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A Challenge

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Tue Aug 07, 2007 2:15 pm    Post subject: A Challenge Reply with quote

Today's puzzle was not challenge enough, so . . .

Code:

+-------------------+----------------+-----------------+
| 259   1259  7     | 2349 24   8    | 345  134   6    |
| 569   569   4     | 39   67   1    | 3578 2     58   |
| 8     3     126   | 24   2467 5    | 47   9     14   |
+-------------------+----------------+-----------------+
| 236   126   1236  | 7    5    24   | 9    13468 1248 |
| 4     12569 12569 | 8    12   3    | 25   16    7    |
| 2357  1257  8     | 124  9    6    | 2345 134   1245 |
+-------------------+----------------+-----------------+
| 679   4     69    | 12   128  79   | 28   5     3    |
| 23579 8     2359  | 6    234  2479 | 1    47    249  |
| 1     279   239   | 5    2348 2479 | 6    478   2489 |
+-------------------+----------------+-----------------+

Play this puzzle online at the Daily Sudoku site

Thanks for any help,

Earl
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Tue Aug 07, 2007 4:50 pm    Post subject: Reply with quote

There's a naked pair in box 2, not that it gets one very far. After that there are W-wings, a finned X-wing and coloring that reduce the PM's somewhat.
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Asellus



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

PostPosted: Tue Aug 07, 2007 7:00 pm    Post subject: Reply with quote

Very interesting puzzle. For me, the key lay in the <2>s. Apart from a Finned X-Wing at the start, all the other steps I used involved eliminating <2>s. Two of those steps were very interesting Color Wraps.

I'll give others a chance to ruminate before posting my steps.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Tue Aug 07, 2007 11:28 pm    Post subject: Reply with quote

Quote:
Two of those steps were very interesting Color Wraps.


Asellus,

Could you provide a definition of "color wrap" in a way that a 10-year-old could understand it? Wink
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Wed Aug 08, 2007 12:35 am    Post subject: Reply with quote

Quote:
Could you provide a definition of "color wrap"...


I'd be interested to hear from where the term comes.
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Wed Aug 08, 2007 12:47 am    Post subject: A Challenge Reply with quote

I used your tips to find a w-wing (pincers R1C5, R4C6) and the finned x-wing (eliminates 1 from R4C8) to arrived here. There is only one strong pair of 2's. I can't see how to eliminate any. A hint?

Earl

Code:

+-----------------+----------------+---------------+
| 259   1259 7    | 2349 24   8    | 345  134 6    |
| 569   569  4    | 39   67   1    | 3578 2   58   |
| 8     3    126  | 24   67   5    | 47   9   14   |
+-----------------+----------------+---------------+
| 236   126  1236 | 7    5    24   | 9    348 1248 |
| 4     259  259  | 8    1    3    | 25   6   7    |
| 2357  1257 8    | 24   9    6    | 2345 134 1245 |
+-----------------+----------------+---------------+
| 679   4    69   | 1    28   79   | 28   5   3    |
| 23579 8    2359 | 6    234  2479 | 1    47  249  |
| 1     279  239  | 5    2348 2479 | 6    478 2489 |
+-----------------+----------------+---------------+

Play this puzzle online at the Daily Sudoku site
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Asellus



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

PostPosted: Wed Aug 08, 2007 12:59 am    Post subject: Reply with quote

Oops! I mistakenly wrote "Color Wrap" in my prior post. I meant to write "Color Wing"!

I also have a bad habit of saying Color Wrap when I mean simple Coloring (also known as a Color Trap) on a single digit. In simple Coloring, the opposite polarities of interconnected strong links for a digit are noted and any candidates which can "see" instances of opposite polarity are eliminated.

(I used Coloring in the solution, also. I try to avoid the term Color Wrap.)

