Discontinouos X-Cycle

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Discontinouos X-Cycle

Postby Jasper32 » Mon Apr 21, 2008 6:41 pm

This is a discontinuous X-Cycle on 4’s. The cells are: r1c1, r1c7, r3c3, r9c3 and r9c7. From this you can see that the strong links are r1,c1, r1c7 and r9c7. It was my impression from what I have read that a (4) could be placed in r1c7. The intersection of two strong links. Not so in this case. Could someone please help me with an explanation? Thank you.

Code: Select all

 
 *--------------------------------------------------------------------*
 | 49     3      2      | 8      7      1      | 49     6      5      |
 | 5789   789    6      | 3      29     4      | 79     279    1      |
 | 479    1      479    | 5      29     6      | 8      2479   3      |
 |----------------------+----------------------+----------------------|
 | 569    2      359    | 4      8      7      | 169    139    69     |
 | 1      79     8      | 2      6      39     | 5      379    4      |
 | 679    4      379    | 1      5      39     | 2679   8      2679   |
 |----------------------+----------------------+----------------------|
 | 3      679    1      | 67     4      8      | 2679   5      2679   |
 | 2      68     47     | 9      1      5      | 3      47     68     |
 | 46789  5      479    | 67     3      2      | 14679  19     6789   |
 *--------------------------------------------------------------------*

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Re: Discontinouos X-Cycle

Postby RW » Mon Apr 21, 2008 7:40 pm

Jasper32 wrote:It was my impression from what I have read that a (4) could be placed in r1c7. The intersection of two strong links.

Could you specify where you have read something that gave you this impression, then it's easier to say where the misunderstanding is...

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Re: Discontinouos X-Cycle

Postby ronk » Mon Apr 21, 2008 8:48 pm

Jasper32 wrote:This is a discontinuous X-Cycle on 4’s. The cells are: r1c1, r1c7, r3c3, r9c3 and r9c7. From this you can see that the strong links are r1,c1, r1c7 and r9c7.

You've listed the five "vertices" of a turbot fish. When there are only two strong links and these strong links are on "adjacent sides", there are no valid eliminations or placements. (See Nick70's seminal post here.)
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Postby Jasper32 » Mon Apr 21, 2008 11:58 pm

Thanks. I got the information from "The Logic of Sudoku" By Andrew Stuaqrt on Page 76

It reads. "A discontinuity occurs when we find two strong links next to each other(That is,with no weak link between them) or two weak links next to each other (with no strong link dividing them). These rules work only if there is exactly one discontinuity, and such a loop will always have an odd number of nodes."

I guess I misunderstood what was written. I am still confused but I will read the recommendation made by Ronk.

Thanks to both of you.
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Postby daj95376 » Tue Apr 22, 2008 12:54 am

Andrew Stuart wrote:"These rules work only if there is exactly one discontinuity, and such a loop will always have an odd number of nodes."

You have weak links in [b1], [c3], and [r9]. Thus, there's a discontinuity in [b1]+[c3] and another discontinuity in [c3]+[r9].

Code: Select all
+-----------------------------------+
| *4  .  .  |  .  .  .  | *4  .  .  |
|  .  .  .  |  .  .  4  |  .  .  .  |
|  4  . *4  |  .  .  .  |  .  4  .  |
|-----------+-----------+-----------|
|  .  .  .  |  4  .  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  .  4  |
|  .  4  .  |  .  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  .  4  .  |  .  .  .  |
|  .  .  4  |  .  .  .  |  .  4  .  |
|  4  . *4  |  .  .  .  | *4  .  .  |
+-----------------------------------+

ronk: If this is incorrect, please send me a pm and I'll delete my message.
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Postby Draco » Tue Apr 22, 2008 2:37 am

Another way to look at this (after getting rid of a couple of locked sets) is as a multi-color chain exclusion on 7's (which is just another way of looking at Turbot Fish). Here's the puzzle with the locked sets removed and the cancellations marked:

Code: Select all
49  3  2   | 8  7  1 | 49   6   5   
5   8  6   | 3  29 4 | 79   279 1   
479 1 -79  | 5  29 6 | 8    249 3   
-----------+---------+--------------
69  2  5   | 4  8  7 | 1    3   69 
1   79 8   | 2  6  3 | 5   -79  4   
6-7 4  3   | 1  5  9 | 267  8   267
-----------+---------+--------------
3  -79 1   | 67 4  8 | 2679 5   2679
2   6  4*7 | 9  1  5 | 3    4*7 8   
8   5  479 | 67 3  2 | 4679 1   679


*7's are the +/- color for one set of colored 7's. -7's (removed) are all the same color. Since these intersect with a +/- pair, one of which must be true, then none of the -7's can be true.

Singletons solve from here.

Cheers...

