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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Thu Jul 17, 2008 5:09 am Post subject: What else is here? |
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This is easily solved with XY-Chains or simple Medusa. What other ways are available?
| Code: |
+-------------+---------+----------+
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38 358 358 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
+-------------+---------+----------+
| 39 1 4 | 7 5 2 | 39 6 8 |
| 6 38 2 | 4 89 1 | 5 37 79 |
| 789 578 58 | 3 89 6 | 2 4 1 |
+-------------+---------+----------+
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 378 38 | 89 2 4 | 6 1 79 |
| 78 2 6 | 89 1 3 | 79 5 4 |
+-------------+---------+----------+
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Jul 17, 2008 5:42 am Post subject: Re: What else is here? |
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| Marty R. wrote: | This is easily solved with XY-Chains or simple Medusa. What other ways are available?
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xy-chains, Medusa ..."easily" ... I love that 
There is an m-wing on 9: pincers r9c7,r4c1 via (7):r9c1=r6c1.
It removes 9 from r4c7. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 6:03 am Post subject: |
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Marty,
I can see why you posted this! Can you buy the following? Medusa remote pairs? | Code: | +-------------+-------------+-------------+
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38 358 358 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
+-------------+-------------+-------------+
| 39 1 4 | 7 5 2 | 39 6 8 |
| 6 38% 2 | 4 89@ 1 | 5 37 79# |
| 789 578 58 | 3 89 6 | 2 4 1 |
+-------------+-------------+-------------+
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 -378 38% | 89@ 2 4 | 6 1 79# |
| 78 2 6 | 89 1 3 | 79 5 4 |
+-------------+-------------+-------------+ |
The cells @ <89> are a (W-wing and a) remote pair, connected by the pair # <79>. (Skyscraper on <9>.) Any cell that sees both @ cannot be <8> (or <9>).
If one of @ must be <8>, one of % must be <3>  Taking out <3> in R8C2. Leading to a UR and a BUG+1.
Keith
Last edited by keith on Thu Jul 17, 2008 6:09 am; edited 1 time in total |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Thu Jul 17, 2008 6:06 am Post subject: |
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I still need one short xy-chain but a hidden UR is nice.
| Code: |
Hidden UR.
.----------------.---------------.---------------.
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38 *35-8 *358 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
:----------------+---------------+---------------:
| 39 1 4 | 7 5 2 | 39 6 8 |
| 6 38 2 | 4 89 1 | 5 37 79 |
| 789 *578 *58 | 3 89 6 | 2 4 1 |
:----------------+---------------+---------------:
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 378 38 | 89 2 4 | 6 1 79 |
| 78 2 6 | 89 1 3 | 79 5 4 |
'----------------'---------------'---------------'
xy-wing.
.-----------------.---------------.---------------.
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38 *35 38-5 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
:-----------------+---------------+---------------:
| 39 1 4 | 7 5 2 | 39 6 8 |
| 6 *38 2 | 4 89 1 | 5 37 79 |
| 789 78-5 *58 | 3 89 6 | 2 4 1 |
:-----------------+---------------+---------------:
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 378 38 | 89 2 4 | 6 1 79 |
| 78 2 6 | 89 1 3 | 79 5 4 |
'-----------------'---------------'---------------'
4-cell xy-chain.
.----------------.---------------.---------------.
| 2 4 7 | 6 3 8 | 1 9 5 |
|*38 5 38 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
:----------------+---------------+---------------:
| 9-3 1 4 | 7 5 2 |*39 6 8 |
| 6 38 2 | 4 89 1 | 5 37 79 |
| 789 78 5 | 3 89 6 | 2 4 1 |
:----------------+---------------+---------------:
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 378 38 | 89 2 4 | 6 1 79 |
|*78 2 6 | 89 1 3 |*79 5 4 |
'----------------'---------------'---------------' |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 6:23 am Post subject: |
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wapati's last grid is an easy BUG+2: | Code: | +-------------+-------------+-------------+
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38 5 38 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
+-------------+-------------+-------------+
| 39 1 4 | 7 5 2 | 39 6 8 |
| 6 3-8 2 | 4 89 1 | 5 37 79 |
|@789 7-8 5 | 3 89 6 | 2 4 1 |
+-------------+-------------+-------------+
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 @378 38 | 89 2 4 | 6 1 79 |
| 78 2 6 | 89 1 3 | 79 5 4 |
+-------------+-------------+-------------+ |
To avoid the DP, either of @ must be <8>, solving R6C2 and R5C2.