A Color Wrap is a special instance of simple Coloring in which a polarity contradiction is discovered, i.e. two cells of the same polarity (color) are discovered in a single house, which is not possible. In these cases, all instances of the conflicting polarity can be eliminated and the other polarity values placed. These don't occur very often.

A Color Wing is a bit more complicated. I believe some people refer to it as two-strand coloring, or something like that. One selects a "Bridge," which is a weak link on the digit, and then two separate strong link Coloring strands are formed from each end of the Bridge with the two bridge cells having the same color. Eliminations occur when a cell can "see" the polarity (or color) opposite that of the bridge from each of the two coloring strands.

Often, Skyscrapers, 2-String Kites and some other named techniques are special instances of Color Wings. (Some of them can also be instances of simple Coloring.)

I plan to post my solution later tonight, which will show how the Color Wing works.

Here is a link to the explanations at Ruud's Sudocue site:

http://www.sudocue.net/guide.php#ConnectedPairs

The explanation is a bit lengthy, but eventually gets around to all of these techniques.
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Asellus



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

PostPosted: Wed Aug 08, 2007 1:02 am    Post subject: Reply with quote

Earl,

I didn't use the <1> Finned X-Wing. There is another one that will help you. But you need to do that naked 24 pair simplification in Box 2 in order to see it.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed Aug 08, 2007 3:54 am    Post subject: Reply with quote

Thanks. The Color Wrap with two cells in a house with the same polarity has been discussed here on one occasion that I recall, but the poster (Tracy, I think) didn't have a separate name for it.

If I correctly understand the Color Wing, that is what is commonly referred to as multi-coloring.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Wed Aug 08, 2007 12:32 pm    Post subject: A Hint Reply with quote

Earl,

This one is a tough one.
You can use the strong links on <2> in Box 2 for eliminating several <2>'s in Box 4


Johan
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Asellus



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

PostPosted: Wed Aug 08, 2007 8:17 pm    Post subject: Reply with quote

Marty,

I find the term "multi-coloring" ambiguous: Medusa Coloring is also known as "multi-dimensional coloring" since it colors on multiple digits.

Even the terms "two-strand" or "multi-strand" coloring are ambiguous since there also exist Medusa Wings, which are two-stranded multi-dimensional coloring! (Phew!)

I prefer to follow Ruud's nomenclature and use Color Wing when there is a bridge and two-strands with single-digit coloring and Medusa Wing for the analogous multi-digit coloring.

The Wing name makes sense to me if the bridge is considered as the pivot. All "Wing" named technigues involve pincer branches (wings) from a pivot of some sort.
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Asellus



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

PostPosted: Wed Aug 08, 2007 9:03 pm    Post subject: Reply with quote

Here is my solution to Earl's puzzle. First, however, I discovered a flaw in one of my "I'm only using <2>s" steps (which worked, as it happened, accidentally), so had to revise the final parts of the solution and resort to some other digits. Still, the <2>s are central. It was a tough nut to crack.

After the 24 Naked Pair (Box 2), the first two steps have already been mentioned:

1: the Finned X-Wing in C47 (eliminates <4> in R3C9)

2: the 24 W-Wing in C56 (eliminates <2> in R5C5). At this point, all of the <1>s are fixed and simplifications expose...

3: XYZ-Wing: Pivot R6C9, eliminates <2> in R6C7

4 and 5: A couple of related Color Wings
Code:
+---------------------+----------------+-----------------+
| 2G59  1      7      | 39  B2R4  8    | 345  34    6    |
| 569   569    4      | 39   67   1    | 3578 2     58   |
| 8     3      26     | 24   67   5    | 47   9     1    |
+---------------------+----------------+-----------------+
|-236   26     1      | 7    5    24   | 9    348   248  |
| 4     2(g)59 2(g)59 | 8    1    3    | 2r5  6     7    |
|-2357  257    8      | 24   9    6    | 345  1     245  |
+---------------------+----------------+-----------------+
| 679   4      69     | 1   B2r8  79   | 2g8  5     3    |
| 2579  8      2359   | 6    234  2479 | 1    47    249  |
| 1     279    239    | 5    2348 2479 | 6    478   2489 |
+---------------------+----------------+-----------------+
Color Wing:  Bridge, B, in C5
             RG branch to R1C1
             rg branch to Box4R5 via C7
             Eliminations in Box4C1

