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Sudoku Assistenten 31 October 2007

 
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arkietech



Joined: 31 Jul 2008
Posts: 1729
Location: Northwest Arkansas USA

PostPosted: Mon Jul 16, 2012 5:25 am    Post subject: Sudoku Assistenten 31 October 2007 Reply with quote

X-Wing_XYZ-Wing_Forcing Chain
or do it in one advanced step
Code:

 *-----------*
 |...|5.4|...|
 |..6|...|1..|
 |.1.|.9.|.3.|
 |---+---+---|
 |2..|...|..4|
 |...|.3.|...|
 |5..|...|..2|
 |---+---+---|
 |.3.|.7.|.1.|
 |..7|...|6..|
 |...|8.2|...|
 *-----------*
 

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SudoQ



Joined: 02 Aug 2011
Posts: 127

PostPosted: Mon Jul 16, 2012 12:04 pm    Post subject: Re: Sudoku Assistenten 31 October 2007 Reply with quote

arkietech wrote:
X-Wing_XYZ-Wing_Forcing Chain
or do it in one advanced step

Is there a definition of an "advanced step"?
To me it looks like one additional link over shortest possible path.

/SudoQ
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arkietech



Joined: 31 Jul 2008
Posts: 1729
Location: Northwest Arkansas USA

PostPosted: Mon Jul 16, 2012 12:55 pm    Post subject: Re: Sudoku Assistenten 31 October 2007 Reply with quote

SudoQ wrote:
arkietech wrote:
X-Wing_XYZ-Wing_Forcing Chain
or do it in one advanced step

Is there a definition of an "advanced step"?
To me it looks like one additional link over shortest possible path.

I don't know about an "official" definition. To me an advanced step is something other than solving with a locked cell or locked set. The shortest possible could use many advanced steps.
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tlanglet



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

PostPosted: Mon Jul 16, 2012 2:51 pm    Post subject: Reply with quote

Code after basics:
Code:
*--------------------------------------------------------------------*
 | 3      7      89     | 5      1      4      | 89     2      6      |
 | 489    5      6      | 37     2      378    | 1      489    789    |
 | 48     1      2      | 67     9      678    | 458    3      578    |
 |----------------------+----------------------+----------------------|
 | 2      689    13     | 1679   58     15679  | 35789  56789  4      |
 | 7      4689   49     | 2      3      569    | 589    5689   1      |
 | 5      689    13     | 14679  48     1679   | 3789   6789   2      |
 |----------------------+----------------------+----------------------|
 | 6      3      458    | 49     7      59     | 2      1      58     |
 | 89     2      7      | 13     45     13     | 6      4589   589    |
 | 1      49     459    | 8      6      2      | 4579   4579   3      |
 *--------------------------------------------------------------------*

(9=4)r9c2-r9c7=(4-5)r3c7=r3c9-(5=8)r7c9-r7c3=r8c1; r8c1<9>
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JC Van Hay



Joined: 13 Jun 2010
Posts: 372
Location: Charleroi, Belgium

PostPosted: Mon Jul 16, 2012 3:11 pm    Post subject: Reply with quote

After LC and LS, analysis of the puzzle from Column 5 yields : +5r4c5 -> solution while +8r4c5 -> contradiction (no 5 in R3).

Extracting the minimal informations gives the following AIC : (4=8)r3c1-8r8c1=8r7c3-(8=5)r7c9-5r3c9=5r3c7 :=> -4r3c7; stte
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SudoQ



Joined: 02 Aug 2011
Posts: 127

PostPosted: Mon Jul 16, 2012 4:13 pm    Post subject: Re: Sudoku Assistenten 31 October 2007 Reply with quote

arkietech wrote:
The shortest possible could use many advanced steps.

I was probably unclear. I meant the shortest/smallest step.

In this case I think that the shortest possible solution is one as JC Van Hay suggests.
This chain is one link longer than the shortest possible for any step.

/SudoQ
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arkietech



Joined: 31 Jul 2008
Posts: 1729
Location: Northwest Arkansas USA

PostPosted: Mon Jul 16, 2012 6:07 pm    Post subject: Reply with quote

How about:
Code:
 *--------------------------------------------------------------------*
 | 3      7      89     | 5      1      4      | 89     2      6      |
 | 489    5      6      | 37     2      378    | 1      489    789    |
 | 4-8    1      2      |a67     9     a678    | 458    3     b578    |
 |----------------------+----------------------+----------------------|
 | 2      689    13     | 1679   58     15679  | 35789  56789  4      |
 | 7      4689   49     | 2      3      569    | 589    5689   1      |
 | 5      689    13     | 14679  48     1679   | 3789   6789   2      |
 |----------------------+----------------------+----------------------|
 | 6      3      458    | 49     7      59     | 2      1     b58     |
 |c89     2      7      | 13     45     13     | 6      4589  b589    |
 | 1      49     459    | 8      6      2      | 4579   4579   3      |
 *--------------------------------------------------------------------*
(8=67)r3c46-(7=589)r378c9-(9=8)r8c1 => -8r3c1; stte
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SudoQ



Joined: 02 Aug 2011
Posts: 127

PostPosted: Mon Jul 16, 2012 6:50 pm    Post subject: Reply with quote

arkietech wrote:
How about:
Code:
(8=67)r3c46-(7=589)r378c9-(9=8)r8c1 => -8r3c1; stte

In my opinion this solution is more complex than JC Van Hay's, as it uses more cells.
But it's just an opinion Smile.

