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 

Set F Puzzle 64

 
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: Thu Dec 11, 2008 4:39 am    Post subject: Set F Puzzle 64 Reply with quote

Last puzzle from this set. Then I'm going to take a break.

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

Play this puzzle online at the Daily Sudoku site
Back to top
View user's profile Send private message
storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Dec 11, 2008 6:45 am    Post subject: Reply with quote

we have seen an example of mixed ends to a W-wing...

This presents an example of mixed ends to a M-wing. this means that the last pincer cell (the fourth cell in the M-wing) will be extended by another digit instead of one of the original pair. in this case the original pair is {4,8}

Code:
.------------------------.------------------------.------------------------.
| 3       12467   24678  | 2678    5       12468  | 9       14      1267   |
| 1468    9       24678  | 2678    3       12468  | 47      5       1267   |
| 1456    124567  2467   | 9       67      1246   | 8       3       1267   |
:------------------------+------------------------+------------------------:
| 9       26      1      | 5       4       26     | 3       7       8      |
| 7       8       5      | 3       1       9      | 6       2       4      |
| 46      3       246    | 268     68      7      | 1       9       5      |
:------------------------+------------------------+------------------------:
| 2       67      3      | 4       9       68     | 5      1-8      17     |
| 15      15     *478    | 78      2       3      |*47      6       9      |
| *468    467     9      | 1       678     5      | 2      *48      3      |
'------------------------'------------------------'------------------------'

notice the marked "*" cells is the M-wing on {4,8} (which normally eliminates the 8 in r9c5, ok?)

(8=4)r9c8 - (4)r8c7 = (4-8)r8c3 = (8)r9c1

but instead of extending from the 8 like we normally would, this example extends from the other candidate 6 in the last cell (r9c1). this makes it a mixed ending M-wing.
---
below we have the extension on 6's.
hopefully this is also recognized as the structure of the x-wing on 6.
however, the strong link on 6 in row 4 will provide a w-wing type of pattern. those strong links on 6 connect the group/hinge (6) in box 7 and the bivalue cell {6,8} in r7c6.
Code:
.------------------------.------------------------.------------------------.
| 3       12467   24678  | 2678    5       12468  | 9       14      1267   |
| 1468    9       24678  | 2678    3       12468  | 47      5       1267   |
| 1456    124567  2467   | 9       67      1246   | 8       3       1267   |
:------------------------+------------------------+------------------------:
| 9      #26      1      | 5       4      #26     | 3       7       8      |
| 7       8       5      | 3       1       9      | 6       2       4      |
| 46      3       246    | 268     68      7      | 1       9       5      |
:------------------------+------------------------+------------------------:
| 2      #67      3      | 4       9      #68     | 5       18      17     |
| 15      15      478    | 78      2       3      | 47      6       9      |
|#468    #467     9      | 1       678     5      | 2       48      3      |
'------------------------'------------------------'------------------------'

these cells form this chain, it almost looks like a w-wing...

(6)r9c1 = (6)r79c2 - (6)r4c2 = (6)r4c6 - (6=8)r7c6

this new chain and the M-wing we formed above start and end in the same cell which makes them weakly linked. so we can connect them like this...

(8=4)r9c8 - (4)r8c7 = (4-8)r8c3 = (8)r9c1 - (6)r9c1 = (6)r79c2 - (6)r4c2 = (6)r4c6 - (6=8)r7c6

our new chain states that either the 8 in r9c8 is true or the 8 in r7c6 is true and that means the 8 in r7c8 is eliminated collapsing the puzzle to singles.

and for those who want to see the contradiction/victim(s) as part of the chain would probably like it this way.

(8)r7c8 - (8=4)r9c8 - (4)r8c7 = (4-8)r8c3 = (8)r9c1 - (6)r9c1 = (6)r79c2 - (6)r4c2 = (6)r4c6 - (6=8)r7c6 - (8)r7c8; r7c8 <> 8
-----------------

I need to cover all bases here because that initial M-wing is also a AIC Loop. as I am sure Danny or Asellus will point out.

so this chain (8=4)r9c8 - (4)r8c7 = (4-8)r8c3 = (8)r9c1 is seen as a M-wing yes, but it has far greater meaning since it does start and end in the same row.

the other inferences we can gather is this...
all other 4's in box 9 can be eliminated
r8c3 is {4,8} => r8c3 <> 7
any other 8's in row 9 can be eliminated, this is the original intent of the m-wing.

Danny, I am not sure anyone who reads this forum would believe you would take a break. just thought was a funny statement on your part. Laughing
Back to top
View user's profile Send private message
cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Thu Dec 11, 2008 2:20 pm    Post subject: Reply with quote

Good One! ER on <6>, Type 4 UR (15), ER on <4>

Enjoy your break - but don't take too long !!
Back to top
View user's profile Send private message
Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Thu Dec 11, 2008 4:17 pm    Post subject: Reply with quote

I used a W-Wing on 67, followed by pincer transport on same. Then an XY-Wing on 478 with pincer transport. A Type 4 UR on 15 was probably useless. Then ERs on 6 and 4 and a W-Wing on 47 finished it.
Back to top
View user's profile Send private message
tlanglet



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

PostPosted: Mon Dec 15, 2008 8:25 pm    Post subject: Reply with quote

My four steps were a kite <4>, x-wing <6>, xy-wing <678> plus one transport, and a xy-wing <478>.

Very similar but yet differenct

Ted
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