+---------------------+-----------------+-----------------+
| 259   1      7      | 39  B2R4   8    | 345  34    6    |
| 569   569    4      | 39   67    1    | 3578 2     58   |
| 8     3      26     | 2G4  67    5    | 47   9     1    |
+---------------------+-----------------+-----------------+
| 36   -26     1      | 7    5     2G4  | 9    348   248  |
| 4     2(g)59 2(g)59 | 8    1     3    | 2r5  6     7    |
| 357   257    8      | 2R4  9     6    | 345  1     245  |
+---------------------+-----------------+-----------------+
| 679   4      69     | 1   B2r8   79   | 2g8  5     3    |
| 2579  8      2359   | 6    234   2479 | 1    47    249  |
| 1     2g79   239    | 5    2348  2479 | 6    478   2489 |
+---------------------+-----------------+-----------------+
Color Wing:  Bridge, B, in C5
             RG branch to R4C6 via C4
             rg branch to Box4R5 via C7
             Elimination in R4C2

These are the "unusual" Color Wings due to the use of a "Box-Row" end of a strong link for the eliminations. I have indicated this by using "(g)" since this polarity is strictly shared by the two cells. Elimination candidates must be able to "see" both "(g)" cells together with a "G" cell. This limits eliminations to Box 4.

6: Simple Coloring on 2 provides more eliminations in sequence:
Code:
+-----------------+-----------------+----------------+
| 2g5   1    7    | 9    2r4   8    | 45   3    6    |
| 569   59   4    | 3    67    1    | 578  2    58   |
| 8     3    2r6  | 2g4  67    5    | 47   9    1    |
+-----------------+-----------------+----------------+
| 3     6    1    | 7    5     2g4  | 9    48   2r48 |
| 4     259  259  | 8    1     3    | 25   6    7    |
| 57    257  8    | 2r4  9     6    | 3    1    245  |
+-----------------+-----------------+----------------+
| 679   4    69   | 1    28    79   | 28   5    3    |
| 2r579 8    2359 | 6    234  -2479 | 1    47   249  |
| 1     279  239  | 5    2348  2479 | 6    478  2489 |
+-----------------+-----------------+----------------+
+-----------------+-----------------+----------------+
| 2g5   1    7    | 9    2r4   8    | 45   3    6    |
| 569   59   4    | 3    67    1    | 578  2    58   |
| 8     3    2r6  | 2g4  67    5    | 47   9    1    |
+-----------------+-----------------+----------------+
| 3     6    1    | 7    5     2g4  | 9    48   2r48 |
| 4     259  259  | 8    1     3    | 2g5  6    7    |
| 57    257  8    | 2r4  9     6    | 3    1   -245  |
+-----------------+-----------------+----------------+
| 679   4    69   | 1    2g8   79   | 2r8  5    3    |
| 2r579 8    2359 | 6   -234   479  | 1    47   249  |
| 1     279  239  | 5   -2348  2r479| 6    478  2489 |
+-----------------+-----------------+----------------+
+-----------------+-----------------+----------------+
| 2g5   1    7    | 9    2r4   8    | 45   3    6    |
| 569   59   4    | 3    67    1    | 578  2    58   |
| 8     3    2r6  | 2g4  67    5    | 47   9    1    |
+-----------------+-----------------+----------------+
| 3     6    1    | 7    5     2g4  | 9    48   2r48 |
| 4     259 -259  | 8    1     3    | 2g5  6    7    |
| 57    2g57 8    | 2r4  9     6    | 3    1    45   |
+-----------------+-----------------+----------------+
| 679   4    69   | 1    2g8   79   | 2r8  5    3    |
| 2r579 8    2359 | 6    34    479  | 1    47   249  |
| 1    -279  239  | 5    348   2r479| 6    478  2489 |
+-----------------+-----------------+----------------+

Now I had to leave the <2>s and turn elsewhere...