/SudoQ
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arkietech



Joined: 31 Jul 2008
Posts: 1729
Location: Northwest Arkansas USA

PostPosted: Mon Jul 16, 2012 7:06 pm    Post subject: Reply with quote

SudoQ wrote:
arkietech wrote:
How about:
Code:
(8=67)r3c46-(7=589)r378c9-(9=8)r8c1 => -8r3c1; stte

In my opinion this solution is more complex than JC Van Hay's, as it uses more cells.
But it's just an opinion Smile.

I count 6 cells in mine and 7 in JC's Confused am I missing something?
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SudoQ



Joined: 02 Aug 2011
Posts: 127

PostPosted: Mon Jul 16, 2012 9:35 pm    Post subject: Reply with quote

arkietech wrote:
I count 6 cells in mine and 7 in JC's Confused am I missing something?

I am counting the cells like this:

JC Van Hay's solution uses the following cells:
r3c1, r8c1, r7c3, r7c9, r3c9 = 5.
I do not count r3c7, because this is a result cell.

You are using: r3c4, r3c6, r3c9, r7c9, r8c9, r1c8 = 6.
r3c1 is your result cell.

One can certainly do it differently!
I don't know if there is an established way to do this...

/SudoQ
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Mon Jul 16, 2012 10:39 pm    Post subject: Reply with quote

In general I think of the most efficient solution as the one with the fewest strong inferences.....but even that can be manipulated.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Jul 16, 2012 11:03 pm    Post subject: Reply with quote

Shortest is a subjective term. The chains below are ordered by the number of characters needed.

Code:
 +-----------------------------------------------------------------------+
 |  3      7      89     |  5      1      4      |  89     2      6      |
 |  489    5      6      |  37     2      378    |  1      489    789    |
 |  48     1      2      |  67     9      678    |  458    3      578    |
 |-----------------------+-----------------------+-----------------------|
 |  2      689    13     |  1679   58     15679  |  35789  56789  4      |
 |  7      4689   49     |  2      3      569    |  589    5689   1      |
 |  5      689    13     |  14679  48     1679   |  3789   6789   2      |
 |-----------------------+-----------------------+-----------------------|
 |  6      3      458    |  49     7      59     |  2      1      58     |
 |  89     2      7      |  13     45     13     |  6      4589   589    |
 |  1      49     459    |  8      6      2      |  4579   4579   3      |
 +-----------------------------------------------------------------------+
 # 89 eliminations remain

JC's chain is one of the three shortest AICs not containing an ALS.

Code:
4-SIS, 3-values: (4=8)r3c1 - r8c1 = r7c3 - (8=5)r7c9 - r3c9 = (5)r3c7  =>  r3c7<>4
4-SIS, 3-values: (8=5)r7c9 - r3c9 = (5-4)r3c7 = r9c7 - r9c23 = (4)r7c3  =>  r7c3<>8
4-SIS, 3-values: (5)r3c9 = (5-4)r3c7 = r9c7 - r9c23 = (4-8)r7c3 = (8)r7c9  =>  r7c9<>5; r3c9<>8

When you allow ALS components, then these four AICs might qualify as shortest.

Code:
3-SIS, 3-values: (9)r2c1 = r8c1 - r8c9 = r2c9 - (89=4)r1c7,r2c8  =>  r2c1<>4; r2c8<>9

3-SIS, 4-values: (8)r8c1 = r7c3 - (8=5)r7c9 - (5=678)r3c469  =>  r3c1<>8
3-SIS, 4-values: (5)r3c9 = (5-4)r3c7 = r2c8 - (4=ALS=895)r8c189  =>  r7c9<>5
3-SIS, 4-values: (9)r8c9 = r2c9 - (89=4)r1c7,r2c8 - (4=589)r7c9,r8c89  =>  r9c78<>9

You may notice that the first ALS chain is an extension to the X-Wing that exists for <9>. Also, the last chain needs an LC to complete the puzzle.
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Marty R.



