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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sat Jan 23, 2010 11:34 pm Post subject: Puzzle 10/01/23 gM-Wing |
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For those who wish to tackle a gM-Wing. (It's not a single-stepper.)
| Code: | +-----------------------+
| 6 . . | . 1 . | . . . |
| . 9 . | 7 . . | . . 4 |
| . . 1 | . . 9 | . . . |
|-------+-------+-------|
| . 1 . | 9 . 6 | . . . |
| 4 . . | . . . | 2 . 5 |
| . . 2 | 4 . 3 | . 6 . |
|-------+-------+-------|
| . . . | . 9 . | 8 2 . |
| . . . | . . 7 | 6 . 9 |
| . 6 . | . 4 . | . 5 3 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 24, 2010 12:49 am Post subject: |
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Danny, could you--once again--explain the difference between an M-Wing and a gM-Wing? Please pretend you're explaining it to a 9-year-old.  |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sun Jan 24, 2010 2:39 am Post subject: |
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Took me two steps: | Quote: |
skyscraper 5 is needed to set up
(7=5)r1c2-(5)r7c2=(5)r7c6-(5=2)r2c6-(2)r2c1=(2-7)r3c1=(7)r3c8
=> r1c8,r3c1<>7 (found while looking for a gM-wing 75)
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 A good one! |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Jan 24, 2010 3:53 am Post subject: |
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| Marty R. wrote: | | Danny, could you--once again--explain the difference between an M-Wing and a gM-Wing? Please pretend you're explaining it to a 9-year-old. |
Well, I'll do what I can.
Keith's original description of an M-Wing was very interesting, but it left some questions unanswered for me about all of the constraints he wished to impose on the technique. In particular, his examples and later discussions indicated that a simple chain might not meet all of the constraints.
I/someone came up with the gM-Wing as a simple chain template that's almost identical in constraints to Keith's M-Wing. This way, my currently awkward chains() module could identify a pattern that almost matches Keith's M-Wing and the half M-Wing.
Apparently, others liked the simpler constraint of the chain as well.
----- ----- ----- -----
Dan, I'm glad you had fun solving it w/o the gM-Wing.
Regards, Danny |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun Jan 24, 2010 10:51 pm Post subject: |
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My three steps were:
| Quote: | xy-wing 17-8 with the vertex in r7c9 and a three cell pseudocell pincer 18 in r6c2 and r7c26,
ER 5,
flightless xy-wing 2-57 with transport completes the puzzle. |
I am not very good at finding m-wings and I proved that to be true once again on this puzzle.
Danny, when appropriate, please post the gM-Wing.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Jan 25, 2010 1:36 am Post subject: |
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| Code: | c8b3 Locked Pair <> 78 r3c7
c7 Naked Pair <> 17 r3c7
c26r7 Skyscraper <> 5 r1c4,r2c13
b2 Naked Pair <> 38 r2c6,r3c4
r1 b1 Locked Candidate 2 <> 5 r3c1
r2 b1 Locked Candidate 2 <> 8 r1c23,r3c1
[gM-Wing] (3=5)r3c7 - r3c4 = (5-3)r8c4 = (3)r1c4 => r3c5<>3
+--------------------------------------------------------------+
| 6 57 357 | d38 1 4 | 9 78 2 |
| 28 9 38 | 7 6 25 | 35 1 4 |
| 27 4 1 | b25 8-3 9 | a35 78 6 |
|--------------------+--------------------+--------------------|
| 57 1 57 | 9 2 6 | 4 3 8 |
| 4 3 6 | 18 7 18 | 2 9 5 |
| 9 8 2 | 4 5 3 | 17 6 17 |
|--------------------+--------------------+--------------------|
| 3 57 4 | 6 9 15 | 8 2 17 |
| 158 2 58 | c1358 38 7 | 6 4 9 |
| 178 6 9 | 128 4 128 | 17 5 3 |
+--------------------------------------------------------------+
# 37 eliminations remain
There is a strong link on <3> in [c3]
There is a strong link on <5> in [c3]
They have a cell in common
finding <35> cell r3c7 then follows
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Jan 25, 2010 1:52 am Post subject: |
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I used more steps but had a lot of fun with it.
XY (578)
M (17)
Fin transport (5)
W (38)
XY (385) with pincer transport |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Jan 26, 2010 9:40 am Post subject: |
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Marty,
its difficult trying to describe why the m-wing that you learned and the gM-wing that Danny is refering to is different. I guess you must first realize that the M-wing you look for in a puzzle is included in gM-wing.
IOW, the type of M-wing you are familiar with has other variations, all of which are included in the gM-wing definition.
these variations include using grouped cells or simply adding extensions. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jan 26, 2010 4:50 pm Post subject: |
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| storm_norm wrote: | Marty,
its difficult trying to describe why the m-wing that you learned and the gM-wing that Danny is refering to is different. I guess you must first realize that the M-wing you look for in a puzzle is included in gM-wing.
IOW, the type of M-wing you are familiar with has other variations, all of which are included in the gM-wing definition.
these variations include using grouped cells or simply adding extensions. |
Well, just looking at Danny's example, if I'm seeing it correctly, it's exactly the same as the original simple M-Wing that I know and love except the 1358 in r8c4 is treated as if it were just another 35 cell.
Can we extrapolate from that one example and say as a generality that any polyvalue cell can be part of an M-Wing if it contains the two cells of the bivalue cell and the other requirements of the M-Wing (i.e., the links) are met? |
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strmckr
Joined: 18 Aug 2009
Posts: 64
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| Posted: Tue Jan 26, 2010 5:36 pm Post subject: |
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yes u can do alot with m-wings
see here
the one above is a type 1a... in the list. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Jan 26, 2010 5:50 pm Post subject: |
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| Marty R. wrote: | Can we extrapolate from that one example and say as a generality that any polyvalue cell can be part of an M-Wing if it contains the two cells of the bivalue cell and the other requirements of the M-Wing (i.e., the links) are met?
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Here is example #4 from keith's thread. It's an M-Wing with (required) bivalue cells {a,c}. It allows polyvalue (multi-value) cells {b,d}. There is also a (required) strong link between cells {a,b}.
| Code: | +----------------+----------------+----------------+
| 2 567 9 | 567 457 3 | 1 46 8 |
| 46 1 3 | 268 9 468 | 7 5 26 |
| 456 567 8 | 1 2457 4567 | 39 469 2369 |
+----------------+----------------+----------------+
| 8 239 56 | 2567 1257 1567 | 4 679 3679 |
| 1 4 56 | 3 578 9 | 58 2 67 |
| 39A 239 7 | 2568 2458 4568 | 3589 68-9 1 |
+----------------+----------------+----------------+
|3569B 56 4 | 589 1358 2 | 89 1789 79 |
| 59 8 1 | 579 6 57 | 2 3 4 |
| 7 39C 2 | 4 138 18 | 6 189D 5 |
+----------------+----------------+----------------+
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Here's all you need to know about the gM-Wing.
There is a strong link on <m> between cells {b,c}
There is a strong link on <n> between cells {c,d}
bivalue cell a=<mn> sees cell {b}, eliminations occur for value <n> in cells that see {a} and {d}
Regards, Danny |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jan 26, 2010 6:41 pm Post subject: |
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| Thank you both. |
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