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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sat Aug 13, 2011 10:09 pm Post subject: Puzzle 11/08/13: ~ XY |
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| Code: | +-----------------------+
| 2 . 8 | 7 . . | 3 . . |
| . 5 6 | 4 . . | 7 8 . |
| 7 3 . | 1 . . | . . . |
|-------+-------+-------|
| 6 8 3 | 5 2 . | . 7 1 |
| . . . | 8 . 3 | . . 5 |
| . . . | . 1 9 | . 3 . |
|-------+-------+-------|
| 8 2 . | . . . | 5 . . |
| . 6 . | 3 . 7 | . 2 . |
| . . . | 2 8 . | . . . |
+-----------------------+
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Sun Aug 14, 2011 11:21 pm Post subject: |
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Continuing DP madness...
If one UR is useful, then two overlapping URs (aka a MUG*) can be also.
The MUG has two internal outs, (6)r3c9 and (1)r8c7.
| Code: | *-----------------------------------------------------------*
| 2 49 8 | 7 569 @56 | 3 1 46 |
| 1 5 6 | 4 3 2 | 7 8 9 |
| 7 3 49 | 1 69 8 |*24 5 *24+6 |
|-------------------+-------------------+-------------------|
| 6 8 3 | 5 2 4 | 9 7 1 |
| 49 149 1249 | 8 7 3 | 246 46 5 |
| 45 7 245 | 6 1 9 |*248 3 *248 |
|-------------------+-------------------+-------------------|
| 8 2 7 | 9 46 1 | 5 46 3 |
| 459 6 1459 | 3 45 7 |*48+1 2 *48 |
| 3 14 145 | 2 8 @56 | 146 9 7 |
*-----------------------------------------------------------* |
Except for the (1)r9c7, there is a (46)w-wing r1c9 and r9c7, strong link on (6)c6.
If the w-wing is true, then there can be no (4) in r3c7, must be (2).
So the idea is really quite short and sweet: If (6)r3c9 isn't true, then
the w-wing is and there can be no (2) in r3c9.
The chain would look too horrible if all the cell designations were spelled out,
so I'll leave it at this:
(6)r3c9=(1)r8c7-(1)r9c7=(46)w-wing-(4=2)r3c7 =>r3c9<>2 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Aug 15, 2011 4:11 am Post subject: |
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| XY-Wing Chain (49-46-46-46-69), flightless with transport; r5c2<>9 |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Mon Aug 15, 2011 7:17 pm Post subject: |
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| Marty R. wrote: | | XY-Wing Chain (49-46-46-46-69), flightless with transport; r5c2<>9 |
That is how this puzzle was meant to be solved 
I often see the use of "flightless w/transport" but I haven't figured out what that means. I do see an xy-chain, but no "wing."
| Code: | *-----------------------------------------------------------*
| 2 49 8 | 7 569 56 | 3 1 46 |
| 1 5 6 | 4 3 2 | 7 8 9 |
| 7 3 49 | 1 69 8 | 24 5 246 |
|-------------------+-------------------+-------------------|
| 6 8 3 | 5 2 4 | 9 7 1 |
| 49 149 1249 | 8 7 3 | 246 46 5 |
| 45 7 245 | 6 1 9 | 248 3 248 |
|-------------------+-------------------+-------------------|
| 8 2 7 | 9 46 1 | 5 46 3 |
| 459 6 1459 | 3 45 7 | 148 2 48 |
| 3 14 145 | 2 8 56 | 146 9 7 |
*-----------------------------------------------------------* |
(9=4)r5c1-(4=6)-(6=4)-(4=6)-(6=9)-(9=4)-(4=9)r1c2 =>r5c2<>9 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Aug 15, 2011 7:57 pm Post subject: |
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| Luke451 wrote: | | Marty R. wrote: | | XY-Wing Chain (49-46-46-46-69), flightless with transport; r5c2<>9 |
That is how this puzzle was meant to be solved
I often see the use of "flightless w/transport" but I haven't figured out what that means. I do see an xy-chain, but no "wing."