Joined: 12 Feb 2006
Posts: 5175
Location: Rochester, NY, USA

PostPosted: Tue Jul 17, 2012 1:08 am    Post subject: Reply with quote

Code:

+--------------+----------------+-----------------+
| 3   7    89  | 5     1  4     | 89    2     6   |
| 489 5    6   | 37    2  378   | 1     489   789 |
| 48  1    2   | 67    9  678   | 458   3     578 |
+--------------+----------------+-----------------+
| 2   689  13  | 1679  58 15679 | 35789 56789 4   |
| 7   4689 49  | 2     3  569   | 589   5689  1   |
| 5   689  13  | 14679 48 1679  | 3789  6789  2   |
+--------------+----------------+-----------------+
| 6   3    458 | 49    7  59    | 2     1     58  |
| 89  2    7   | 13    45 13    | 6     4589  589 |
| 1   49   459 | 8     6  2     | 4579  4579  3   |
+--------------+----------------+-----------------+

Play this puzzle online at the Daily Sudoku site

I don't do well at finding one-step chains, among other things. The solution is simple, albeit two steps.

X-Wing (9), c19; r2c8<>9
W-Wing (48), SL 8 in r1; r3c7<>4. This exposes a puzzle-ending 589 triple in c7.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jul 17, 2012 8:39 pm    Post subject: Reply with quote

daj95376 wrote:
Shortest is a subjective term.
...
When you allow ALS components, then these four AICs might qualify as shortest.

Code:
3-SIS, 3-values: (9)r2c1 = r8c1 - r8c9 = r2c9 - (89=4)r1c7,r2c8  =>  r2c1<>4; r2c8<>9

3-SIS, 4-values: (8)r8c1 = r7c3 - (8=5)r7c9 - (5=678)r3c469  =>  r3c1<>8
3-SIS, 4-values: (5)r3c9 = (5-4)r3c7 = r2c8 - (4=ALS=895)r8c189  =>  r7c9<>5
3-SIS, 4-values: (9)r8c9 = r2c9 - (89=4)r1c7,r2c8 - (4=589)r7c9,r8c89  =>  r9c78<>9

It's hardly fair for a chain with a 2-cell ALS to be considered the same length as a chain with a 3-cell ALS.

Several years ago Steve Kurzhals coined the "native strong inference" term. He may have also coined the "derived strong inference" term. The single derived strong inference of an ALS may be due to 2, or 3, or 4, ... or up to 8 native strong inferences of the cells that comprise the ALS. Therefore, while the derived SIS counts for the above are the counts shown, the native SIS counts are 4, 5, 5, and 6, respectively.

This POV has a couple of advantages: 1) Whether or not someone writes an xy-chain as an als-chain, the intrinsic length remains the same, and 2) the lengths match the truth counts in XSUDO.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Jul 17, 2012 11:31 pm    Post subject: Reply with quote

ronk wrote:
It's hardly fair for a chain with a 2-cell ALS to be considered the same length as a chain with a 3-cell ALS.

Several years ago Steve Kurzhals coined the "native strong inference" term. He may have also coined the "derived strong inference" term. The single derived strong inference of an ALS may be due to 2, or 3, or 4, ... or up to 8 native strong inferences of the cells that comprise the ALS. Therefore, while the derived SIS counts for the above are the counts shown, the native SIS counts are 4, 5, 5, and 6, respectively.

This POV has a couple of advantages: 1) Whether or not someone writes an xy-chain as an als-chain, the intrinsic length remains the same, and 2) the lengths match the truth counts in XSUDO.

That shows how you and I perceive things differently.

For instance, I consider an ALS to be a network that's expressed as a strong inference so that it can be placed in an AIC. Consider:

Code:
(9)r2c9 - (89=4)r1c7,r2c8

is in reality ...

(9)r2c9 - (9=8)r1c7 - (8)r2c8 \
        -             (9)r2c8  \
                                 - (89=4)r2c8

I only count the strong inference shown in the AIC because counting inferences in a network doesn't make sense to me.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Wed Jul 18, 2012 10:06 am    Post subject: Reply with quote

daj95376 wrote:
I consider an ALS to be a network that's expressed as a strong inference so that it can be placed in an AIC. Consider:

Code:
(9)r2c9 - (89=4)r1c7,r2c8

is in reality ...

(9)r2c9 - (9=8)r1c7 - (8)r2c8 \
        -             (9)r2c8  \
                                 - (89=4)r2c8

I only count the strong inference shown in the AIC because counting inferences in a network doesn't make sense to me.

It makes much more sense when shown as:
Code:
          |<------------ ALS -------->|
                 n-SIS      n-SIS
(9)r2c9 ---+-- (9=8)r1c7 - (8)r2c8     
            \                 ||
              ------------ (9)r2c8
                              ||
                           (4)r2c8 ----- (4)r2c1
"n-SIS" <--> native SIS

As you can see, the number of native SIS is simply the number of cells in the ALS. Very easy to count the cells IMO, without any need to sketch the inner workings.
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