep 08, 2010 8:33 pm    Post subject: Reply with quote

Mogulmeister wrote:
We have a situation where the x and z or restricted common and common candidates can do each others job - that is to say, become interchangeable:

A={1,4,6,7,9}
B={1,6}
x = 1 or 6 (r23c5)
z = 1 or 6 (r23c5)

We can therefore eliminate both 1 and 6 from r2c6 and r3c46

Congratulations, you've found a doubly-linked ALS-xz, this one aka a Sue De Coq. There are four more eliminations, but I won't spoil the fun by telling you what they are. Smile
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Sep 08, 2010 9:24 pm    Post subject: Reply with quote

It's already obvious that there are better solutions available, but I still find this interesting. Besides the X-Wing (#) used by JC, there's a conjugate Swordfish (*) network that can be embedded in a discontinuous loop:

Code:
             Swordfish
 *********************************
 (4)r4c5 - r8c5 = r8c7 - r2c7 = (4-7)r2c6 = r2c5 - (7=4)r8c5 - (4)r4c5
 +--------------------------------------------------------------------------------+
 |  8       16      4       |  3       2       16      |  5       7       9       |
 |  9       16      2       |  5      *1467   *1467    | *146     3       8       |
 |  5       7       3       | #1468    1469    14689   |  1246   #14      12      |
 |--------------------------+--------------------------+--------------------------|
 |  1       3       57      |  2      *49     *49      |  8       6       57      |
 |  2       9       567     |  1678    13567   135678  |  137     15      4       |
 |  4       8       567     |  167     13567   13567   |  1237    9       12357   |
 |--------------------------+--------------------------+--------------------------|
 |  6       2       8       | #147     13457   13457   |  9      #145     1357    |
 |  3       5       1       |  9      *47      2       | *47      8       6       |
 |  7       4       9       |  16      8       1356    |  13      2       135     |
 +--------------------------------------------------------------------------------+
 # 90 eliminations remain
Back to top
View user's profile Send private message
tlanglet



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

PostPosted: Wed Sep 08, 2010 10:11 pm    Post subject: Reply with quote

I finally took some time to work on a puzzle. I did not find anything similar to the great solutions already posted, but I did find a circumstance which I do not fully appreciate/understand.

Code:

 *-----------------------------------------------------------------------------*
 | 8       16      4       | 3       2       16      | 5       7       9       |
 | 9       16      2       | 5       1467    1467    | 146     3       8       |
 | 5       7       3       | 1468    1469    14689   | 1246    14      12      |
 |-------------------------+-------------------------+-------------------------|
 | 1       3       57      | 2       49      49      | 8       6       57      |
 | 2       9       567     | 1678    13567   135678  |*137     15      4       |
 | 4       8       567     | 167     13567   13567   |*1237    9       12357   |
 |-------------------------+-------------------------+-------------------------|
 | 6       2       8       | 147     13457   13457   | 9       145     1357    |
 | 3       5       1       | 9       47      2       | 47      8       6       |
 | 7       4       9       | 16      8       1356    |*13      2       135     |
 *-----------------------------------------------------------------------------*

Consider the ANT(1237)r569c7, marked *.

ANT(2=137)r569c7-(7)r8c7=(7)r7c9-(7=5)r4c9-(5=1)r5c8

What now? I don't believe that we have a contradiction on 1 since r5c8=1 does not see all three occurrences of 1 in the ls:(137)r569c7. But does this circumstance cause r9c7=1? If so, then

ANT(2=137)r569c7-(7)r8c7=(7)r7c9-(7=5)r4c9-(5=1)r5c8*-LS(137)r569c7[(1)r56c7=(1)r9c7]-(1)r23c7|r3c8*=(1-2)r3c9=(2)r6c9; r6c7<>2 to complete.

