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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Mon Jul 16, 2012 5:25 am Post subject: Sudoku Assistenten 31 October 2007 |
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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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Play/Print online |
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SudoQ
Joined: 02 Aug 2011
Posts: 127
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| Posted: Mon Jul 16, 2012 12:04 pm Post subject: Re: Sudoku Assistenten 31 October 2007 |
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| arkietech wrote: | X-Wing_XYZ-Wing_Forcing Chain
or do it in one advanced step
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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: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Jul 16, 2012 12:55 pm Post subject: Re: Sudoku Assistenten 31 October 2007 |
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| SudoQ wrote: | | arkietech wrote: | X-Wing_XYZ-Wing_Forcing Chain
or do it in one advanced step
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Is there a definition of an "advanced step"?
To me it looks like one additional link over shortest possible path.
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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: 2468
Location: Northern California Foothills
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| Posted: Mon Jul 16, 2012 2:51 pm Post subject: |
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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 |
*--------------------------------------------------------------------*
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(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: 494
Location: Charleroi, Belgium
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| Posted: Mon Jul 16, 2012 3:11 pm Post subject: |
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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
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| Posted: Mon Jul 16, 2012 4:13 pm Post subject: Re: Sudoku Assistenten 31 October 2007 |
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| 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: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Jul 16, 2012 6:07 pm Post subject: |
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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
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| Posted: Mon Jul 16, 2012 6:50 pm Post subject: |
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| arkietech wrote: | How about:
| Code: | | (8=67)r3c46-(7=589)r378c9-(9=8)r8c1 => -8r3c1; stte |
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In my opinion this solution is more complex than JC Van Hay's, as it uses more cells.
But it's just an opinion  .
/SudoQ |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Jul 16, 2012 7:06 pm Post subject: |
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| SudoQ wrote: | | arkietech wrote: | How about:
| Code: | | (8=67)r3c46-(7=589)r378c9-(9=8)r8c1 => -8r3c1; stte |
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In my opinion this solution is more complex than JC Van Hay's, as it uses more cells.
But it's just an opinion . |
I count 6 cells in mine and 7 in JC's  am I missing something? |
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SudoQ
Joined: 02 Aug 2011
Posts: 127
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| Posted: Mon Jul 16, 2012 9:35 pm Post subject: |
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| arkietech wrote: | | I count 6 cells in mine and 7 in JC's 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
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| Posted: Mon Jul 16, 2012 10:39 pm Post subject: |
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| 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: 3854
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| Posted: Mon Jul 16, 2012 11:03 pm Post subject: |
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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
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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
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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
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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: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jul 17, 2012 1:08 am Post subject: |
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| 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 |
+--------------+----------------+-----------------+
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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: 398
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| Posted: Tue Jul 17, 2012 8:39 pm Post subject: |
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| 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
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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: 3854
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| Posted: Tue Jul 17, 2012 11:31 pm Post subject: |
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| 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
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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: 398
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| Posted: Wed Jul 18, 2012 10:06 am Post subject: |
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| 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
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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
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(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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