[Edit: And solving R9C1.]
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 6:31 am Post subject: |
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Marty,
Please post the original puzzle (or a link).
Thank you,
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Jul 17, 2008 3:57 pm Post subject: |
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Thanks for the responses. Nataraj, I can't follow it, I don't see an M-Wing, at least based on what my understanding of an M-Wing is.
Keith, nice reasoning, but beyond what I can do.
Wapiti, I wasn't able to do anything the UR.
At Keith's request, the original is:
| Code: |
+-------+-------+-------+
| 2 . 7 | . . . | 1 9 . |
| . . . | 1 . 9 | . . 6 |
| . . 9 | . 4 . | . . . |
+-------+-------+-------+
| . 1 . | . 5 . | . 6 8 |
| 6 . 2 | 4 . . | . . . |
| . . . | 3 . 6 | 2 . . |
+-------+-------+-------+
| . 9 . | . . 7 | . . . |
| 5 . . | . 2 . | . 1 . |
| . . 6 | . . 3 | . 5 4 |
+-------+-------+-------+
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Jul 17, 2008 7:30 pm Post subject: |
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| Marty R. wrote: | Thanks for the responses. Nataraj, I can't follow it, I don't see an M-Wing, at least based on what my understanding of an M-Wing is.
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Marty, let me first explain how the pattern works, and then why I called it an m-wing.
Starting from your grid
| Code: |
----------------+---------+-----------+
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38 358 358 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 78 78 3 |
+---------------+---------+-----------+
| 39* 1 4 | 7 5 2 | 3-9 6 8 |
| 6 38 2 | 4 89 1 | 5 37 79 |
| 7#89* 578 58 | 3 89 6 | 2 4 1 |
+---------------+---------+-----------+
| 4 9 1 | 5 6 7 | 38 38 2 |
| 5 378 38 | 89 2 4 | 6 1 79 |
| 7#8 2 6 | 89 1 3 | 79* 5 4 |
+---------------+---------+-----------+
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If r9c7=9 then r4c7 cannot be 9.
If r9c7=7 then r9c1<>7 then (strong link on 7 in col 1) r6c1=7 then (strong link on 9) r4c1=9.
The "classical" m-wing would look something like this (again starting in r9c7 and ending in r4):
79-79-79-39
same reasoning: if the starting cell is 7 then (because of the conjugate pair 79/79) r6c1=7 and (because of the strong link in 9) r4c2=9 (cannot be r4c1 but r4c2 would work).
The general principle:
one strong link in "x".
one end of the strong link "sees" a bi-value cell (x,y) - pincer cell 1
the other end is strongly linked in y to pincer cell 2
any cell that sees pincer cells 1 and 2 cannot contain y.
For comparison, the w-wing:
one strong link in "x".
one end of the strong link sees a bi-value cell (x,y) - pincer cell 1
the other end sees another bi-value cell also with (x,y) - pincer cell 2
any cell that sees pincer cells 1 and 2 cannot contain y. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Jul 17, 2008 8:51 pm Post subject: |
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I really like Keiths reasoning ...
| keith wrote: | Can you buy the following? The cells @ <89> are a (W-wing and a) remote pair
[...]
If one of @ must be <8>, one of % must be <3> |
(w-wing transported at both ends?)
This pattern is present in the grid once more in another flavor:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 2 4 7 | 6 3 8 | 1 9 5 |
| 38w 358 358 | 1 7 9 | 4 2 6 |
| 1 6 9 | 2 4 5 | 7%8 78 3 |
+--------------------------+--------------------------+--------------------------+
| 3w9 1 4 | 7 5 2 | 3w9 6 8 |
| 6 38 2 | 4 89 1 | 5 37 79 |
| 789 578 58 | 3 89 6 | 2 4 1 |
+--------------------------+--------------------------+--------------------------+
| 4 9 1 | 5 6 7 | 38w 38 2 |
| 5 378 38 | 89 2 4 | 6 1 79 |
| 7%8 2 6 | 89 1 3 | -79 5 4 |
+--------------------------+--------------------------+--------------------------+
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w-wing 38 (r2c1,r7c7 connected by strong link on 3 in row 4), useless at first, can be transported:
if r2c1=8 then r9c8=7 and
if r7c7=8 then r3c7=7 thus
r9c7<>7 and the puzzle is solved
____
edit 2320 GMT+2: when I said "the pattern is present ONCE more" that might have been a low estimate. In fact, there are about 25 "useless" m-wings and w-wings in the grid, and I am sure that many of them can be transported in keith's "shocking" (  )way:
w-wing(8 ) r2c1,r7c7 via (3):r4c1=r4c7.
