| View previous topic :: View next topic |
| Author |
Message |
arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
|
 Posted: Mon Aug 11, 2008 11:10 am Post subject: One Trick Pony 8/10/08 |
 |
|
My daily lesson in the wild world of w,m and v wings has led me to Sunday's One Trick Pony
| Code: |
*-----------*
|...|...|.17|
|37.|..6|...|
|..8|4..|9..|
|---+---+---|
|..4|57.|...|
|..9|...|5..|
|...|.23|8..|
|---+---+---|
|..5|..4|6..|
|...|3..|.89|
|81.|...|...|
*-----------*
*-----------------------------------------------------------*
| 49 49 6 | 28 358 258 | 23 1 7 |
| 3 7 12 | 12 9 6 | 4 5 8 |
| 15 25 8 | 4 13 7 | 9 236 236 |
|-------------------+-------------------+-------------------|
| 126 38 4 | 5 7 189 | 123 2369 1236 |
| 1267 38 9 | 168 4 18 | 5 2367 1236 |
| 1567 56 17 | 169 2 3 | 8 679 4 |
|-------------------+-------------------+-------------------|
| 79 29 5 | 1278 18 4 | 6 23 123 |
| 46 46 *27 | 3 15 15-2 |*127 8 9 |
| 8 1 3 |#297 6 #29 |*27 4 5 |
*-----------------------------------------------------------*
|
r8c3 and r9c7 must be the same.
r8c3=2 then r8c6<>2
r8c7=7 then r9c7=7 then there is a (29) pair in r9 then r8c6<>2
solves the puzzle with singles and pairs.
anyone know what this is other than fun?  |
|
| Back to top |
|
 |
ravel
Joined: 21 Apr 2006
Posts: 536
|
| Posted: Mon Aug 11, 2008 1:04 pm Post subject: Re: One Trick Pony 8/10/08 |
|
|
| arkietech wrote: | | r8c3 and r9c7 must be the same. |
Yes, so you have an M-wing pair (from the strong links for 7 to r8c7).
Next you would look for strong links from one of the pair cells (for both candidates).
There is a useful strong link for 2 in box 7 to r7c2, which now means, that r7c2 or r9c7 must be 2 (if r9c7<>2, then r9c7=7 => r8c3=7 => r8c2=2). So you can eliminate 2 from r7c89.
For your elimination above you dont even need the 29 pair. It is enough, that you have this grouped strong link for 2 in row 9 between r9c7 and r9c46, what meeans that r8c3 or one of r9c46 must be 2. |
|
| Back to top |
|
|
arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
|
| Posted: Mon Aug 11, 2008 2:56 pm Post subject: Re: One Trick Pony 8/10/08 |
|
|
Ravel said:
| Quote: | Yes, so you have an M-wing pair (from the strong links for 7 to r8c7).
|
Thanks Ravel. I don't know why my brain can't get around this concept. |
|
| Back to top |
|
|
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
| Posted: Tue Aug 12, 2008 7:01 am Post subject: |
|
|
let me draw a picture to help with wrapping the head around it.
first you need the complimentary pair as shown below...
in the image you see the black lines as the strong links on 7 connecting the {2,7} pairs.
in order for an m-wing to make eliminations, you need another strong link with the opposite number. in this case its the {2} marked in green.
now that you have this link, any other two's seen by the 2 in r9c7 and r7c2 can be eliminated. or in notation..
(2=7)r9c7-(7)r8c7=(7-2)r8c3=(2)r7c2; r7c89 cannot be 2 |
|
| Back to top |
|
|
nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
|
| Posted: Tue Aug 12, 2008 9:19 am Post subject: |
|
|
In fact, a (generalized) m-wing elimination can be performed even without a "pair" (equivalent, or complementary, whatever you wish to call it):
A strong link (in "a") alone is enough, provided its one end is seen by a matching bi-value cell ({a,b}) and the other end starts a strong link in that other candidate "b".
In arkietech's grid, we can re-use the strong link marked "#" (7) r8c3=r8c7.
One end (r8c3) is "seen" by the "7" in r6c3 (the other candidate in that cell is 1). Note that it is not necessary that this link be strong as well, although it happens to be, in this case.
The other end starts a strong link (1) in col 7: (1) r4c7=r8c7
| Code: |
+--------------------------+--------------------------+--------------------------+
| 49 49 6 | 28 358 258 | 23 1 7 |
| 3 7 12 | 12 9 6 | 4 5 8 |
| 15 25 8 | 4 13 7 | 9 236 236 |
+--------------------------+--------------------------+--------------------------+
|-126 38 4 | 5 7 189 | 123* 2369 1236 |
| 1267 38 9 | 168 4 18 | 5 2367 1236 |
| 1567 56 17* | 169 2 3 | 8 679 4 |
+--------------------------+--------------------------+--------------------------+
| 79 29 5 | 1278 18 4 | 6 23 123 |
| 46 46 27# | 3 15 152 | 127# 8 9 |
| 8 1 3 | 297 6 29 | 27 4 5 |
+--------------------------+--------------------------+--------------------------+
|
Together, the two cells marked "*" eliminate "1" from r4c1.