| Code: | *-----------------------------------------------------------*
| 2 49 8 | 7 569 56 | 3 1 46 |
| 1 5 6 | 4 3 2 | 7 8 9 |
| 7 3 49 | 1 69 8 | 24 5 246 |
|-------------------+-------------------+-------------------|
| 6 8 3 | 5 2 4 | 9 7 1 |
| 49 149 1249 | 8 7 3 | 246 46 5 |
| 45 7 245 | 6 1 9 | 248 3 248 |
|-------------------+-------------------+-------------------|
| 8 2 7 | 9 46 1 | 5 46 3 |
| 459 6 1459 | 3 45 7 | 148 2 48 |
| 3 14 145 | 2 8 56 | 146 9 7 |
*-----------------------------------------------------------* |
(9=4)r5c1-(4=6)-(6=4)-(4=6)-(6=9)-(9=4)-(4=9)r1c2 =>r5c2<>9 |
"Flightless" is a term we use when a wing of any type doesn't make a direct elimination. Transport means pincer transport.
In my move, the three 46 cells act as a single XY cell in an XY-Wing. One end of the three-cell chain sees the 49 in r5c1 and the other end sees the 69 in r3c5. It's flightless because no cell seeing both the 49 and 69 has a 9 that could be eliminated. Transporting the 9 from r3c5 to r1c2 now sees r5c2 along with the 49 in r5c1 and eliminates the 9 from r5c2. This also works with a chain of five identical cells, but those are rare.
Hope this is clear enough. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Mon Aug 15, 2011 8:12 pm Post subject: |
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| Luke451 wrote: | I often see the use of "flightless w/transport" but I haven't figured out what that means. I do see an xy-chain, but no "wing."
...
(9=4)r5c1-(4=6)-(6=4)-(4=6)-(6=9)-(9=4)-(4=9)r1c2 =>r5c2<>9 |
The "w/transport" makes sense if Marty used the bilocal in b1 ...
(9=4)r5c1-(4=6)-(6=4)-(4=6)-(6=9)r3c5-r3c3=(9)r1c2 =>r5c2<>9
... using notation that's perhaps too cryptic.
Other comments FWIW:- A bivalued chain of three cells is the shortest possible length of an xy-chain, and is usually called an xy-wing.
- The "flightless" term only makes sense for wings, including w-wings, m-wings, etc., but excluding x-wings.
- For wings, the terms "flightless" and "w/ transport" are redundant.
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Aug 15, 2011 9:42 pm Post subject: |
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| Quote: | The "w/transport" makes sense if Marty used the bilocal in b1 ...
(9=4)r5c1-(4=6)-(6=4)-(4=6)-(6=9)r3c5-r3c3=(9)r1c2 =>r5c2<>9
... using notation that's perhaps too cryptic. |
I have no idea of what you're saying and I don't know what "bilocal" means. The transport made sense to me since it solved the puzzle. Keep in mind that I'm about 27 levels below you when it comes to discussing these things. To me, this is a simple case of finding the pattern--which some others call Extended XY-Wing--and a simple transport of a 9 from box 2 to box 1. |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Mon Aug 15, 2011 10:52 pm Post subject: |
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| Marty R. wrote: | In my move, the three 46 cells act as a single XY cell in an XY-Wing. One end of the three-cell chain sees the 49 in r5c1 and the other end sees the 69 in r3c5. It's flightless because no cell seeing both the 49 and 69 has a 9 that could be eliminated. Transporting the 9 from r3c5 to r1c2 now sees r5c2 along with the 49 in r5c1 and eliminates the 9 from r5c2. This also works with a chain of five identical cells, but those are rare.
Hope this is clear enough. |
Absolutely, and thank you.
The xy-wing structure is preserved by the identical (46) cells. The "transport" portion is the extention of the chain necessary to actually perform the elimination. I think I've got it 
I do apologize for the shorthand and cryptic notation. I'll rethink that practice.