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Postby ronk » Tue Apr 22, 2008 3:11 am

Jasper32, the asterisks below mark a turbot fish (aka skyscraper) for digit 7 in the pencilmarks you posted. Can you find the discontinuity?

Code: Select all
 49    3     2     | 8     7     1     | 49    6     5
 5789  789   6     | 3     29    4     | 79    279   1
 479   1     479   | 5     29    6     | 8     2479  3
-------------------+-------------------+------------------
 569   2     359   | 4     8     7     | 169   139   69
 1    *79    8     | 2     6     39    | 5    *379   4
 679   4     379   | 1     5     39    | 2679  8     2679
-------------------+-------------------+------------------
 3    *679   1     | 67    4     8     | 2679  5     2679
 2     68   *47    | 9     1     5     | 3    *47    68
 46789 5     479   | 67    3     2     | 14679 19    6789
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Postby Jasper32 » Tue Apr 22, 2008 11:51 pm

Ronk,
I think the disoontinuity is that the (7) r7c2 can be excluded. I think at times I have this down pat and then something comes along like the problem described above. If I am wrong about the discontinuity please let me know. I also printed out the URL you sent me yesterday but have not been able to get to it today. I have some free time tomorrow and I will definitely read it. Ronk, thank you for taking the time to answer to me. It is appreciated.
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Postby ronk » Wed Apr 23, 2008 1:36 am

Jasper32 wrote:I think the disoontinuity is that the (7) r7c2 can be excluded.

Correct. Strong and weak links alternate ... except for the adjacent weak links in c2 and b7.
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Re: Discontinouos X-Cycle

Postby Luke » Sun Apr 27, 2008 5:25 am

Jasper32 wrote:This is a discontinuous X-Cycle on 4’s. The cells are: r1c1, r1c7, r3c3, r9c3 and r9c7. From this you can see that the strong links are r1,c1, r1c7 and r9c7. It was my impression from what I have read that a (4) could be placed in r1c7. The intersection of two strong links. Not so in this case. Could someone please help me with an explanation? Thank you.

Code: Select all

 
 *--------------------------------------------------------------------*
 | 49     3      2      | 8      7      1      | 49     6      5      |
 | 5789   789    6      | 3      29     4      | 79     279    1      |
 | 479    1      479    | 5      29     6      | 8      2479   3      |
 |----------------------+----------------------+----------------------|
 | 569    2      359    | 4      8      7      | 169    139    69     |
 | 1      79     8      | 2      6      39     | 5      379    4      |
 | 679    4      379    | 1      5      39     | 2679   8      2679   |
 |----------------------+----------------------+----------------------|
 | 3      679    1      | 67     4      8      | 2679   5      2679   |
 | 2      68     47     | 9      1      5      | 3      47     68     |
 | 46789  5      479    | 67     3      2      | 14679  19     6789   |
 *--------------------------------------------------------------------*

Jasper,

Did the book say what the elimination is? I'm having trouble finding it.
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Postby Jasper32 » Mon Apr 28, 2008 11:30 am

I quoted the book verbatim and drew my conclusions based on my belief on what it it said. I might suggest the if you are also having problems in thia area. you read the link that Ronk referred to in his reply to me. It is excellent and I am it will be benificial to you as it has been to me. Good luck.
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Postby eleven » Mon Apr 28, 2008 1:47 pm

ronk wrote:Jasper32, the asterisks below mark a turbot fish (aka skyscraper) for digit 7 in the pencilmarks you posted. Can you find the discontinuity?

For me the skyscraper is much easier to see and it makes 2 eleiminations.
Code: Select all
 49    3     2     | 8     7     1     | 49    6     5
 5789  789   6     | 3     29    4     | 79    279   1
 479   1     479   | 5     29    6     | 8     2479  3
-------------------+-------------------+------------------
 569   2     359   | 4     8     7     | 169   139   69
 1    #79    8     | 2     6     39    | 5    #379   4
 679   4    3-79   | 1     5     39    | 2679  8     2679
-------------------+-------------------+------------------
 3    6-79   1     | 67    4     8     | 2679  5     2679
 2     68   #47    | 9     1     5     | 3    #47    68
 46789 5     479   | 67    3     2     | 14679 19    6789
Also i would remommend this link for beginners: http://forum.enjoysudoku.com/viewtopic.php?t=3326.

After all i have the feeling, that there are no players on this "Players Forum", but only programmers and theoreticians (though probably the best).

Bye.
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Postby Jasper32 » Mon Apr 28, 2008 3:13 pm

Eleven,

I thank you for your posting and I will definitely go to the link you sent
me. Thank you. As for the people who post replies., I have nothing to comment on that other than the fact they are smarter me. They have been polite, helpful and patient to me. I do appreciate their help and I apprreciate your sending me this link as well.

Best regards,

jasper
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