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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sun Sep 19, 2010 4:21 am Post subject: Puzzle 10/09/19: B |
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| Code: | +-----------------------+
| . . 8 | . 1 9 | 2 . . |
| . . 3 | . 8 . | 1 . . |
| 9 4 1 | 2 . . | 8 7 . |
|-------+-------+-------|
| . . 2 | 3 7 4 | . . . |
| 8 9 . | 6 2 . | 7 . . |
| 7 . . | 9 . . | . . . |
|-------+-------+-------|
| 2 8 9 | . 4 . | 3 . . |
| . . 7 | . . . | . 9 . |
| . . . | . . . | . . 2 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sun Sep 19, 2010 10:32 am Post subject: |
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| Quote: | S Wing : 8B9 (81)R8C4 1R7 : (8)r9c8=(1)r7c8 : => r9c8<>1
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sun Sep 19, 2010 4:09 pm Post subject: |
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Seems very common that there is a corresponding m-wing to an s-wing? I've only started noticing s-wings recently so can't judge if that is the norm.
| Quote: | | m-wing(18) (1=8)r8c4 - r8c9=(8-1)r9c8=r7c8 ; r7c4<>1 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Sep 19, 2010 5:30 pm Post subject: |
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| peterj wrote: | Seems very common that there is a corresponding m-wing to an s-wing?
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My observation as well. If I reverse the direction of JC's S-Wing and compare it to Peter's M-Wing:
| Code: | +--------------------------------------------------------------+
| 56 7 8 | 45 1 9 | 2 3456 3456 |
| 56 2 3 | 457 8 567 | 1 456 9 |
| 9 4 1 | 2 36 356 | 8 7 56 |
|--------------------+--------------------+--------------------|
| 1 56 2 | 3 7 4 | 9 568 568 |
| 8 9 45 | 6 2 1 | 7 345 345 |
| 7 3 46 | 9 5 8 | 46 2 1 |
|--------------------+--------------------+--------------------|
| 2 8 9 | 15 4 56 | 3 16 7 |
| 34 156 7 | 18 36 2 | 456 9 468 |
| 34 156 56 | 178 9 367 | 456 1468 2 |
+--------------------------------------------------------------+
# 56 eliminations remain
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| Code: | JC's: s-wing(18) (1)r7c8 = r7c4 - (1=8)r8c4 - r8c9 = (8 )r9c8 ; r9c8<>1
Peter's: m-wing(18) (1=8)r8c4 - r8c9 = (8-1)r9c8 = r7c8 ; r7c4<>1
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Then the distinction is in which end of the chain contains the strong link on <1>. In this case, the two chains can be merged into a discontinuous loop.
| Code: | discontinuous loop: (1)r7c8 = r7c4 - (1=8)r8c4 - r8c9 = (8-1)r9c8 = r7c8 ; r7c8=1
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Note, it is not necessary for the chains to form a discontinuous loop for there to be an overlap.
| Code: | daj's: s-wing(18) (1)r9c2 = r8c2 - (1=8)r8c4 - r8c9 = (8 )r9c8 ; r9c8<>1
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sun Sep 19, 2010 8:55 pm Post subject: S Wings versus M Wings |
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Comparison of a Split Wing and a Medusa Wing :
S Wing : A=A-(A=B)-B=B : 1 strong cell (A=B), 2 strengths in location A=A & B=B, 2 candidates, possible eliminations on both candidates.
M Wing : (A=B)-B=(B-A...)=A : 2 "complementary" cells (at least one strong) (A=B) & (B-A...), 2 strengths in location B=(B...) & (...A)=A weakly connected in the "hub" cell (B-A...), 2 candidates, possible elimination on one candidate, A.
S Wing and M Wing are two XY Wing Styles : the first has a strong cell as a pivot, while the second has a strength in location (ALC) as a pivot. Example of an S Wing not reducible to an M Wing :
| Code: | 920100600600005003000700800070000060000080020005004009000600000403009000080000100
+-------------------+---------------------+-------------------------+
| 9 2 78 | 1 34 38 | 6 457 457 |
| 6 14 78 | 2489 249 5 | 2479 1479 3 |
| 35 35 (14) | 7 2469 26 | 8 149 24(1) |
+-------------------+---------------------+-------------------------+
| 238 7 29(4) | 2359 1259 123 | 35(4) 6 58(4) |
| 13 3469 1469 | 359 8 67 | 3457 2 57-4(1) |
| 1238 136 5 | 23 67 4 | 37 1378 9 |
+-------------------+---------------------+-------------------------+
| 1257 159 129 | 6 123457 12378 | 234579 345789 24578 |
| 4 156 3 | 258 1257 9 | 257 578 25678 |
| 257 8 269 | 2345 23457 237 | 1 34579 24567 |
+-------------------+---------------------+-------------------------+
S Wing : 1C9 (14)R3C3 4R4 : (1)r5c9=(1)r3c9-(1=4)r3c3-(4)r4c3=(4)r4c79 : => r5c9<>4
Other S Wings may be found, but no M Wing yields the same elimination. |
Regards, JC |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Sep 19, 2010 11:34 pm Post subject: |
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Thanks JC for the presentation!!! I'm partial to an alternate S-Wing for your elimination because it overlays an unnamed pattern using a 3-SIS for two candidates, but doesn't need a bivalue cell.
| Code: | S-Wing : 4C2 (41)r3c3 1C9 : (4)r5c2 = (4 )r2c2 - (4=1)r3c3 - r3c9 = (1)r5c9 ; r5c9<>4
unnamed: 4C2 1B1 1C9 : (4)r5c2 = (4-1)r2c2 = ( 1)r3c3 - r3c9 = (1)r5c9 ; r5c9<>4
+--------------------+---------------------+-------------------------+
| 9 2 78 | 1 34 38 | 6 457 457 |
| 6 1(4) 78 | 2489 249 5 | 2479 1479 3 |
| 35 35 (14) | 7 2469 26 | 8 149 24(1) |
+--------------------+---------------------+-------------------------+
| 238 7 249 | 2359 1259 123 | 345 6 458 |
| 13 369(4) 1469 | 359 8 67 | 3457 2 57-4(1) |
| 1238 136 5 | 23 67 4 | 37 1378 9 |
+--------------------+---------------------+-------------------------+
| 1257 159 129 | 6 123457 12378 | 234579 345789 24578 |
| 4 156 3 | 258 1257 9 | 257 578 25678 |
| 257 8 269 | 2345 23457 237 | 1 34579 24567 |
+--------------------+---------------------+-------------------------+
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| Code: | = - = - =
w-wing: (A=B) - B = B - (B=A)
gM-wing: (A=B) - B = (B-A) = A
s-wing: A = A - (A=B) - B = B {1st A and last B in the same house}
unnamed: A = (A - B) = B - B = B {1st A and last B in the same house}
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Dang!!! Now that I have a "confirmed" template for the S-Wing, I might need to add it to my MW-Wing routine.
(I refused to work my way through strmckr's incomplete exemplars to derive the template.) |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Sep 20, 2010 1:20 am Post subject: |
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I used:
XYZ-Wing (356)
UR 56 forces an elimination
UR 34 forces a couple of cells
XY-Wing (346) |
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