All the cell designations take so long to write out in long xy-chains. It seems so obvious what they must be, so sometimes I take the lazy (time-challenged) way out. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Mon Aug 15, 2011 11:18 pm Post subject: |
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| Marty R. wrote: | | To me, this is a simple case of finding the pattern--which some others call Extended XY-Wing--and a simple transport of a 9 from box 2 to box 1. |
As is sometimes the case, there was more than one way to make that "transport", and the way one chooses may influence the "proper" name of the pattern. Only you know what you chose.
[edit: "sometimes" was "often"]
Last edited by ronk on Tue Aug 16, 2011 9:49 am; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Aug 16, 2011 1:10 am Post subject: |
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Luke, if you're interested--coincidentally--the same pattern appeared in today's VH puzzle, also flightless, but fruitful with transport.
| Code: |
+---------------+--------------+--------------+
| 19 6 58 | 7 4 139 | 2 38 59 |
| 129 25 7 | 8 35 139 | 4 36 569 |
| 49 458 3 | 59 6 2 | 589 7 1 |
+---------------+--------------+--------------+
| 7 3 259 | 1569 25 89 | 1568 268 4 |
| 6 1259 2459 | 159 7 489 | 158 28 3 |
| 8 125 245 | 156 235 34 | 156 9 7 |
+---------------+--------------+--------------+
| 5 289 289 | 3 1 7 | 69 4 269 |
| 3 249 6 | 24 8 5 | 7 1 29 |
| 24 7 1 | 24 9 6 | 3 5 8 |
+---------------+--------------+--------------+
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Aug 16, 2011 2:02 am Post subject: |
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My notes on some of the "special" XY-Wing patterns used in this forum.
===== ===== ===== ===== ===== ===== extended/transported XY-Wing
| Code: | 3-cell XY-Chain; i.e., XY-Wing
** ** **
XY-Wing: ZX-XY-YZ => eliminations in Z
.. pivot
.. .. pincers
ZX = 12, XY = 23, YZ = 31
+-----------------------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | 12 . . | . -1 . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | 23 . . | . 31 . |
| . . . | . . . | . . . |
+-----------------------------------+
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| Code: | 4-cell XY-Chain; i.e., XY-Wing with 2-cell pseudo-cell as center cell
** * * **
Ext. #1: ZX-XV-VY-YZ => eliminations in Z
ZX = 12, XV = 24, VY = 43, YZ = 31; XV-VY splits the 23 across two cells
+-----------------------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | 12 . . | . -1 . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | 24 . . | . . . |
| . . . | . . 43 | . 31 . |
| . . . | . . . | . . . |
+-----------------------------------+
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| Code: | 5-cell XY-Chain; i.e., XY-Wing with two bivalue cells added
** ** **
Ext. #2: ZX-XY-YZ-ZW-WZ => eliminations in Z
Ext. #3: WZ-ZX-XY-YZ-ZW => eliminations in W
ZX = 12, XY = 23, YZ = 31, ZW = 16, WZ = 61
+-----------------------------------+
| . . . | . . . | . . . |
| . 61 . | . . . | . 16 . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . -1 . | 12 . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | 23 . . | . 31 . |
| . . . | . . . | . . . |
+-----------------------------------+
WZ = 61, ZX = 12, XY = 23, YZ = 31, ZW = 16
+-----------------------------------+
| . . . | . . . | . . . |
| . -6 . | . . . | . 16 . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . 61 . | 12 . . | . -6 . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | 23 . . | . 31 . |
| . . . | . . . | . . . |
+-----------------------------------+
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| Code: | 3-cell XY-Chain w/Strong Link (transport); i.e., XY-Wing w/transport
** ** ** @...@
Ext. #4: ZX-XY-YZ-Zw=vZ => eliminations in Z
ZX = 12, XY = 23, YZ = 31, Zw = 1w, vZ = v1
+-----------------------------------+
| . . . | . . . | . . . |
| / v1 / | / / / | / 1w / | strong link on <1> and other
| . . . | . . . | . . . | candidates ignored
|-----------+-----------+-----------|
| . -1 . | 12 . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | 23 . . | . 31 . |
| . . . | . . . | . . . |
+-----------------------------------+
|
| Code: | Craig Gordon; i.e., XY-Wing with 3-cell pseudo-cell as center cell
** * * **
Ext. #5: ZX-XY-YX-XY-YZ => eliminations in Z
ZX = 12, XY = 23, YX = 32, XY = 23, YZ = 31
+-----------------------------------+
| . . . | . . . | . . . |
| . 31 . | -1 . . | . 23 . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . -1 . | 12 . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . . |
| . . . | 23 . . | . 32 . |
| . . . | . . . | . . . |
+-----------------------------------+
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You'll notice that Marty's "XY-Wing Chain" matches Ext. #5.