m-wing(8 ) r2c1,r5c5 via (3):r4c1=r5c2.
w-wing(8 ) r5c2,r7c7 via (3):r4c1=r4c7 or r5c8=r4c7 or r5c8=r7c8
m-wing(8 ) r5c2,r3c8 via (3):r5c8=r7c8.
m-wing(8 ) r5c2,r7c7 via (3):r5c8=r7c8.
m-wing(8 ) r7c8,r5c5 via (3):r5c8=r5c2.
m-wing(8 ) r3c7,r9c4 via (7):r9c7=r9c1.
w-wing(8 ) r3c8,r9c1 via (7):r3c7=r9c7.
m-wing(9 ) r5c9,r4c7 via (7):r8c9=r9c7.
m-wing(9 ) r5c9,r9c4 via (7):r8c9=r9c7.
m-wing(8 ) r9c1,r3c8 via (7):r9c7=r3c7.
m-wing(8 ) r9c1,r7c7 via (7):r9c7=r3c7.
m-wing(9 ) r9c7,r4c7 via (7):r8c9=r5c9.
m-wing(9 ) r9c7,r5c5 via (7):r8c9=r5c9.
m-wing(9 ) r9c7,r6c5 via (7):r9c1=r6c1.
w-wing(8 ) r5c5,r8c4 via (9):r5c9=r8c9.
m-wing(7 ) r5c9,r3c7 via (9):r4c7=r9c7.
m-wing(7 ) r5c9,r8c9 via (9):r4c7=r9c7.
m-wing(7 ) r5c9,r9c1 via (9):r4c7=r9c7.
m-wing(7 ) r5c9,r3c7 via (9):r8c9=r9c7.
m-wing(7 ) r5c9,r9c1 via (9):r8c9=r9c7.
m-wing(7 ) r9c7,r5c8 via (9):r4c7=r5c9 or r8c9=r5c9
m-wing(7 ) r9c7,r8c9 via (9):r4c7=r5c9.
Last edited by nataraj on Thu Jul 17, 2008 9:26 pm; edited 2 times in total |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Jul 17, 2008 9:11 pm Post subject: |
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| My understanding of an M-Wing is still limited to the original definition, whereby it involves identical bivalue cells in different houses. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Jul 17, 2008 9:26 pm Post subject: |
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| I believe that Keith's elimination is easiest to see as a 38 W-Wing. The only "catch" is that the external strong link on <8> that "activates" the 38 W-Wing is itself a W-Wing. Most of us are comfortable with W-Wings activated by such things as Kites or XY-Wings, so why look at it any differently if it is activated by another W-Wing? |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Jul 17, 2008 9:33 pm Post subject: |
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| Asellus wrote: | | so why look at it any differently if it is activated by another W-Wing? |
I quite agree. The strong link which connects the two identical bi-values in a w-wing does not have to be a "simple" strong link like a house with only 2 cells that contain a certain candidate, but might be any pattern that effectively asserts that "either cell a is x or cell b is x (or both)" |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 9:40 pm Post subject: |
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| Marty R. wrote: |
Wapiti, I wasn't able to do anything the UR.
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Marty,
The UR is a Type 6. It is an X-wing on <5>. <8> in R2C2 forces the DP.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 9:56 pm Post subject: |
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| nataraj wrote: | | Asellus wrote: | | so why look at it any differently if it is activated by another W-Wing? |
I quite agree. The strong link which connects the two identical bi-values in a w-wing does not have to be a "simple" strong link like a house with only 2 cells that contain a certain candidate, but might be any pattern that effectively asserts that "either cell a is x or cell b is x (or both)" |
Asellus,
Because the logic is subtly different?
WX-aX=bX-WX
The pincers WX of a W-wing are not a remote pair (one is W, one is X), nor are they a complementary pair (both are W).
