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8-29 competition

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sun Aug 31, 2008 2:42 am    Post subject: 8-29 competition Reply with quote

Code:
. . 3|. . .|. 4 .
. 1 .|6 4 .|. . .
. . .|1 . 8|7 . 2
-----+-----+-----
. 8 7|. . .|2 . .
9 . .|. 2 .|. . 5
. . 2|. . .|1 6 .
-----+-----+-----
3 . 1|9 . 4|. . .
. . .|. 6 5|. 1 .
. 9 .|. . .|8 . .


Code:
.------------------.------------------.------------------.
| 8     27    3    | 5     79    279  | 6     4     1    |
| 27    1     59   | 6     4     27   | 39    3589  389  |
| 456   456   4569 | 1     3     8    | 7     59    2    |
:------------------+------------------+------------------:
| 1     8     7    | 34    5     6    | 2     39    349  |
| 9     346   46   | 78    2     1    | 34    78    5    |
| 45    345   2    | 3478  79    379  | 1     6     78   |
:------------------+------------------+------------------:
| 3     267   1    | 9     8     4    | 5     27    67   |
| 27    247   8    | 237   6     5    | 349   1     3479 |
| 456   9     456  | 237   1     37   | 8     237   46   |
'------------------'------------------'------------------'
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Earl



Joined: 30 May 2007
Posts: 623
Location: Victoria, KS

PostPosted: Sun Aug 31, 2008 3:15 am    Post subject: challenge Reply with quote

An xy-chain eliminates the 2 in R7C2, which leads to coloring (7) to solve the puzzle.

Earl
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sun Aug 31, 2008 7:39 am    Post subject: Reply with quote

I'll add this one from the telegraph, for friday the 29th. it can also be solved in the same manner.

Code:
. . .|. 6 .|3 . .
. . 6|. 4 .|. 1 8
. . 5|. . .|7 . .
-----+-----+-----
. 9 .|2 8 .|. . .
. . 4|. . .|. . .
. . .|. 5 7|. 6 .
-----+-----+-----
. 4 1|. . .|9 . .
6 2 .|. 9 .|5 . .
3 . 9|. . .|. . .
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Sun Aug 31, 2008 12:03 pm    Post subject: Re: challenge Reply with quote

Earl wrote:
An xy-chain eliminates the 2 in R7C2
A very long one.
Code:
 *-----------------------------------------------------------*
 | 8    #27    3     | 5     79    29    | 6     4     1     |
 |*27    1     59    | 6     4    #27    | 39    3589  389   |
 | 456   456   4569  | 1     3     8     | 7     59    2     |
 |-------------------+-------------------+-------------------|
 | 1     8     7     | 34    5     6     | 2     39    349   |
 | 9     346   46    |@78    2     1     | 34   @78    5     |
 | 45    345   2     | 3478  79    39    | 1     6     78    |
 |-------------------+-------------------+-------------------|
 | 3    -267   1     | 9     8     4     | 5    #27    67    |
 | 27    247   8     | 23    6     5     | 349   1     3479  |
 | 456   9     456   |@237   1    @37    | 8     23    46    |
 *-----------------------------------------------------------*
An alternative for the same elimination is the w-wing 27 in r2c6/r7c8 connected by the skyscraper for 7 in rows 59.
The 2 in r2c6 easlily transports to the 2 in r1c2.

The second puzzle only neds an extended xy-wing (aka generalized/grouped xy-wing or 4-cell-xy-chain).
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Aug 31, 2008 4:03 pm    Post subject: Re: challenge Reply with quote

ravel wrote:
A very long one.

Is the XY-Chain really all that long? Besides, it's also a generalized Remote Naked Pair linking <27> cells via <7>.

