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Long VH+ by JPF (game 0042)
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Fri Jul 25, 2008 7:18 pm    Post subject: Long VH+ by JPF (game 0042) Reply with quote

Code:
 1 . 2 | . 3 . | 4 . 5
 . . . | . . . | . . .
 5 . . | 2 . 1 | . . 6
-------+-------+-------
 . . 7 | . . . | 2 . .
 8 . . | . 7 . | . . 1
 . . 3 | . . . | 6 . .
-------+-------+-------
 6 . . | 7 . 9 | . . 8
 . . . | . . . | . . .
 3 . 1 | . 5 . | 9 . 4 JPF

Heavy coloring (3 strong links) in 2 numbers (hint 7 and 2) plus an intermediate advanced technique were needed to get a start.
3 techniques then to get it down to where we normally begin to puzzle.
Then i found a finned xy-wing (alternatively there was an M-wing plus xy-wing) to solve it.
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tlanglet



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

PostPosted: Fri Jul 25, 2008 8:29 pm    Post subject: Reply with quote

Well, I will be the first to suggest that this puzzle is VH+++, not VH+.

For me, basics consisted of two Box/Line interactions! I then found three finned x-wings and an xy-wing using my favorite techniques. I am now about to proceed to my next set of techniques. Wish me luck .......

Ted
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Asellus



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PostPosted: Sat Jul 26, 2008 2:46 am    Post subject: Reply with quote

One of those colorings is particularly nice. However, I set for myself a different challenge: Could I solve this thing using only "finned" methods? And, given the nature of this puzzle, I can't say that this route was any more difficult than another! Here's the result:

[1] Finned X-Wing c15 r8c6<>2
[2] Finned X-Wing c17 r2c89<>7
[3] Finned X-Wing r39 r1c8<>7

Now, ignoring the XY Wing...
Code:
+--------------------+---------------------+-----------------+
| 1     678     2    | 68     3      678   | 4     9      5  |
| 479   346789  4689 | 459    4689   45678 | 1378  123   b23 |
| 5     34789   489  | 2      489    1     | 378  b37     6  |
+--------------------+---------------------+-----------------+
|a49    14569   7    | 13459  14689  34568 | 2     3458  a39 |
| 8     24569   4569 | 3459   7      23456 | 35   a345    1  |
| 249   12459   3    | 1459   12489  2458  | 6     4578   79 |
+--------------------+---------------------+-----------------+
| 6     245     45   | 7      124    9     | 135   1235   8  |
| 2479  245789  4589 | 134    12468  3468  | 157   12567  27 |
| 3     278     1    | 68     5      268   | 9    b267    4  |
+--------------------+---------------------+-----------------+

[4] Finned XY Wing (349) r4c19|r5c8, Fin: (5)r5c8 ... marked "a" above.
A short XY Chain from the Fin leads to r4c1=4, which has the same victims as the alternate XY Wing.

(5)r5c8=[XY Wing] - (4)r5c23|r4c8
and
(5)r5c8 - (5=3)r5c7 - (3=9)r4c9 - (9=4)r4c1
thus, r5c23|r4c8<>4

[5] Finned XY Wing (237) r2c9|r39c8, Fin: (6)r9c8 ... marked "b" above.
The 2-cell ALS in r9c46 converts the Fin to the <2> at r9c6, which can be "seen" by the <2> at r8c9 via the ERs in boxes 5, 4 and 7. (The relatively easy to see ERs are obscured in the notation below.)