7: Color Wing (or 2-String Kite) on 5: Bridge in Box 3; Pincers R1C1 & R6C9; eliminates <5> in R6C1

This fixes some <7>s, then there is a 69 Naked Pair in Box 7 followed by a 25 Naked Pair in C1

8: XY Chain: Pincers R1C7 & (via C5/R7) R5C7; eliminates <5> in R2C7

9: Coloring 5 eliminates <5> in R5C2

10: XY Chain: Pincers R8C5 & (via R1/C1) R9C3; eliminates <3> in R9C5

There is now a 48 Naked Pair in R9. (We are down to a BUG+3!)

11: Color Wing on 4:
Code:
+--------------+--------------+---------------+
| 25  1    7   | 9   24G  8   | 45   3   6    |
| 69  59   4   | 3   67   1   | 78   2   58   |
| 8   3    26  | 24R 67   5   | 47   9   1    |
+--------------+--------------+---------------+
| 3   6    1   | 7   5   B24R | 9   B4r8 248  |
| 4   29   59  | 8   1    3   | 25   6   7    |
| 7   25   8   | 24G 9    6   | 3    1   45   |
+--------------+--------------+---------------+
| 69  4    69  | 1   28   7   | 28   5   3    |
| 25  8    235 | 6   34   49  | 1    7   249  |
| 1   7    23  | 5  -48   29  | 6    4g8 29   |
+--------------+--------------+---------------+

Bridge R4C68; Pincers R1C5 & R9C8; eliminates <4> in R9C5... and the puzzle succumbs at last!
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Wed Aug 08, 2007 9:46 pm    Post subject: Reply with quote

Asellus wrote:
First, however, I discovered a flaw in one of my "I'm only using <2>s" ...


This may be the understatement of the year. Very Happy

As for the color wings that you used with the <2>'s, they are the same as multi-coloring, but the way you applied it was excellent, in that your exclusion came from cells that were not, strictly speaking, conjugates.

The thing I found frustrating, yet oddly enjoyable, was that every time I figured out an exclusion and expected the puzzle to break, it didn't.
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Asellus



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

PostPosted: Wed Aug 08, 2007 11:54 pm    Post subject: Reply with quote

Tracy wrote:
your exclusion came from cells that were not, strictly speaking, conjugates


Yes, the conjugate is the entire row segment within the box, not the individual cells. It can be very useful to consider such row segments or column segments as conjugates.

It occurs to me that there are some important things to note about using this approach. First, a warning...

In the Color Wing in the solution posted above, there was no <2> in R5C1. However, there could have been. It is important to note that, had there been, that <2> would not have been a candidate for elimination:
Code:
+-------------+
|  G   .   .  |
|  .   .   .  |
|  .   .   .  |
+-------------+
|  *   .   .  |
|@(g) (g) (g) |
|  *   .   .  |
+-------------+

The candidate at @, which is part of the conjugate row segment, cannot be eliminated by the G. Only the * cells are available for eliminations.

A strong link can exist between two such segments (row or column) within a box, as illustrated below:
Code:
+--------+---------+-------------+
|  . . . | Br . BR |  .   .   .  |
|  . . . |  . .  . |  .   .   .  |
|  . . . |  . .  . |  .   .   .  |
+--------+---------+-------------+
|  . . . |  . .  . |  .   .   .  |
|  . * * |  . .  G |  .   .   .  |
|  g . . |  . .  . |  .   .   .  |
+--------+---------+-------------+
|  . . . |  g .  . | (r) (r) (r) |
|  . . . |  . .  . |  X   X   X  |
|  r . . |  . .  . | (g) (g) (g) |
+--------+---------+-------------+

The candidate cannot be present in the cells marked X (or else there is no strong link).