| Code: | | *************** Marty's XY-Wing Chain *************** |
(9=4)r5c1 - (4=6)r5c8 - (6=4)r7c8 - (4=6)r7c5 - (6=9)r3c5 - (9=4)r3c3 - (4=9)r1c2 => r5c2<>9
|
I would contract this XY-Chain notation to:
| Code: | (9=4)r5c1 =6r5c8 =4r7c8 =6r7c5 =9r3c5 =4r3c3 - (4=9)r1c2 => r5c2<>9
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Regards, Danny |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Aug 16, 2011 3:46 am Post subject: |
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| Marty R. wrote: | | Luke, if you're interested--coincidentally--the same pattern appeared in today's VH puzzle, also flightless, but fruitful with transport. |
Sure, I'm interested. You could not have planned this any better. I will never look at three such identical cells the same way again
| Code: | *-----------------------------------------------------------*
| 19 6 58 | 7 4 139 | 2 38 59 |
| 129 25 7 | 8 35 139 | 4 36 569 |
| 49 458 3 | 59 6 2 | 89 7 1 |
|-------------------+-------------------+-------------------|
| 7 3 259 | 1569 25 89 | 1568 268 4 |
| 6 1259 2459 | 159 7 489 | 158 28 3 |
| 8 125 245 | 156 235 34 | 156 9 7 |
|-------------------+-------------------+-------------------|
| 5 289 289 | 3 1 7 | 69 4 269 |
| 3 249 6 | 24 8 5 | 7 1 29 |
| 24 7 1 | 24 9 6 | 3 5 8 |
*-----------------------------------------------------------* |
(9=4)r3c1-(4=2)r9c1-(2=4)r9c4-(4=2)r8c4-(2=9)r8c9-r7c7=(9)r3c7 =>r3c4<>9 ...Singles Nite, woo hoo
I wrote it that way just because I see most everything as an AIC. The good thing is, I was able to recognize it as a pattern. Hopefully you will not be dismayed to learn that my first thought was, "Wow, something new to 'almost'! "
Thank you, always delighted to learn something I didn't know. Knowledge only reveals how much we all have left to learn.
Please reply, becuz whatever you say next will be your 4000th POST <Cue confetti!>  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Aug 16, 2011 3:51 am Post subject: |
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| Quote: | | Please reply, becuz whatever you say next will be your 4000th POST |
OK, here's #4000, but I think Jim Thome's 600th home run was better. I'm not proud to have the posts record since it just proves I've got diarrhea of the keyboard.  |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Aug 16, 2011 3:54 am Post subject: |
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| Congrats, man. It does mean something here in our little pond . |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Tue Aug 16, 2011 10:22 am Post subject: |
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| Marty R. wrote: | | ... coincidentally--the same pattern appeared in today's VH puzzle, also flightless, but fruitful with transport. |
Mostly the same. In this case, due to a weak link (9)r3c7-(9)r3c1 between the start and end of your chain, there exists a continuous loop. Both strong and weak links become conjugate links yielding additional eliminations ... r8c2<>2 and r7c9<>9. Moreover, to identify all the elims, the <24> pseudo-cell POV must be abandoned.