(6)r9c8=[XY Wing] - (2)r8c9
and
(6)r9c8 - ALS[(6)r9c46=(2)r9c6] - (2)r56c6=(2)r6c56 - (2)r6c12=(2)r56c2 - (2)r789c2=(2)r8c12
thus, r8c9<>2

After some simplification...
Code:
+--------------+-----------------+-----------+
| 1  c68   2   | 68    3    7    | 4  9    5 |
| 7   3    469 | 459   469  456  | 8  1    2 |
| 5   489 c489 | 2     489  1    | 7  3    6 |
+--------------+-----------------+-----------+
| 49  15   7   | 1459  469  456  | 2  8    3 |
| 8   269 c69  | 39    7    23   | 5  4    1 |
| 24  15   3   | 145   248  2458 | 6  7    9 |
+--------------+-----------------+-----------+
| 6   24   45  | 7     1    9    | 3  25   8 |
| 29  289  589 | 34    246  346  | 1  256  7 |
| 3   7    1   | 68    5    268  | 9  26   4 |
+--------------+-----------------+-----------+

Ignoring the X-Wing on 2, there is one more step:

[6] Finned XY Wing (689) r1c2|r35c3, Fin: (4)r3c3 ... marked "c" above.
The Fin is transported to <6> at r5c3 via and XY Chain that includes the strongly linked <2>s in r9.

(4)r3c3=[XY Wing] - (6)r2c3|r5c2
and
(4)r3c3 - (4=5)r7c3 - (5=2)r7c8 - (2)r9c8=(2)r9c6 - (2=3)r5c6 - (3=9)r4c5 - (9=6)r5c3
thus, r2c3|r5c2<>6

[Edit to remove erroneous "unidirectional link" notations.]


Last edited by Asellus on Mon Jul 28, 2008 10:21 am; edited 1 time in total
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Sat Jul 26, 2008 11:12 am    Post subject: Reply with quote

Great solution, Asellus.

If you do use the x-wing in the last grid you can see the finned xy-wing 249 i had found.
Code:
+--------------+-----------------+-----------+
| 1   6-8  2   | 68    3    7    | 4  9    5 |
| 7   3    469 | 459   469  456  | 8  1    2 |
| 5  #489  489 | 2     489  1    | 7  3    6 |
+--------------+-----------------+-----------+
| 49  15   7   | 1459  469  456  | 2  8    3 |
| 8   269  69  | 39    7    23   | 5  4    1 |
| 24  15   3   | 145   248  458  | 6  7    9 |
+--------------+-----------------+-----------+
| 6  #24   45  | 7     1    9    | 3  25   8 |
|#29 *89   589 | 34    246  346  | 1  56   7 |
| 3   7    1   | 68    5    268  | 9  26   4 |
+--------------+-----------------+-----------+
Either the fin r3c2=8 is true or one of r3c2 and r8c1 must be 9, therefore r8c2=8.
So we can eliminate 8 from r1c2.

Keith, enough samples for a thread about finned xy-wings ?
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nataraj



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PostPosted: Sat Jul 26, 2008 11:32 am    Post subject: Reply with quote

"Usual" methods (coloring, xy-wing and a 15 UR) get me to here:

Code:

+--------------------------+--------------------------+--------------------------+
| 1       68      2        | 68      3       7        | 4       9       5        |
| 7       3       469      | 459     469     456      | 8       1       2        |
| 5       489     489      | 2       489     1        | 7       3       6        |
+--------------------------+--------------------------+--------------------------+
| 49      15      7        | 149     469     456      | 2       8       3        |
| 8       269     69       | 39      7       23       | 5       4       1        |
| 24      15      3        | 145     248     458      | 6       7       9        |
+--------------------------+--------------------------+--------------------------+
| 6       24      45       | 7       1       9        | 3       25      8        |
| 29      89      589      | 34      246     346      | 1       56      7        |
| 3       7       1        | 68      5       268      | 9       26      4        |
+--------------------------+--------------------------+--------------------------+


At which point I can see an xy-chain (r1c2 to r5c3 via r8c2,r8c1,r6c1) and it does solve the puzzle.

