Problem with short forcing chain

Advanced methods and approaches for solving Sudoku puzzles

Problem with short forcing chain

I cannot understand why I seem to half right. I know there is no such thing as half right. Hopefully, someone can point out the error in my thinking because I am baffled!

The forcing chain goes starts in r6c9 and ends in r4c1

r6c9=8 r5c8=6 r5c3=3 r4c1=8

Since the begining and ending cells are(8) , they both "see" the (8) in r6c1 and r4c9. However and my problem, only the (8) in r6c1 can be deleted but not the (8) in r4c9.

Thanks

*-----------*
|...|.68|...|
|.2.|7.9|.1.|
|..1|...|..4|
|---+---+---|
|.57|6..|.9.|
|2..|.8.|..1|
|.1.|..7|54.|
|---+---+---|
|5..|...|4..|
|.9.|5.6|.3.|
|...|47.|...|
*-----------*

*-----------*
|4..|168|...|
|.2.|749|.1.|
|..1|352|..4|
|---+---+---|
|.57|614|.9.|
|24.|985|..1|
|.1.|237|54.|
|---+---+---|
|5..|891|4..|
|.94|526|.3.|
|...|473|...|
*-----------*

Code: Select all
` *-----------* |...|.68|...| |.2.|7.9|.1.| |..1|...|..4| |---+---+---| |.57|6..|.9.| |2..|.8.|..1| |.1.|..7|54.| |---+---+---| |5..|...|4..| |.9.|5.6|.3.| |...|47.|...| *-----------* *-----------* |4..|168|...| |.2.|749|.1.| |..1|352|..4| |---+---+---| |.57|614|.9.| |24.|985|..1| |.1.|237|54.| |---+---+---| |5..|891|4..| |.94|526|.3.| |...|473|...| *-----------*  *--------------------------------------------------------------------* | 4      37     359    | 1      6      8      | 2379   257    23579  | | 368    2      3568   | 7      4      9      | 68     1      3568   | | 679    678    1      | 3      5      2      | 679    678    4      | |----------------------+----------------------+----------------------| | 38     5      7      | 6      1      4      | 238    9      238    | | 2      4      36     | 9      8      5      | 367    67     1      | | 689    1      689    | 2      3      7      | 5      4      68     | |----------------------+----------------------+----------------------| | 5      367    236    | 8      9      1      | 4      267    267    | | 178    9      4      | 5      2      6      | 178    3      78     | | 16     68     26     | 4      7      3      | 1269   2568   2569   | *--------------------------------------------------------------------*`
Jasper32

Posts: 60
Joined: 04 January 2008

Reading from left to right, what your chain says is that, if r6c9 contains 8, r4c1 contains 8. So you can only eliminate 8 from the “buddy” cells if r6c9 contains 8.

To make the eliminations you are looking for the chain would need to run

r6c9 = 6 => … => r4c1 = 8.

Then the logic would be:

Either r6c9 contains 8 or (it contains 6 and so) r4c1 contains 8.

8 could indeed be eliminated from the common associates of the end points.

Of course there is no such chain. Here is a chain starting from r5c8:

r5c8 = 6 => r6c9 = 8 => r8c9 = 7

Now either r5c8 contains 7 or r8c9 does: 7 may be eliminated from r7c8.

This doesn’t get you very far with the puzzle but I hope it helps with the logic.

Steve
Steve R

Posts: 74
Joined: 03 April 2006

Re: Problem with short forcing chain

Jasper32 wrote:I cannot understand why I seem to half right. I know there is no such thing as half right. Hopefully, someone can point out the error in my thinking because I am baffled!