The generalization is possible because of the weak links present in the AIC. Taking Norm's AIC:
| Code: |
(2=7)r9c7-(7)r8c7=(7-2)r8c3=(2)r7c2; r7c89 cannot be 2
^ ^
| |
+----------+---- ... no strong link needed
|
The first point, where the pairs/strong link requirement can be abandoned, is between r9c7 and r8c7 ("7" sees "7", but there could be other sevens in col 7)
The other point is within r8c3 (might be a multi-value cell)
On the other hand it is essential that the first cell r9c7 is bi-value, otherwise the start of the chain "(2=7)r9c7..." would not work
---
edit 18:29 GMT+2 to correct error "One end (r8c7) is ..." to "One end (r8c3) ..."
Last edited by nataraj on Tue Aug 12, 2008 4:31 pm; edited 1 time in total |
|
| Back to top |
|
|
arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
|
| Posted: Tue Aug 12, 2008 12:58 pm Post subject: |
|
|
Norm: Excellent work  The drawing was very helpfull
nataraj said | Quote: | | In fact, a (generalized) m-wing elimination can be performed even without a "pair" |
I will have future questions on generalized wings. Like in this puzzle. The basic m-wing was there but I found different candidates to remove.
My problem in other patterns is when I know the basics I no longer look for what else is there. I have to learn to explore more.
Thanks all for the excellent help. |
|
| Back to top |
|
|
wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
|
| Posted: Tue Aug 12, 2008 2:14 pm Post subject: |
|
|
| nataraj wrote: | | In fact, a (generalized) m-wing elimination can be performed even without a "pair" (equivalent, or complementary, whatever you wish to call it): |
I'm not very happy with the drift into chains, yet using the terms M-wing and W-wing.
Yes, I am aware that those are specific short chains. The simplest case is a 4-cell remote pair.
The thing is that when one says W-wing or M-wing a visual pattern is possible to envisage.
Just as "sue de coq" is a specific ALS, "M-wing" is a specific short chain.
Anyways, that's my opinion, and unlikely to change!  |
|
| Back to top |
|
|
nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
|
| Posted: Tue Aug 12, 2008 3:28 pm Post subject: |
|
|
| wapati wrote: | | I'm not very happy with the drift into chains, yet using the terms M-wing and W-wing. |
wapati,
happiness is very personal, still I'd much prefer to see you happy than unhappy
In contrast to x-wings and xy-wings, I doubt that m-wings (or even w-wings) can be described without that basic building block of any chain, the concept of weak and strong links. My feeling is that it will not be possible to avoid chains altogether.
I think we both look for patterns. Maybe where we differ is in the kind of pattern we search (almost like the difference between morphology and physiology)
- the anatomical approach: look for 2 (or 3) identical bi-value cells and try to find a connection. This approach works "from form to function"
- the physiological approach: look for strong links and find "pincers" from there - "from function to form". In the end the results are fairly similar.
I tend to have a common name for everything that works alike, you prefer to have a common name for everything that looks alike
In the case of the w-wing I am pretty sure our definitions match, it is a pure question which point of view one takes:
Definition a: two identical bi-value cells that each see one end of a strong link in one of the candidates.
Definition b: a strong link in a, and both ends "see" identical bi-value cells {a,b}
With the m-wing I am not so sure.
My definition would be: two strong links (one in "a", one in "b") that meet in a single cell (like in a hockey stick: _/ ). A bi-value cell made up of these two candidates {a,b} that sees either end of the hockey stick.
No chains in that definition. But a visual pattern very different from
ab-ab-ab-ax |
|
| Back to top |
|
|
wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
|
| Posted: Tue Aug 12, 2008 3:49 pm Post subject: |
|
|
As I learn more chainlike things the whole matter blurs anyways. 
Good answer, btw. |
|
| Back to top |
|
|
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
| Posted: Tue Aug 12, 2008 5:25 pm Post subject: |
|
|
| Quote: | In fact, a (generalized) m-wing elimination can be performed even without a "pair" (equivalent, or complementary, whatever you wish to call it):
|
Nataraj,
sure, its fine to learn the generalizations.
sure, its fine to know the aic implications.
however, what isn't stressed enough sometimes is how much more fun it is to spot those remote pairs and solve that puzzle in ONE MOVE 
and when I say remote pair, I mean anything from classic remote pair to m-wings to w-wings.
again,
its FUN and when learned can make a puzzle much easier to solve.
third time.
its FUN
cmon, nataraj, have some fun with this.
geez
you told me once in a PM that this is a relaxed type of affair and to not stress out. how long did you ponder your answer?? did you stress?? I mean WOW
|
|
| Back to top |
|
|
nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
|
| Posted: Tue Aug 12, 2008 8:36 pm Post subject: |
|
|
lol.
point taken.
---
It also gives me plesure to write serious answers ...
(and to draw colorful diagrams, that seems to be a vice we share  ) |
|
| Back to top |
|
|
Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
|
| Posted: Tue Aug 12, 2008 9:31 pm Post subject: |
|
|
We aren't done with the fun yet...
This puzzle has an "ER Loop" in b1397. In the dreaded AIC notation:
Loop: - (2)r3c2=(2)r2c2 - (2)r2c89=(2)r1c7 - (2)r89c7=(2)r7c89 - (2)r7c2=(2)r8c3 -
(Or, Loop: - [Box1 ER] - [Box3 ER] - [Box9 ER] - [Box7 ER] - )
All of the links become conjugate which eliminates <2> from r4c7 and r7c4.
While that is somewhat novel, it is not what is REALLY interesting.
If we consider the ERs and those complementary 27s together, then the 27s must both be <7> since the <2>s can "see each other" via the ERs in Boxes 1 and 3. |
|
| Back to top |
|
|
|
|
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
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