But where are those other creatures?
The xy-wing 24-29-49 is useless and I cannot find a way to connect it to an m-wing like ravel said. Also, I am not yet into finned wings so please, I'd appreciate a hint ...
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Sat Jul 26, 2008 12:10 pm    Post subject: Reply with quote

The UR 15 also eliminates 5 in r6c4, placing it r2c4. This gives an xyz-wing, which brings you here:
Code:
 *--------------------------------------------------*
 | 1    68   2    | 68   3    7    | 4    9    5    |
 | 7    3    469  | 5    49   46   | 8    1    2    |
 | 5   @489  489  | 2   -489  1    | 7    3    6    |
 |----------------+----------------+----------------|
 | 49   1    7    | 49   6    5    | 2    8    3    |
 | 8    269  69   | 39   7    23   | 5    4    1    |
 | 24   5    3    | 1    248  48   | 6    7    9    |
 |----------------+----------------+----------------|
 | 6   #24   45   | 7    1    9    | 3    25   8    |
 |*29   89   589  | 34  #24   346  | 1    56   7    |
 | 3    7    1    | 68   5    268  | 9    26   4    |
 *--------------------------------------------------*

Beside of the finned xy-wing above now there is the M-wing 24 (connected with the strong link for 2, then strong long for 4 in column 2), which eliminates 4 from r3c5.
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cgordon



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Location: ontario, canada

PostPosted: Sat Jul 26, 2008 3:13 pm    Post subject: Reply with quote

This is over my head. I thought for colouring you had to link up connected pairs (in boxes, rows and cols). I can't see any numbers where this is possible (at least for more than two pairs. Have I not gone far enough with the basics? Very confused and sorely troubled !!

(Edited Note: So far I used two ER's and a Finned x-wing (my first eh) to remove 2 from R8C6 and 7 from R12C8)


Last edited by cgordon on Sat Jul 26, 2008 3:37 pm; edited 1 time in total
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nataraj



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PostPosted: Sat Jul 26, 2008 3:24 pm    Post subject: Reply with quote

Thanks, ravel!

Sloppy work on that first UR, I should have taken out both 5s in col 4, of course.

Back on track again, I found the UR 46, xyz-wing and m-wing, and then another xyz-wing (4,8,9 box 1), which finally solved the puzzle... Smile
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nataraj



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PostPosted: Sat Jul 26, 2008 3:51 pm    Post subject: Reply with quote

Craig,

after basics, which consist of only a few box/line interactions (as Ted remarked rightly), this is the position where coloring can help:



Code:

+--------------------------+--------------------------+--------------------------+
| 1       6789    2        | 689     3       678      | 4       79      5        |
| 479     346789  4689     | 45689   4689    45678    | 1378    12379   2379     |
| 5       34789   489      | 2       489     1        | 378     379     6        |
+--------------------------+--------------------------+--------------------------+
| 49      14569   7        | 1345689 14689   34568    | 2       34589   39       |
| 8       24569   4569     | 34569   7       23456    | 35      3459    1        |
| 249     12459   3        | 14589   12489   2458     | 6       45789   79       |
+--------------------------+--------------------------+--------------------------+
| 6       245     45       | 7       124     9        | 135     1235    8        |
| 2479    245789  4589     | 13468   12468   23468    | 157     12567   27       |
| 3       278     1        | 68      5       268      | 9       267     4        |
+--------------------------+--------------------------+--------------------------+

There is a kite (2), not really spectacular, in row 2 col 1, it removes 2 from r8c6

If you plot the positions for "7", though, and their strong links:

Code:

++++
  o      *  9 
         |     
* o      *o o o
|              
| o       o o 
+|+++
|              
|              
|              
|              
|           *-9
+|+++
|              
|              
* o       o o 2
               
  *-----------* 
++++


you can see that 2 can be removed from r1c8, r2c8 and r2c9.
How?

First there is a simple kite col 1, row 9. It removes from r2c8. But how?
There are two strong links (r9c8=r9c2 and r8c1=r2c1).
That means: if r9c8 is NOT 7, then r9c2=7
But since r9c2 sees r8c1 in box 7, if r9c2=7 then r8c1<>7
Again using a strong link (col 1), we continue: if r8c1<>7 then r2c1=7.

Taken together, we find that either r9c8=7 or r2c1=7 and 7 in r2c8 is toast.

This method of daisy-chaining is not limited to just two strong links.

