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No Rating: Puzzle CD_2

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Sep 25, 2008 6:25 pm    Post subject: No Rating: Puzzle CD_2 Reply with quote

This puzzle gets interesting near the end when an XY-Chain or other chain will crack it. However, there's an annoying (59) UR in [r12c67] that will crack it as well -- provided you find the right elimination. Maybe you will find something that I've missed. Enjoy.

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



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Thu Sep 25, 2008 8:59 pm    Post subject: Reply with quote

Well, you stumped me this time. After basics, a finned x-wing and a xy-wing, I was here.
Code:

*--------------------------------------------------*
 | 6    8    2    | 3    7    59   | 159  145  145  |
 | 7    3    1    | 2    49   459  | 59   8    6    |
 | 9    5    4    | 8    16   16   | 7    3    2    |
 |----------------+----------------+----------------|
 | 2    16   7    | 5    8    46   | 3    9    14   |
 | 4    16   8    | 9    2    3    | 15   156  7    |
 | 5    9    3    | 1    46   7    | 2    46   8    |
 |----------------+----------------+----------------|
 | 3    7    6    | 4    19   2    | 8    15   159  |
 | 8    4    5    | 7    3    19   | 6    2    19   |
 | 1    2    9    | 6    5    8    | 4    7    3    |
 *--------------------------------------------------*


I found the UR and make two eliminations but that did not crack the puzzle; I still needed a chain. My deletions were:
Quote:
r1c7<>5 & r2c6<>9 based on the strong links on both <5> & <9>.
It seems that I did NOT find the right elimination.

Ted
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Asellus



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

PostPosted: Thu Sep 25, 2008 10:58 pm    Post subject: Reply with quote

It still involves a "dreaded chain," but the diagonal trivalues of the 59 UR create a "pseudo" 14 bivalue that can be used in a short XY Chain
[51] - UR[14] - [49] - [91] - [15]
to remove <5> from r5c8 and solve the puzzle.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Sep 25, 2008 11:43 pm    Post subject: Reply with quote

Asellus wrote:
It still involves a "dreaded chain," ...

Unfortunately, yes! That's because chains are actually allowed as part of Unique Rectangle solutions.

In the Uniqueness Test page of Sudopedia is: a list of tests Type 1-6, a Hidden Unique Rectangle, and a section titled Unique Rectangle and Implications. The first entry in this section is:

Quote:
Unique Rectangle and Forcing Chains

A Unique Rectangle with extra candidates means that at least one of the extra candidates must be placed in its cell. This means that each of the extra candidates can be the starting point of a Forcing Chain.

Code:
 +-----------------------------------------------------+
 |  6    8    2    |  3    7    59   |  159  145  145  |
 |  7    3    1    |  2    49   459  |  59   8    6    |
 |  9    5    4    |  8    16   16   |  7    3    2    |
 |-----------------+-----------------+-----------------|
 |  2    16   7    |  5    8    46   |  3    9    14   |
 |  4    16   8    |  9    2    3    |  15   156  7    |
 |  5    9    3    |  1    46   7    |  2    46   8    |
 |-----------------+-----------------+-----------------|
 |  3    7    6    |  4    19   2    |  8    15   159  |
 |  8    4    5    |  7    3    19   |  6    2    19   |
 |  1    2    9    |  6    5    8    |  4    7    3    |
 +-----------------------------------------------------+
 # 28 eliminations remain

For the (59) UR in [r12c67], either [r1c7]=1 or [r2c6]=4.

Code:
[r1c7]=1, [r1c6]=9,                                          [r2c5]=4 => [r2c6]<>4
[r2c6]=4, [r2c7]=5, [r5c7]<>5, [r5c8]=5, [r7c8]=1, [r7c5]=9, [r2c5]=4 => [r2c6]<>4
__________________________________________________________________________________

Not all UR solutions are fun! That's why I said "annoying".
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Asellus



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

PostPosted: Fri Sep 26, 2008 12:52 am    Post subject: Reply with quote

Quote:
That's because chains are actually allowed as part of Unique Rectangle solutions.

"Actually allowed"? Why? Because Sudopedia says so?!!! Who are Sudopedia? The Sudoku police, or something? Perhaps this statement was meant as a sly joke?

Either one embraces chains (as I do) and has no complaint about their use, or one decides that chains are undesirable and eschews their use.

Sudopedia could just as easily (and for all I know does) point out that the pincers of some wing or other could be used as the starting point of a Forcing Chain. So, if it did, then that would make it okay? I don't get it.