These added elims are not needed for this puzzle, but for another they might well be useful.
| Code: |
+---------------+--------------+--------------+
| 19 6 58 | 7 4 139 | 2 38 59 |
| 129 25 7 | 8 35 139 | 4 36 569 |
|*49 458 3 | 5-9 6 2 |*589 7 1 |
+---------------+--------------+--------------+
| 7 3 259 | 1569 25 89 | 1568 268 4 |
| 6 1259 2459 | 159 7 489 | 158 28 3 |
| 8 125 245 | 156 235 34 | 156 9 7 |
+---------------+--------------+--------------+
| 5 289 289 | 3 1 7 |*69 4 26-9|
| 3 49-2 6 |*24 8 5 | 7 1 *29 |
|*24 7 1 |*24 9 6 | 3 5 8 |
+---------------+--------------+--------------+
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[dajEdit: corrected typo in cells for weak link.] |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Aug 16, 2011 9:45 pm Post subject: |
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The puzzle of this thread has all sorts of opportunities for the transport of wing pincers for those who want to practice such things.
Take, for instance, the 246 XYZ-Wing in boxes 3 and 6. The grouped <4>s of r5c78 can be transported to the grouped <4>s of box 4 r6 to eliminate <4> from r6c7. Also, the UR (or conjugate pair) in box 1 together with r3c7 eliminates <4> from r5c2.
Another nice example is the 149 XYZ-Wing in boxes 4 and 9. The grouped <4>s in r5c12 can be transported via the conjugates in c8 to r7c8, eliminating <4> from r9c7, and then again via the conjugates in c5 to r8c5 eliminating <4> from r8c13. Going the other way, r9c2 is transported to r3c3 eliminating <4> from r56c3.
There are more such transports possible in the grid.
Next, a notation suggestion for that "finned W-Wing" in Luke's MUG-based AIC. The pincer digits of a wing can be represented as a group in the AIC, just as one would group instances of a digit in, say, a box-row:
248MUG[(6)r3c9=(1)r8c7] - (1)r9c7=46w-wing(4)r1c9|r9c7 - (4=2)r3c7; r3c9<>2
I like to see folks using wings as AIC nodes! As far as I'm concerned it is fine to exclude the inferences internal to the wing from the notation as long as the wing has been clearly identified in accompanying explanation, as Luke did.
Some may have trouble understanding the inference between a "fin" and a wing. Here is where representing the wing according to the resulting grouped pincer digits is especially helpful, I believe. For the strong inference it must be impossible for both items to be false. Clearly, if the fin (here, the <1>) is false the wing will be true and thus at least one member of the grouped pincers will be true. On the other hand, the wing being false requires that the group is false (all its members are false). This can only happen if the wing structure does not exist and only the fin destroys that structure so it must then be true. The bidirectional requirement is met: both items cannot be false.
If you are tempted to believe the inference is also weak, take note: The fin and the group CAN both be true. While the fin being true destroys the wing structure, it does not prevent the grouped pincer digits from being true. In this particular case the fin prevents the digit it shares a cell with from being true but the state of the other pincer digit remains unknown. |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Wed Aug 17, 2011 1:19 am Post subject: |
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@ Marty, I think the only real issue with your presentation was the omission of some kind of transport notation.
Ronk, nice observation on the loop. Continuous always trumps.
Danny, thanks for posting your notes. I’ll save that.
I see that you too are not averse to truncated xy notation. I very much like the notion that that the first and last cells must be spelled out. I’m up in the air on the rest, and on my own alternative notation.
Asellus, nice to hear from you again. I’ll save your notation suggestions as well. I particularly like the idea of spelling out the pincer components.
248MUG[(6)r3c9=(1)r8c7] - (1)r9c7=46w-wing(4)r1c9|r9c7 - (4=2)r3c7; r3c9<>2 |
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