## Discontinouos X-Cycle

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### Discontinouos X-Cycle

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.

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`  *--------------------------------------------------------------------* | 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   | *--------------------------------------------------------------------*`
Jasper32

Posts: 60
Joined: 04 January 2008

### Re: Discontinouos X-Cycle

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...

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

### Re: Discontinouos X-Cycle

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.)
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.
Jasper32

Posts: 60
Joined: 04 January 2008

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].

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`+-----------------------------------+| *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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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:

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`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   26792   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...

- drac
Draco

Posts: 143
Joined: 14 March 2008

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

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` 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`
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.
Jasper32

Posts: 60
Joined: 04 January 2008

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Discontinouos X-Cycle

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.

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`  *--------------------------------------------------------------------* | 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.

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

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.
Jasper32

Posts: 60
Joined: 04 January 2008

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.
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` 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.
eleven

Posts: 1710
Joined: 10 February 2008

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
Jasper32

Posts: 60
Joined: 04 January 2008