Code:
 -2r1c2 7r1c2 -7r1c5 7r6c5 -7r5c4 7r5c8 -7r7c8 2r7c8  =>  [r7c2]<>2
 +--------------------------------------------------------------+
 |  8    *27    3     |  5    *79    279   |  6     4     1     |
 |  27    1     59    |  6     4     27    |  39    3589  389   |
 |  456   456   4569  |  1     3     8     |  7     59    2     |
 |--------------------+--------------------+--------------------|
 |  1     8     7     |  34    5     6     |  2     39    349   |
 |  9     346   46    | *78    2     1     |  34   *78    5     |
 |  45    345   2     |  3478 *79    379   |  1     6     78    |
 |--------------------+--------------------+--------------------|
 |  3     267   1     |  9     8     4     |  5    *27    67    |
 |  27    247   8     |  23    6     5     |  349   1     3479  |
 |  456   9     456   |  237   1     37    |  8     23    46    |
 +--------------------------------------------------------------+
 # 63 eliminations remain

Note: I don't normally list the internal eliminations. So don't get spoiled Very Happy
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Mon Sep 01, 2008 12:14 am    Post subject: Reply with quote

Danny,

I'm not sure about the Remote Naked Pair, but r1c2 and r7c8 are certainly a Semi-RNP (aka W-Wing) activated by the 7 Kite that pivots in box 5, as you've marked it... eliminating the need for ravel's "transport".
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Mon Sep 01, 2008 6:38 am    Post subject: Reply with quote

Code:
6 2 .|5 . .|1 . .
. . .|. . .|. 4 6
4 7 .|6 . 1|. . .
-----+-----+-----
. . .|8 . .|. 6 .
5 . 6|. . .|7 . 9
. 4 .|. . 9|. . .
-----+-----+-----
. . .|. . 8|. 3 1
7 8 .|. . .|. . .
. . 2|. . .|. . 5


this is the sunday competition. doesn't need xy-chains this time.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon Sep 01, 2008 10:05 am    Post subject: Re: challenge Reply with quote

daj95376 wrote:
Is the XY-Chain really all that long?
The one i found had 8 cells (from r8c1 to r7c8). Thats the problem i have with xy-chains. There are so much possibilities, that even when you know, that there is one, you will not always find the shortest one first.

But ok, i also missed the kite-w-wing, because i saw the skyscraper-w-wing first Smile
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Sep 01, 2008 3:53 pm    Post subject: Reply with quote

Asellus wrote:
Danny,

I'm not sure about the Remote Naked Pair, but r1c2 and r7c8 are certainly a Semi-RNP (aka W-Wing) activated by the 7 Kite that pivots in box 5, as you've marked it... eliminating the need for ravel's "transport".

I wrote:
generalized Remote Naked Pair

keith calls it a General Remote Pair in (E) below. I reworded it slightly. A Semi-RNP works for me as well. In fact, it's also been called a Y-Wing Styles, but that created lots of confusion with people shortening it to Y-Wing, so I stay away from using it.

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=9097&sid=7a26270a8dc247c7ac3a256634efa790#9097
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Sep 01, 2008 4:37 pm    Post subject: Reply with quote

daj95376 wrote:
Asellus wrote:
Danny,

I'm not sure about the Remote Naked Pair, but r1c2 and r7c8 are certainly a Semi-RNP (aka W-Wing) activated by the 7 Kite that pivots in box 5, as you've marked it... eliminating the need for ravel's "transport".

I wrote:
generalized Remote Naked Pair

keith calls it a General Remote Pair in (E) below. I reworded it slightly. A Semi-RNP works for me as well. It's also been called a Y-Wing Styles, but that created lots of confusion with people shortening it to Y-Wing, so I stay away from using it.

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=9097&sid=7a26270a8dc247c7ac3a256634efa790#9097
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Sep 02, 2008 3:20 am    Post subject: Reply with quote

Danny,

I have to disagree: As far as I can see, and based on your asterisk markings, your 27 pair is not what Keith was describing as a General Remote (Naked) Pair. He describes a pair that is connected by an odd number of strong (by which he means conjugate) links in one of the digits such that the two instances of that digit (and thus of both digits) of the remote pair are conjugate with each other. Your chain of <7> links contains a weak link in box 5. Thus, a weak inference link (not a conjugate, let alone a strong, link) is induced between the <7>s in the remote 27 pair. In turn, this induces a strong inference between the <2>s (ie, W-Wing). However, it is possible that both cells are <2>, which is not a RNP in my book.... only "half" of one.