Ted
Back to top
View user's profile Send private message
JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Wed Sep 08, 2010 11:05 pm    Post subject: Reply with quote

daj95376 wrote:
It's already obvious that there are better solutions available, but I still find this interesting. Besides the X-Wing (#) used by JC, there's a conjugate Swordfish (*) network that can be embedded in a discontinuous loop:

Code:
             Swordfish
 *********************************
 (4)r4c5 - r8c5 = r8c7 - r2c7 = (4-7)r2c6 = r2c5 - (7=4)r8c5 - (4)r4c5
 +--------------------------------------------------------------------------------+
 |  8       16      4       |  3       2       16      |  5       7       9       |
 |  9       16      2       |  5      *1467   *1467    | *146     3       8       |
 |  5       7       3       | #1468    1469    14689   |  1246   #14      12      |
 |--------------------------+--------------------------+--------------------------|
 |  1       3       57      |  2      *49     *49      |  8       6       57      |
 |  2       9       567     |  1678    13567   135678  |  137     15      4       |
 |  4       8       567     |  167     13567   13567   |  1237    9       12357   |
 |--------------------------+--------------------------+--------------------------|
 |  6       2       8       | #147     13457   13457   |  9      #145     1357    |
 |  3       5       1       |  9      *47      2       | *47      8       6       |
 |  7       4       9       |  16      8       1356    |  13      2       135     |
 +--------------------------------------------------------------------------------+
 # 90 eliminations remain

Danny, nice move, congratulations Exclamation Here is an equivalent interpretation based on the Finned X-Wing on 4 in the rows 2 & 8 (same set of SIS):
    4-SIS t chain : [4R8 4R2] 7R2 (74)R8C5 : [X Wing (4)R82/c57]=(4-7)r2c6=r2c5-(7=8)r8c5 : (4)r2c5[z term in the t chain]=(4)r8c5 : => r347c5<>4
Regards, JC
Back to top
View user's profile Send private message
JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Thu Sep 09, 2010 1:12 am    Post subject: Reply with quote

Ted, nice find too. Congratulations Exclamation

The first chain you wrote eliminates (1)r6c7 (Note : the SIS 7B9 is superfluous). The second chain is a continuous network.
Let me rewrite it so as to make as clear as possible the strong and the weak inferences :
Code:
 *------------------------------------------------------------------------------*
 | 8       16      4       | 3       2       16      | 5       7       9        |
 | 9       16      2       | 5       1467    1467    |[1*]46   3       8        |
 | 5       7       3       | 1468    1469    14689   |[1*]246 [1**]4  [1][2]    |
 |-------------------------+-------------------------+--------------------------|
 | 1       3       57      | 2       49      49      | 8       6      [57]      |
 | 2       9       567     | 1678    13567   135678  |[1*37]  [1**5]   4        |
 | 4       8       567     | 167     13567   13567   |[1*237]  9       1[2]3-5-7|
 |-------------------------+-------------------------+--------------------------|
 | 6       2       8       | 147     13457   13457   | 9      -145     1357     |
 | 3       5       1       | 9       47      2       | 47      8       6        |
 | 7       4       9       | 16      8       1356    |[1*3]    2       135      |
 *------------------------------------------------------------------------------*
    7-SIS continuous t loop or Symmetric Pigeonhole Matrix :

    [(2371*)R6C7 (31*)R9C7 (31*7)R5C7] (75)R4C9 (51**)R5C8 (1*1**1)B3 2C9 loop

    (2)r6c7=NT(1*37)r569c7-(7=5)r4c9-(5=1**)r5c8 (pause)-{(1*)r23c7,(1**)r3c8}=(1)r3c9-(2)r3c9=(2)r6c9 loop : => (pause r6c7<>1), r6c9<>7, r6c9<>5, r7c8<>1.
There are 7 WIS : [1*c7 3c7 7c7] 7b6 5b6 1**c8 r3c9. Therefore, as in a Finless Fish (equal number of SIS and WIS), the weak links become strong.