The forcing chain goes starts in r6c9 and ends in r4c1

r6c9=8 r5c8=6 r5c3=3 r4c1=8

Since the begining and ending cells are(8) , they both "see" the (8) in r6c1 and r4c9. However and my problem, only the (8) in r6c1 can be deleted but not the (8) in r4c9.
Code: Select all
` *--------------------------------------------------------------------* | 4      37     359    | 1      6      8      | 2379   257    23579  | | 368    2      3568   | 7      4      9      | 68     1      3568   | | 679    678    1      | 3      5      2      | 679    678    4      | |----------------------+----------------------+----------------------| | 38     5      7      | 6      1      4      | 238    9      238    | | 2      4      36     | 9      8      5      | 367    67     1      | | 689    1      689    | 2      3      7      | 5      4      68     | |----------------------+----------------------+----------------------| | 5      367    236    | 8      9      1      | 4      267    267    | | 178    9      4      | 5      2      6      | 178    3      78     | | 16     68     26     | 4      7      3      | 1269   2568   2569   | *--------------------------------------------------------------------*`

Yes, you appear completely baffled. Chains will do that to you -- especially forcing chains.

1) First, r6c9=8 => r5c8=6 is incorrect

2) Even if your chain from [r6c9]=8 to [r4c1]=8 was correct, you can't perform eliminations with this logic. If you had a chain from [r6c9]<>8 to [r4c1]=8, then you could perform eliminations.

3) Finally, a forcing chain involves more than one chain from a cell. You might want to practice on single-chain logic a little more.

Would you like for me to pm a copy of my (short) notes file on chains?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Re: Problem with short forcing chain

daj95376 wrote:Would you like for me to pm a copy of my (short) notes file on chains?

daj95376, I don't know about Jasper32, but I certainly would
hobiwan
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Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

pm with (short) notes file on chains sent to Jasper32 and hobiwan.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Thanks daj95376 for your PM. This will take some time to absorb.....definitely. You PM is appreciated. I do have one question about what you wrote in a previous post above. You wrote, "First, r6c9=8 =>r5c8=6s incorrect". From my limited knowledge of forcing chains and my thoughts from various things I have read about forcing chains, (both of the above are bi-value cells and 6 is common to both), I had made a valid assumption that r6c9=8 and r5c8=6. Could you please let me know in what way my assumption is incorrect. That will be a help for me.
Jasper32

Posts: 60
Joined: 04 January 2008

Jasper32 wrote:I do have one question about what you wrote in a previous post above. You wrote, "First, r6c9=8 =>r5c8=6s incorrect". From my limited knowledge of forcing chains and my thoughts from various things I have read about forcing chains, (both of the above are bi-value cells and 6 is common to both), I had made a valid assumption that r6c9=8 and r5c8=6. Could you please let me know in what way my assumption is incorrect. That will be a help for me.

None of what you wrote above makes any sense to me. Especially with regard to forcing chains. I strongly suggest that you go to Sudopedia and read everything carefully about chains and loops.

http://www.sudopedia.org/wiki/Category:Chains_and_Loops
daj95376
2014 Supporter

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An example of a short forcing chain from your post here ...

http://forum.enjoysudoku.com/viewtopic.php?p=52718#p52718

Code: Select all
` After basic eliminations ... a short forcing chain on [r4c9] *--------------------------------------------------------------------* | 1      2459   258    | 3      57     89     | 579    27-45  6      | | 289    6      258    | 4      57     189    | 1579   3      2579   | | 349    359    7      | 6      2      19     | 8      15     459    | |----------------------+----------------------+----------------------| | 6      127    9      | 5      8      3      | 4      127   *27     | | 378    1357   358    | 2      4      6      | 1579   1578   35789  | | 238    235    4      | 9      1      7      | 6      258    2358   | |----------------------+----------------------+----------------------| | 479    79     1      | 78     3      5      | 2      6      48     | | 237    8      23     | 1      6      4      | 357    9      57     | | 5      347    6      | 78     9      2      | 37     48     1      | *--------------------------------------------------------------------*`

[r4c9] has two candidates. One must be true. What can we conclude if we assume that each candidate, in turn, is true?