Perhaps "generalized RNP" has some meaning in the Players' Forum beyond what Keith was describing. But, quite a bit of the lingo in that forum is an alien tongue in this forum.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Sep 02, 2008 4:09 am    Post subject: Reply with quote

Asellus wrote:
I have to disagree

I concede the point.
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keith



Joined: 19 Sep 2005
Posts: 3342
Location: near Detroit, Michigan, USA

PostPosted: Tue Sep 02, 2008 4:58 am    Post subject: Reply with quote

Thge way I see it is this. Ignoring the UR:
Code:
+----------------+----------------+----------------+
| 8    27c  3    | 5    79B  279  | 6    4    1    |
| 27   1    59   | 6    4    27   | 39   3589 389  |
| 456  456  4569 | 1    3    8    | 7    59   2    |
+----------------+----------------+----------------+
| 1    8    7    | 34   5    6    | 2    39   349  |
| 9    346  46   | 78a  2    1    | 34   78A  5    |
| 45   345  2    | 3478 79b  379  | 1    6    78   |
+----------------+----------------+----------------+
| 3   -267  1    | 9    8    4    | 5    27C  67   |
| 27   247  8    | 23   6    5    | 349  1    3479 |
| 456  9    456  | 237  1    37   | 8    23   46   |
+----------------+----------------+----------------+
aA and bB are a kite (turbot fish, whatever). Any cell that sees both A and B cannot be <7>. One, or both, of A and B are <7>. Therefore, one or both of c and C are <2>. R6C2 cannot be <2>. Which solves the puzzle.

However, in the solution, R7C2 is <6>. It is not <27>. Is there an argument that says cC are indeed a remote pair? (Any cell that sees both of them is not <27>.) Or, a separate chain that eliminates <7> from R7C2?

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Sep 02, 2008 1:46 pm    Post subject: Reply with quote

keith wrote:
Or, a separate chain that eliminates <7> from R7C2?

I did not find a basic chain. However, there is a SIN for the elimination.

Code:
 SIN:  7r7c2  7r5c8  8r2c8  5r2c3  5r9c1  6r9c3  [b4]~4  =>  [r7c2]<>7

 state after SIN
 *-----------------------------------------------------------*
 | 8     2     3     | 5     79    279   | 6     4     1     |
 | 27    1    d5     | 6     4     27    | 39   c8     39    |
 | 46    46    49    | 1     3     8     | 7     59    2     |
 |-------------------+-------------------+-------------------|
 | 1     8     7     | 34    5     6     | 2     39    349   |
 | 9     346  #4     | 8     2     1     | 34   b7     5     |
 |#4     345   2     | 3478  79    379   | 1     6     8     |
 |-------------------+-------------------+-------------------|
 | 3    a7     1     | 9     8     4     | 5     2     6     |
 | 2     24    8     | 23    6     5     | 349   1     3479  |
 |e5     9    f6     | 237   1     37    | 8     23    4     |
 *-----------------------------------------------------------*
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Sep 03, 2008 1:36 am    Post subject: Reply with quote

keith wrote:
However, in the solution, R7C2 is <6>. It is not <27>. Is there an argument that says cC are indeed a remote pair?


If, as you say, r7c2 is <6> in the solution, then it is impossible to demonstrate that r1c2 and r7c8 are a RNP because they must both be <2> in the solution. Anything that claimed to show a conjugate RNP relationship between these cells would be in error.

Danny,

I'm glad to hear that we don't have some confusing clash of terminology and that this was just an inapt example. Thanks for clarifying.
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