Eliminations :
    (2)r6c7=(1)r5c8 : => r6c7<>1 (pause)
    (7)r569c7=(7)r4c9 : => r6c9<>7
    (5)r4c9=(5)r5c8 : => r6c9<>5
    (1**)r5c8=(1**)r3c8 : => r7c8<>1
    the last WL is already strong : => no elimination
Regards, JC
Back to top
View user's profile Send private message
daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Sep 09, 2010 2:19 am    Post subject: Reply with quote

tlanglet wrote:
Code:

 *-----------------------------------------------------------------------------*
 | 8       16      4       | 3       2       16      | 5       7       9       |
 | 9       16      2       | 5       1467    1467    | 146     3       8       |
 | 5       7       3       | 1468    1469    14689   | 1246    14      12      |
 |-------------------------+-------------------------+-------------------------|
 | 1       3       57      | 2       49      49      | 8       6       57      |
 | 2       9       567     | 1678    13567   135678  |*137     15      4       |
 | 4       8       567     | 167     13567   13567   |*1237    9       12357   |
 |-------------------------+-------------------------+-------------------------|
 | 6       2       8       | 147     13457   13457   | 9       145     1357    |
 | 3       5       1       | 9       47      2       | 47      8       6       |
 | 7       4       9       | 16      8       1356    |*13      2       135     |
 *-----------------------------------------------------------------------------*

ANT(2=137)r569c7-(7)r8c7=(7)r7c9-(7=5)r4c9-(5=1)r5c8

As JC mentioned, I see a conclusion of r6c7<>1.

Quote:
ANT(2=137)r569c7-(7)r8c7=(7)r7c9-(7=5)r4c9-(5=1)r5c8*-LS(137)r569c7[(1)r56c7=(1)r9c7]-(1)r23c7|r3c8*=(1-2)r3c9=(2)r6c9; r6c7<>2 to complete.

I don't agree with your conclusion here because your initial premise is that r6c7<>2 and so you already have the strong link (2)r6c7=(2)r6c9 without running around most of [stack 3].

It does appear that you (almost) have a continuous networked loop:

...=(2)r6c9-(2)r6c7

I'm guessing this is what JC derived. I'll let you check to see if the eliminations match those from JC's handywork. Personally, I wouldn't go near a continuous networked loop with a 20-foot pole!

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



Joined: 07 May 2006
Posts: 398

PostPosted: Thu Sep 09, 2010 11:28 am    Post subject: Reply with quote

JC Van Hay wrote:
Code:
 *------------------------------------------------------------------------------*
 | 8       16      4       | 3       2       16      | 5       7       9        |
 | 9       16      2       | 5       1467    1467    |[1*]46   3       8        |
 | 5       7       3       | 1468    1469    14689   |[1*]246 [1**]4  [1][2]    |
 |-------------------------+-------------------------+--------------------------|
 | 1       3       57      | 2       49      49      | 8       6      [57]      |
 | 2       9       567     | 1678    13567   135678  |[1*37]  [1**5]   4        |
 | 4       8       567     | 167     13567   13567   |[1*237]  9       1[2]3-5-7|
 |-------------------------+-------------------------+--------------------------|
 | 6       2       8       | 147     13457   13457   | 9      -145     1357     |
 | 3       5       1       | 9       47      2       | 47      8       6        |
 | 7       4       9       | 16      8       1356    |[1*3]    2       135      |
 *------------------------------------------------------------------------------*
    7-SIS continuous t loop or Symmetric Pigeonhole Matrix :

    [(2371*)R6C7 (31*)R9C7 (31*7)R5C7] (75)R4C9 (51**)R5C8 (1*1**1)B3 2C9 loop

    (2)r6c7=NT(1*37)r569c7-(7=5)r4c9-(5=1**)r5c8 (pause)-{(1*)r23c7,(1**)r3c8}=(1)r3c9-(2)r3c9=(2)r6c9 loop : => (pause r6c7<>1), r6c9<>7, r6c9<>5, r7c8<>1.

Hmm, in this case two separate moves can be more elegant than one. If not more elegant, then at least easier to understand.

ALS-xz: (1=3)[r4c9,r5c78] - (3=1)r9c7 ==> r6c7<>1

AIC: (5=7)r4c9 - (7)r7c9 = (7-4)r8c7 = (4-5)r7c8 = (5)r5c8 - loop ==> r6c9<>7, r7c8=45, r6c9<>5
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Fri Sep 10, 2010 12:47 am    Post subject: Reply with quote

Type 1 UR (16) sets up
W-Wing (47)
Multi-coloring (4) + one extension
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Puzzles by daj All times are GMT
Page 1 of 1

 
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