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Free Press 4 September, 2009

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri Sep 04, 2009 3:23 pm    Post subject: Free Press 4 September, 2009 Reply with quote
Not yet done:
Code:
Puzzle: FP090409
+-------+-------+-------+
| 9 5 . | . 3 . | . 2 4 |
| . . . | . 8 . | 9 . 1 |
| . . . | . . . | . 7 . |
+-------+-------+-------+
| . . . | 3 7 1 | . . 6 |
| 5 . . | . . . | . . 7 |
| 2 . . | . 9 6 | . . . |
+-------+-------+-------+
| . 9 . | . . . | . . . |
| 8 . 3 | . 5 . | . . . |
| 7 2 . | . 1 . | . 3 9 |
+-------+-------+-------+
Keith
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
PostPosted: Fri Sep 04, 2009 4:36 pm    Post subject: Free Reply with quote
A Solution

An xy-chain from R3C5 to R9C4 eliminates the 6 in R1C4 and solves the puzzle.

Earl
of the chain gang
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Fri Sep 04, 2009 4:39 pm    Post subject: Reply with quote
One stepper:
Quote:
xy-chain starting with 16 in B1 and ending with 16 in B2
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri Sep 04, 2009 6:58 pm    Post subject: Reply with quote
Well, then. After basics:
Code:
+----------------+----------------+----------------+
| 9    5    16d  | 16c  3    7    | 8    2    4    |
| 3    7    2    | 4    8    5    | 9    6    1    |
| 16e  4    8    | 129  26   29   | 35   7    35   |
+----------------+----------------+----------------+
| 4    8    9    | 3    7    1    | 2    5    6    |
| 5    136  16   | 28   24   248  | 13   9    7    |
| 2    13   7    | 5    9    6    | 14   148  38   |
+----------------+----------------+----------------+
| 16f  9    45   | 27   246  3    | 1457 148  58   |
| 8    16g  3    | 679  5   -49   | 1467 14h  2    |
| 7    2    45   | 68b  1    48a  |-456  3    9    |
+----------------+----------------+----------------+
Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri Sep 04, 2009 10:49 pm    Post subject: Reply with quote
Code:
 my solver's basics didn't eliminate <3> in [r6c7]
 +-----------------------------------------------------------------------+
 |  9      5      16     |  16     3      7      |  8      2      4      |
 |  3      7      2      |  4      8      5      |  9      6      1      |
 |  16     4      8      |  1269   26     29     |  35     7      35     |
 |-----------------------+-----------------------+-----------------------|
 |  4      8      9      |  3      7      1      |  2      5      6      |
 |  5     *13+6   16     |  28     24     248    | *13     9      7      |
 |  2     *13     7      |  5      9      6      | *13+4   148    38     |
 |-----------------------+-----------------------+-----------------------|
 |  16     9      45     |  267    246    3      |  14567  148    58     |
 |  8      16     3      |  679    5      49     |  1467   14     2      |
 |  7      2      45     |  68     1      48     |  456    3      9      |
 +-----------------------------------------------------------------------+
 # 50 eliminations remain

 *** UR 2x bivalue cells:   <13> [r56c27]   cand count =  4/2,3,3,2

From here, I found:

Code:
 <13> UR [r56c27] => [r5c2]=6 or [r6c7]=4

 [r5c2]=6 => [r8c2]=1 => [r6c2]=3 => [r6c7]<>3
                      || [r8c8]=4 =>            [r6c8]<>4

 [r6c7]=4 =>                         [r6c7]<>3, [r6c8]<>4

This doesn't crack the puzzle, but it does bypass the XY-Chain by allowing an X-Wing, a turbot fish, and an XY-Wing.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Sep 05, 2009 9:23 pm    Post subject: Reply with quote
Danny:

Quote:
my solver's basics didn't eliminate <3> in [r6c7]
You are correct. The elimination can be made by an insanely long XY-chain. Here is the "correct" "after basics":
Code:
+----------------+----------------+----------------+
| 9    5    16   | 16   3    7    | 8    2    4    |
| 3    7    2    | 4    8    5    | 9    6    1    |
| 16a  4    8    |1-29  26g  29f  | 35   7    35   |
+----------------+----------------+----------------+
| 4    8    9    | 3    7    1    | 2    5    6    |
| 5    136  16   | 28   24   248  | 13   9    7    |
| 2    13   7    | 5    9    6    | 134  148  38   |
+----------------+----------------+----------------+
| 16b  9    45   | 27   246  3    | 1457 148  58   |
| 8    16c  3    | 679  5    49e  |-1-467 14d 2    |
| 7    2    45   | 68   1    48   | 456  3    9    |
+----------------+----------------+----------------+
Sudoku Susser points out the interesting XY loop that is a one-stepper.

I don't recall ever seeing a loop that makes two eliminations in a cell.

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat Sep 05, 2009 11:53 pm    Post subject: Reply with quote
keith wrote:
daj wrote:
my solver's basics didn't eliminate <3> in [r6c7]

You are correct. The elimination can be made by an insanely long XY-chain.

If you combine the strong links on <3> in the UR with the bivalue <13> cells in the UR, then you can deduce [r6c7]<>3 by itself. However, this doesn't advance the solution, so I needed to use logic that also performed [r6c8]<>4.

keith wrote:
I don't recall ever seeing a loop that makes two eliminations in a cell.

This is why I use only one minus "-" sign in a cell and place the elimination(s) after it.

Code:
 Ted's Insane puzzle for Sep. 4, 2009
 +-----------------------------------------------------------------------+
 |  4      16     3      |  8     b17     2      |  5     c67     9      |
 |  58     68     2      |  567    9     e36     |  4     d3678   1      |
 |  158    9      7      |  156   f134    146-3  |  68     368    2      |
 |-----------------------+-----------------------+-----------------------|
 |  2      5      4      |  3      8      7      |  9      1      6      |
 |  6      3      8      |  12     12     9      |  7      4      5      |
 |  9      7      1      |  4      6      5      |  3      2      8      |
 |-----------------------+-----------------------+-----------------------|
 |  138    1248   5      |  1267 ag37-124 1346   |  68     9      47     |
 |  138    148    9      |  167    5      1346   |  2      68     47     |
 |  7      24     6      |  9      24     8      |  1      5      3      |
 +-----------------------------------------------------------------------+
 # 55 eliminations remain

 (7)r7c5 = r1c5 - r1c8 = (7-3)r2c8 = r2c6 - r3c5 = (3)r7c5; => r7c5<>124,[r3c6]<>3

Now you've seen one that does three eliminations in a cell.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Sat Sep 19, 2009 10:22 pm    Post subject: Reply with quote
As an alternative to the loops and long chains, you might like to note that that 13 UR creates a 46 "pseudo-bivalue" that forms a a 146 "XY-Wing" with r8c28. The <4> pincers are at r6c7 and r8c8.

Or, 13UR[(4)r6c7=(6)r5c2] - (6=1)r8c2 - (1=4)r8c8; r6c8|r789c7<>4

After this there is a Finned X-Wing on 1 and a 268 XY-Wing.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Sep 20, 2009 6:37 pm    Post subject: Reply with quote
Asellus wrote:
As an alternative to the loops and long chains, you might like to note that that 13 UR creates a 46 "pseudo-bivalue" that forms a a 146 "XY-Wing" with r8c28. The <4> pincers are at r6c7 and r8c8.

Or, 13UR[(4)r6c7=(6)r5c2] - (6=1)r8c2 - (1=4)r8c8; r6c8|r789c7<>4

After this there is a Finned X-Wing on 1 and a 268 XY-Wing.

Asellus,

Very impressive!
Keith
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