With an important caveat, an ER-type box can be used similarly. The strong link is then between a row segment and a column segment within the same box. The caveat is that the candidate digit cannot be present in the cell at the intersection IF you are using this link to extend the chain:
Code:
+----------+-------------+          +---------+------------+
| Br . BR |  .    .   .  |          | Br . BR |  .  .   .  |
|  . .  . |  .    .   .  |          |  . .  . |  .  .   .  |
|  . .  . |  .    .   .  |          |  . .  . |  r  .   g  |
+---------+--------------+          +---------+------------+
|  . .  . |  .    .   .  |          |  . .  . |  .  .   .  |
|  . .  G |  *    .   .  |    or    |  . .  G |  .  .   *  |
|  . .  . |  .    .   .  |          |  . .  . |  .  .   .  |
+---------+--------------+          +---------+------------+
|  g .  . | (rg) (r) (r) |          |  g .  . |  X (r) (r) |
|  . .  . | (g)   .   .  |          |  . .  . | (g) .   .  |
|  . .  . | (g)   .   .  |          |  . .  . | (g) .   .  |
+---------+--------------+          +---------+------------+

On the left, the lower-right box performs the elimination as a standard ER (* can "see" G directly and g via the ER) and the candidate is allowed at the intersection. On the right, the row-column link extends the r-g chain and the candidate may not occur at the intersection, X.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Aug 09, 2007 3:35 pm    Post subject: Reply with quote

------- the Cheshire Cat way
Quote:

...Alice speaks to Cheshire Cat...

`Would you tell me, please, which way I ought to go from
here?'

`That depends a good deal on where you want to get to,' said the
Cat.

`I don't much care where--' said Alice.

`Then it doesn't matter which way you go,' said the Cat.

`--so long as I get somewhere,' Alice added as an explanation.

`Oh, you're sure to do that,' said the Cat, `if you only walk
long enough.'


Color wings tend to hurt my eyes and brain. I can't seem to find the buggers...
Main reason of course is that I don't know what pattern to look for, exactly.

So when I finally arrived at THE position (I think it is the same Asellus posted 9:03pm last night)

... there were no more patterns I could find. So... in desperation I started a forcing chain approach which solved the puzzle in a very short time.

Basically "coloring" is an euphemism for bifurcation and forcing chains is it not?
Problem mostly is to choose a good starting point.

Starting with the very prominent feature of this puzzle: 4 strongly linked cells
r1c5, r3c4, r4c6 and r6c4. On the left: choice A, on the right - choice B

Code:

+--------------------+---------------------+--------------------+
| 259   1     7      |  39  4(24)2  8      | 345   34    6      |
| 569   569   4      |  39    67    1      | 3578  2     58     |
| 8     3     26     |2(24)4  67    5      | 47    9     1      |
+--------------------+---------------------+--------------------+
| 236   26    1      |  7     5  2(24)4    | 9     348   248    |
| 4     259   259    |  8     1     3      | 25    6     7      |
| 37    257   8      |4(24)2  9     6      | 345   1     245    |
+--------------------+---------------------+--------------------+
| 679   4     69     |  1     28    79     | 28    5     3      |
| 2579  8     2359   |  6     234   2479   | 1     47    249    |
| 1     279   239    |  5     2348  2479   | 6     478   2489   |
+--------------------+---------------------+--------------------+

So far, so good.
Continuing on the left side, a few steps down the road
in row 1: 4 in c2 => 3 in c8 => 5 in c7.
At this point we could go on a few more steps but notice that r6c7 will have 3 on the left side (marked x)
Code:

+--------------------+---------------------+--------------------+
| 259   1     7      |  39  4(24)2  8      |5(345) 3(34) 6      |
| 569   569   4      |  39    67    1      | 3578   2    58     |
| 8     3     26     |2(24)4  67    5      | 47     9    1      |
+--------------------+---------------------+--------------------+
| 236   26    1      |  7     5  2(24)4    | 9     348   248    |
| 4     259   259    |  8     1     3      | 25    6     7      |
| 37    257   8      |4(24)2  9     6      |x345   1     245    |
+--------------------+---------------------+--------------------+
| 679   4     69     |  1     28     79    | 28    5     3      |
| 2579  8     2359   |  6     234   2479   | 1     47    249    |
| 1     279   239    |  5     2348  2479   | 6     478   2489   |
+--------------------+---------------------+--------------------+

Same procedure on the right side.
2 in r1c5 => 8 in r7c5 => 2 in r7c7 => 5 in r5c7.
Again, notice that r6c9 must be 4 (marked y) and thus:

r6c7 must be 3(marked x)
Code:

+--------------------+---------------------+--------------------+
| 259   1     7      |  39  4(24)2  8      |5(345) 3(34) 6      |
| 569   569   4      |  39    67    1      | 3578   2    58     |
| 8     3     26     |2(24)4  67    5      | 47     9    1      |
+--------------------+---------------------+--------------------+
| 236   26    1      |  7     5  2(24)4    | 9     348   248    |
| 4     259   259    |  8     1     3      |(25)5  6     7      |
| 37    257   8      |4(24)2  9     6      |x345x  1     245y   |
+--------------------+---------------------+--------------------+
| 679   4     69     |  1    (28)8  79     |(28)2  5     3      |
| 2579  8     2359   |  6     234   2479   | 1     47    249    |
| 1     279   239    |  5     2348  2479   | 6     478   2489   |
+--------------------+---------------------+--------------------+

Entering 3 as a secured result into r6c7 opens up the puzzle for a while.
After some easy eliminations, another difficult point where nothing seems to give easily. Rather than start another long search ...
... I decide to continue the left/right way (at this stage there are so many cells with very few candidates). I found another 3 cells where left and right branch give the same content:
r9c8=4, r4c8=8, and finally r9c3=3.

From there everything is smooth elimination. After some steps it becomes obvious that cell r8c6=4 which shows that the right branch is wrong (it had "2" there). Fill in all choices from left path and be done.

Very very difficult puzzle.Shocked

In the end, I ask myself (and you, fellow solvers):
- is it really worth the effort to try and find extremely elaborate patterns (which I tried on the Asellus position for a long time!)
- if it is possible to solve even a monster like this one in 5-10 minutes after deciding to go the forced chain way (especially if there are many bi-value cells)

On the other hand, there is a certain lack of satisfaction. Sad

hmmm
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Aug 09, 2007 9:04 pm    Post subject: Reply with quote

nataraj wrote:
Basically "coloring" is an euphemism for bifurcation and forcing chains is it not?


Coloring is a technique that allows one to see the relationship between conjugate cells. No values are assigned, no assumptions are made. It is definitely not a "euphemism for bifurcation".
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Asellus



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

PostPosted: Thu Aug 09, 2007 9:12 pm    Post subject: Reply with quote

nataraj,

I don't believe those Color Wings are really all that elaborate... apart from the little conjugate Box-Row bit in these particular instances. Elsewhere you've posted much the same thing, though limited to "wings" of single strong links. Perhaps it would help make them easier to see by using your "dot diagram" approach:
Code:
 G-----------------R   .     .   .   .
 .   .   .     .   w   .     .   o   .
 .   .   o     o   w   .     .   .   .
            +      w      +
 x   o   .     .   w   o     .   .   o
 .  (g)-(g)------------------r   .   .
 x   o   .     o   w   .     |   .   o
            +      w      +  |
 .   .   .     .   r---------g   .   .
 o   .   o     .   o   o     .   .   o
 .   o   o     .   o   o     .   .   o

Once you find two strong links with a weak link (w) Bridge, you can look for additional strong links that extend the "wings." Then, mind the polarity to find potential eliminations. It's actually a very useful and easy technique. They occur often (and without having to resort to Box-Row things!).