By the way, I am not in favor of Forcing Chains understood in the large sense of that term (even if Sudopedia does make them "okay".) It is Alternate Implication Chains that I have no problem with. Some forcing chains are nothing but trial and error.
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Fri Sep 26, 2008 2:05 am    Post subject: Reply with quote

Quote:
Because Sudopedia says so?!!! Who are Sudopedia? The Sudoku police, or something?

I think Danny is saying something that has come up here before, which is that UR's can serve as the start points of bifurcations to seek chains.

Maybe I would change the phrase "Sudopedia allows" [gives permission] to "Sudopedia allows for" [includes].

Sudopedia is supposed to be something anyone can author. Maybe so, but I have had zero success in posting discussions of articles before revising them. (Meaning, I have had no response to any of my discussion posts.)

Maybe, I will just start editing and revising the Sudopedia articles.

Keith
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nataraj



Joined: 03 Aug 2007
Posts: 1029
Location: Vienna, Austria

PostPosted: Fri Sep 26, 2008 6:07 am    Post subject: Reply with quote

No dreadchain needed, I think.

My solution path, after basics:
- multi-coloring(6) (remove 6 from cells r1c6,r3c2,r5c1,r6c1)
(- noticing, but not using URs)
- next is xy-wing(4) r4c9=r5c1; r5c8<>4
- after cleanup, (half- generalized whatever) m-wing here

Code:

+--------------------------+--------------------------+--------------------------+
| 6       8       2        | 3       7       59*      | 159     145     145#     |
| 7       3       1        | 2       4-9     459      | 59      8       6        |
| 9       5       4        | 8       16      16       | 7       3       2        |
+--------------------------+--------------------------+--------------------------+
| 2       16      7        | 5       8       46       | 3       9       14       |
| 4       16      8        | 9       2       3        | 15      156     7        |
| 5       9       3        | 1       46      7        | 2       46      8        |
+--------------------------+--------------------------+--------------------------+
| 3       7       6        | 4       19*     2        | 8       15      159#     |
| 8       4       5        | 7       3       1-9      | 6       2       19       |
| 1       2       9        | 6       5       8        | 4       7       3        |
+--------------------------+--------------------------+--------------------------+


(9) r1c6=r7c5 [via (5)r1c9=r7c9];r8c6,r2c5<>9
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Asellus



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

PostPosted: Fri Sep 26, 2008 7:48 am    Post subject: Reply with quote

keith wrote:
I think Danny is saying something that has come up here before, which is that UR's can serve as the start points of bifurcations to seek chains.

That isn't the point. As a proponent of chains, I would never argue against the use of strong inferences (not "bifurcations") induced by URs to form AICs! What Danny said is:
Quote:
an XY-Chain or other chain will crack it. However, there's an annoying (59) UR in [r12c67] that will crack it as well

This implies (though does not say explicitly) that the 59 UR provides an alternative to the use of a chain to find a solution. Ted understood this likewise, since he said:
Quote:
I found the UR and make two eliminations but that did not crack the puzzle; I still needed a chain.

Poor Ted, like me, is suffering under the impression that a chain is a chain is a chain. But, Danny informs us that if Sudopedia says that a UR can be used to form a chain, then a chain formed by a UR somehow isn't a chain and Ted and I (and perhaps others) shouldn't object to his use of a "non-chain" chain to solve a puzzle that he seemed to imply could be solved without using a chain if one was clever enough with the UR.

I am not objecting to the use of a chain based upon a UR. I am objecting to suggesting that there is a non-chain solution based on a UR and then revealing that that UR solution involves a "chain" that, somehow, isn't a chain because of a Sudopedia statement. That is Sophistry and unfair to folks who were trying to find that non-chain use of the UR.

That is my point.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Fri Sep 26, 2008 11:40 am    Post subject: Reply with quote

Didn't like it. I got to the same position as Ted using an ER on <6> and an xy-wing <145>. After that it seems the solutions are too abstruse and esoteric. Don't like those!!
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Sep 26, 2008 12:00 pm    Post subject: Reply with quote

I am very sorry for my poor intro to this puzzle and the (incorrect) implication that chains weren't involved Exclamation

I was fixated on the fact that this UR existed and presented two non-productive eliminations as well as a horrific alternative elimination.

My only defense is that I was traumatized by the response I received when I asked:

I wrote:
What is the scope of the cells that can be used to resolve a bivalue deadly pattern?


keith wrote:
You can use any chain to explore the implications.

in this thread:

http://www.sudoku.com/boards/viewtopic.php?p=47514#47514
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Sep 26, 2008 1:37 pm    Post subject: Reply with quote

nataraj wrote:


(9) r1c6=r7c5 [via (5)r1c9=r7c9];r8c6,r2c5<>9


Once again Nataraj, you easily win the prize with your solution Exclamation

Ted
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