From r2c1, we can connect to the next strong link: r2c6=r1c6.
What does it mean?
r2c1 "sees" r2c6: If r2c1=7 then r2c6<>7
r2c6 and r1c6 are strongly linked: if r2c6<>7 then r2c1=7

And that makes our next elimination possible: either r9c8=7 or r1c6=7 and 7 in r1c8 is gone ...

What about the other end of the daisy-chain?

r9c8 "sees" r6c8 and r6c8=r6c9.
Strong link r6c9=r6c8 means: if r6c9<>7 then r6c8=7
"sees" means: if r6c8=7 then r9c8<>7 and again (using the same logic as before) we find that either r6c9=7 or r2c1=7 and we can remove 7 from r2c9.

The method is called "multi-coloring" but I never used any actual colors ...

Only "strong link" -"weak link" - "strong link".
Always make sure you have strong links at the ends of the chain and you'll be OK... Smile
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cgordon



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PostPosted: Sat Jul 26, 2008 5:08 pm    Post subject: Reply with quote

Nataraj: Thanks for the explanation. I can now see the Kite (which I had previously read about). It's just that this doesn't fit in with my neophyte understanding of colouring - which I thought was linking up a min. of 4 conjugal pairs (or whatever they are called). Though perhaps colouring (strong links with peers) is the basis for a multidude of patterns or solutions.
Thanks again
PS I had gotten one step further than your grid by placing a 9 in R1C8. using a Finned x-wing on 7. Also an ER removes the 2 from R8C6 and the 7 from R2C8.
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nataraj



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PostPosted: Sat Jul 26, 2008 6:06 pm    Post subject: Reply with quote

Glad to have helped, Craig! I can see both the ER and the finned x-wing in the diagram for "7": the ER uses the strong link in row 9 and the group of 7s in col2/ box 1, the fin of the x-wing is in row 3 col 7. Amazing how different people look at the same sudoku grid in totally different ways... Myself, I do look for finned and other creatures, including ERs, swordfish et al., but only when the search for multi-coloring patterns turns up nothing.

I think the term coloring did indeed originate with a method where only strong links (only two cells in a house have x) were considered. On Andrew Stuart's site there is a good explanation of this basic coloring with very colorful graphics.

But he goes on to explain the more general concept of alternating weak and strong links in the section about X-cycles (part 1 and 2), which first introduced me to alternating inference chains (AICs) and "nice loops".
You don't have to completely understand the "theory". All one really needs is 3 simple rules
1. "strong"-"weak"-"strong"-...
2. begin and end with a strong link
3. a strong link can stand in for a weak link (and not the other way round)
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Asellus



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PostPosted: Sat Jul 26, 2008 9:58 pm    Post subject: Reply with quote

Craig,

You might want to examine the <2>s in the early grid of this puzzle. There is another example of the "strong-weak-strong-weak-strong" string of links elimination. See if you can spot it.

The "strong-weak-strong" structure is the essential characteristic of the techniques variously known as Turbot Fish, Kite and/or Skyscraper. These are also the simplest examples of multi-coloring (when that central link is "weak only" and not a conjugate link substituting for the weak position, as nataraj pointed out is possible ... since in the all-conjugate case basic coloring suffices). As such, they are also examples of what some call a "Color Wing." Essentially, you can string two or more of these "Turbot Fish" things end to end, as we've done here. And, as long as you take care, as nataraj nicely explained, no explicit coloring is necessary.

As ravel hinted initially, this puzzle is interesting in that it had two examples of this sort of coloring, one in each of two digits.
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cgordon



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PostPosted: Sat Jul 26, 2008 11:21 pm    Post subject: Reply with quote

Quote:
You might want to examine the <2>s in the early grid of this puzzle. There is another example of the "strong-weak-strong-weak-strong" string of links elimination. See if you can spot it.


Asellus: Theses are my early 2's. I can see the Kite removal of R8C6 but can't see anything else.