No doubt you can use the pincers to excite something like a W- or M-wing, but be careful!
In my book, this is something like a Type-6 UR, or a Bug+n: You need to argue the logic each time.
Keith |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Jul 17, 2008 10:16 pm Post subject: |
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| keith wrote: | | The pincers WX of a W-wing are not a remote pair (one is W, one is X) |
Run that by me again, please. I might have had a long day and not bee too quick any more, but now you are pulling the rug out from under me, Keith.
I thought in this short discussion that the (mostly academic) question was whether the elimination is a "w-wing with transported pincers" or a "w-wing where the connecting strong link consists of more than one chainlink"
In both cases we'd have a "remote pair" in the sense that both cells have the same two candidates (3 and 8 ) and a connecting AIC that makes sure at least one of the "pincer" ends is 3. BTW, I am still talking about the "shock" elimination
| Quote: | | If one of @ must be <8>, one of % must be <3> |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 10:23 pm Post subject: |
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| Marty R. wrote: | | My understanding of an M-Wing is still limited to the original definition, whereby it involves identical bivalue cells in different houses. |
As the one who baptized the M-wing, here is my opinion:
The M-wing is so named because, if you do Medusa coloring, it WILL show up as a (minimum) four-cell chain making a Medusa elimination.
| Quote: | | (That, and the fact that the initial of my last name is M.) |
So, my question is: If you do Medusa coloring on this grid, will Nataraj' chain show up, making the elimination he identifies? (I have not tried this.)
If yes, I agree it is an M-wing, albeit harder to recognize.
If no, maybe it has another name?
In any event, we should document how to find it in the "Solution Techniques" thread.
By the way, I really had fun with this one. The fact that the whole thing occurs in only two rows is also cause for
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jul 17, 2008 10:54 pm Post subject: |
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| nataraj wrote: | | keith wrote: | | The pincers WX of a W-wing are not a remote pair (one is W, one is X) |
Run that by me again, please. I might have had a long day and not bee too quick any more, but now you are pulling the rug out from under me, Keith.
I thought in this short discussion that the (mostly academic) question was whether the elimination is a "w-wing with transported pincers" or a "w-wing where the connecting strong link consists of more than one chainlink"
In both cases we'd have a "remote pair" in the sense that both cells have the same two candidates (3 and 8 ) and a connecting AIC that makes sure at least one of the "pincer" ends is 3. BTW, I am still talking about the "shock" elimination
| Quote: | | If one of @ must be <8>, one of % must be <3> |
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Nataraj,
I should have said , "In the general case, the pincers of a W-wing are not a remote pair ..."
In my message, I intended to address what Asellus said, but also to include your quote.
I am not questioning anything you have said, I intended merely to add my thoughts to Asellus' message.
Best wishes,
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Jul 18, 2008 12:34 am Post subject: |
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| keith wrote: | | No doubt you can use the pincers to excite something like a W- or M-wing, but be careful! |
A W-Wing only requires that a remote pair of matching bivalue cells each be able to "see" the alternate ends of an external strong inference (the "external strong link") in one of their digits. This induces a strong inference between the other digit of these two cells, creating the W-Wing pincers. No special care is required other than being certain that this "external link" is really a strong link.
Any kind of strong link (and not just a conjugate strong link) serves this purpose. Examples using XY-Wing or Chain pincers, Kite pincers and other sorts of wings have been posted various times on this site.
The first W-Wing above is activated by the strong (conjugate) link between the <9>s in c9:
(8=9)r5c5-(9)r5c9=(9)r8c9-(9=8)r8c4
We now have the induced strong link of those pincer <8>s:
(8)r5c5=(8)r8c4
With that, we get the second W-Wing with identical inferential logic:
(3=8)r5c2-(8)r5c5=(8)r8c4-(8=3)r8c3
If you wish to go further and determine whether or not the induced strong link is also conjugate (thus creating a Remote Naked Pair), that's fine; but you are leaving the realm of essential W-Wing logic. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Jul 18, 2008 12:59 am Post subject: |
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| Quote: | | So, my question is: If you do Medusa coloring on this grid, will Nataraj' chain show up, making the elimination he identifies? (I have not tried this.) |
I started the Medusa in r9c7 and quickly ended up with a wrap in r6c1 before there were any traps. |
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