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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Thu Dec 11, 2008 4:39 am Post subject: Set F Puzzle 64 |
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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 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Dec 11, 2008 6:45 am Post subject: |
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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.  |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Thu Dec 11, 2008 2:20 pm Post subject: |
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Good One! ER on <6>, Type 4 UR (15), ER on <4>
Enjoy your break - but don't take too long !! |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 11, 2008 4:17 pm Post subject: |
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| 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. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Dec 15, 2008 8:25 pm Post subject: |
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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 |
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