Code:
            
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | . . . | . 2 2 |   
| . . . | . . . | . . . |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . 2 . | . . 2 | . . . |   
| 2 2 . | . 2 2 | . . . |   
+-------+-------+-------+   
| . 2 . | . 2 . | . 2 . |   
| 2 2 . | . 2 2 | . 2 2 |   
| . 2 . | . . 2 | . 2 . |
+-------+-------+-------+
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keith



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PostPosted: Sun Jul 27, 2008 2:56 am    Post subject: Reply with quote

Quote:
Keith, enough samples for a thread about finned xy-wings ?


Yes, but tomorrow. I just got home after driving 435 miles and having a "special random inspection" at US Customs.

Keith
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Marty R.



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PostPosted: Sun Jul 27, 2008 3:52 am    Post subject: Reply with quote

Quote:
Yes, but tomorrow. I just got home after driving 435 miles and having a "special random inspection" at US Customs.

And they discovered a cache of Sudoku puzzles and determined that you're unbalanced and a threat to the US of A? Laughing
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ravel



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PostPosted: Sun Jul 27, 2008 10:32 am    Post subject: Reply with quote

cgordon wrote:
Asellus: Theses are my early 2's. I can see the Kite removal of R8C6 but can't see anything else.
Too early, i think. Both the coloring in 7 and an xy-wing were needed for me to place 7 in r9c2, which gave another strong link for 2.
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nataraj



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PostPosted: Sun Jul 27, 2008 5:20 pm    Post subject: Reply with quote

Yes, too early. At this stage, there is only the one kite.
After the xy-wing and cleanup, this is where multi-coloring can be used again:
Code:


+--------------------------+--------------------------+--------------------------+
| 1       68      2        | 68      3       7        | 4       9       5        |
| 7       34689   4689     | 459     4689    4568     | 138     123     23       |
| 5       3489    489      | 2       489     1        | 378     37      6        |
+--------------------------+--------------------------+--------------------------+
| 49      14569   7        | 13459   14689   34568    | 2       3458    39       |
| 8       24569   4569     | 3459    7       23456    | 35      345     1        |
| 249     12459   3        | 1459    12489   2458     | 6       4578    79       |
+--------------------------+--------------------------+--------------------------+
| 6       245     45       | 7       124     9        | 135     1235    8        |
| 249     24589   4589     | 134     1246    346      | 157     1256    27       |
| 3       7       1        | 68      5       268      | 9       26      4        |
+--------------------------+--------------------------+--------------------------+


The plot for "2" shows that 2 can be eliminated from r8c8 and r8c9:

Code:

++++
               
               
            *-3
              |
              |
+++|+
              |
              |
  *-------*    |
              |
* o    o o    |
+|++|+
| o    o    o |
|             |
* o    o    o 7
               
         *---6 
++++


Hint: the chain starts at r8c1.
strong link: r8c1=r6c1. r6c1 sees the next
strong link: r5c2=r5c6. r5c6 sees
strong link: r9c6=r9c8.

All cells that see both ends (r8c1 and r9c8) lose their "2"s
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cgordon



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PostPosted: Sun Jul 27, 2008 6:40 pm    Post subject: Reply with quote

Yeah - got it at last (though I needed the hint). I had been looking for "formal" patterns eg Finned x wings. Thanks.
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keith



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PostPosted: Sun Jul 27, 2008 7:38 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
Yes, but tomorrow. I just got home after driving 435 miles and having a "special random inspection" at US Customs.

And they discovered a cache of Sudoku puzzles and determined that you're unbalanced and a threat to the US of A? Laughing

Marty,

It was actually the Ginger Beer that tipped them off. Zehr's in Canada has the best (strongest) ginger beer I have ever had, it is 99 cents for a 2 liter bottle. A trunk full of ginger beer, a brief case full of Nataraj diagrams.

Up against the wall!!

So it goes.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Sun Jul 27, 2008 8:12 pm    Post subject: Reply with quote

Quote:
It was actually the Ginger Beer that tipped them off.

That reply cost me a trip to Google for "ginger beer." Embarassed
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