Code: Select all
`[r4c9]-2-[r46c8]=2=[r1c8] => [r1c8]<> 457[r4c9]-7-[r45c8]=7=[r1c8] => [r1c8]<>245`

Since each chain forces eliminations in [r1c8], any eliminations common to both chains can be eliminated based on the forcing chain.

Code: Select all
`r1c8    <> 45    Forcing Chain on [r4c9]`

Note: A forcing chain always has an implication chain associated with each candidate value in the starting cell. You look for any commonality between all implication chains!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 wrote:What can we conclude if we assume that each candidate, in turn, is true?
Code: Select all
`[r4c9]-2-[r46c8]=2=[r1c8] => [r1c8]<> 457[r4c9]-7-[r45c8]=7=[r1c8] => [r1c8]<>245`

Since each chain forces eliminations in [r1c8], any eliminations common to both chains can be eliminated based on the forcing chain.
Code: Select all
`r1c8    <> 45    Forcing Chain on [r4c9]`

That's an excellent example of a continuous loop -- with five eliminations.
Code: Select all
` 1     2459  258   | 3     57    89    | 579    A27-45 6 289   6     258   | 4     57    189   | 1579    3     2579 349   359   7     | 6     2     19    | 8       15    459-------------------+-------------------+---------------------- 6     127   9     | 5     8     3     | 4     BD127  C27 378   1357  358   | 2     4     6     | 159-7  B1578  3589-7 238   235   4     | 9     1     7     | 6      D258   358-2-------------------+-------------------+---------------------- 479   79    1     | 78    3     5     | 2       6     48 237   8     23    | 1     6     4     | 357     9     57 5     347   6     | 78    9     2     | 37      48    1 A         B        C         D         Ar1c8 =7= r45c8 -7- r4c9 -2- r46c8 =2= r1c8 = continuous loop,   implies r1c8<>45, r5c79<>7, r6c9<>2     `

Due to the continuous nature of the loop, each weak inference becomes a conjugate inference. This includes the implied weak inference within r1c8.

I don't think one would find many examples like this posted on the Players' Forum though, because we've generally avoided loops with overlaps.
ronk
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Location: Southeastern USA

And I need to go read up on continuous loops, but not in Sudopedia.
daj95376
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Don't confuse "overlap" with "continuous". Overlap are discontinuous nice loops where the start and end nodes share one or more common cells. Continuous are when the start and end nodes are the same and obey the nice loop rules for links. There are lots of examples of the latter in Ocean's Bicycle Collection
Mike Barker

Posts: 458
Joined: 22 January 2006

I couldn't follow ronk's continuous loop, so I thought of it as an extension to my forcing chain that included additional common eliminations. This is probably an incorrect perspective.

Code: Select all
`[r4c9]-2-[r46c8]=2=[r1c8]=7=[r45c8]}                                   } => [r1c8]<>45,[r5c79]<>7,[r6c9]<>2[r4c9]-7-[r45c8]=7=[r1c8]=2=[r46c8]}`
Last edited by daj95376 on Mon Feb 25, 2008 5:38 pm, edited 1 time in total.
daj95376
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Posts: 2624
Joined: 15 May 2006

Mike Barker wrote:Don't confuse "overlap" with "continuous". Overlap are discontinuous nice loops where the start and end nodes share one or more common cells. Continuous are when the start and end nodes are the same and obey the nice loop rules for links.

Both discontinuous and continous loops can overlap somewhere within the loop, so I'm not sure I understand your point. BTW isn't your first case for discontinuous loops commonly referred to as "endpoint" overlap?
ronk
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Location: Southeastern USA

Just because of the way I came to understand things I tend to think of overlap and endpoint overlap as synonomous and talk about "internal overlap" as common cells, but overlap = endpoint overlap + internal overlap is probably a better parsing. The point of my post was that overlap is not, in general, the same as continuous.

Danny, you might also check out Jeff's post to better understand continuous nice loops. Another perspective is a continuous nice loops requires alternating inferences around the loop as described in Myth's AIC post.
Mike Barker

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