I am not as particular as others about what techniques I find aesthetically, or otherwise, acceptable. But, forcing methods come closest to teetering over the edge into unacceptability. Basing them on a noticeable and potentially promising pattern, as you did, is certainly easiest to defend, especially if the implications reveal themselves in just a few steps, as in your example. Still, as you say, there is something unsatisfying about them.

Since many solvers object to forcing, I only post solutions that do not use them. I similarly avoid posting chains more elaborate than XY Chains unless I can find no other approach and none has been posted.
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Asellus



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

PostPosted: Thu Aug 09, 2007 11:55 pm    Post subject: Reply with quote

As Tracy says, Coloring is not forcing. And, Coloring on a single digit is easy to do and is often useful.

On this board, we rarely see multi-digit Coloring (a.k.a. Medusa Coloring). That might be because it can get very extensive and other, more commonly used options are often possible. However, if one is tempted to resort to forcing, it can be worth trying some Medusa Coloring first. It isn't always extensive or messy.

For instance, it can provide an elimination in the R6C7 cell involved in nataraj's forcing. Start by noting that there are several bivalue cells involving 2, 5 and 8. So, pick one and start coloring. The bivalue strong links allow the coloring to spread to multiple digits:
Code:
+----------------+----------------+--------------------+
| .    .    .    | .   24    .    | 345   .     .      |
| .    569  .    | .   .     .    | 3578g .     5g8r   |
| .    .    26   | 24  .     .    | .     .     .      |
+----------------+----------------+--------------------+
| .    26   .    | .   .     24   | .     348   248    |
| .    259  259  | .   .     .    | 2r5g  .     .      |
| .    257  .    | 24  .     .    | 34-5  .     245r   |
+----------------+----------------+--------------------+
| .    .    .    | .   2r8g  .    | 2g8r  .     .      |
| 2579 .    2359 | .   234   2479 | .     .     249    |
| .    279  239  | .   2348  2479 | .     478   2489   |
+----------------+----------------+--------------------+

To help a bit with clarity, I show only unsolved cells containing those three digits. Quickly, we find an r-g <5> pair in Box 6 that eliminates <5> in R6C7.

It may not get one very far, but is another tool preferable to forcing.

Basically, coloring is a way to do implication chains without doing the implication chains!
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Fri Aug 10, 2007 7:59 am    Post subject: Reply with quote

Thank you, Tracy and Asellus!

Thank you so much indeed - your post especially Asellus made me look at coloring in a completely new light. I used to think one would color the whole cell (as it is shown in so many explanations on the net) when in fact Idea you go and color the indiviual candidates in the pencil marks.

Bear in mind I do sudoku on paper only and my main problem with forcing and coloring as I understood it up to now is that once you've started the grid is changed for good and if it turns out the initial choice was a dead end you've had it.

Now I understand that green really means all candidates that belong together in one implication chain and red belong to the other, much like my "left" and "right" but without scribbling into the grid.

Really makes it much easier to see relationships. Very Happy

I'll look at color wings again, I promise.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Fri Aug 10, 2007 3:57 pm    Post subject: Reply with quote

Quote:
Bear in mind I do sudoku on paper only and my main problem with forcing and coloring as I understood it up to now is that once you've started the grid is changed for good and if it turns out the initial choice was a dead end you've had it.


I have a suggestion for you. Keep a supply of blank grids handy for testing coloring, chains or whatever else you're not sure of. Then your actual puzzle stays intact. I keep a sheet of six grids on a page and it lasts forever, since I just erase when I'm done.

http://www.dailysudoku.com/sudoku/pdf/blank6.pdf
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