The New Sudoku Players' Forum

[daj95376]

My understanding of chain notation is limited. Plowing through all of the threads on the topic, with their point and counter-point discussions, only leaves me confused ... not enlightened.

This is my (basic) understanding of Implication Chains/Streams and Inference Chains using chain notation. I have questions!

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Sample PM
 *-----------------------------------------------------------------------------*
 | 6       1       47      | 2       3       8       | 4579    479     4579    |
 | 5       9       8       | 4       6       7       | 3       1       2       |
 | 3       47      2       | 1       9       5       | 47      8       6       |
 |-------------------------+-------------------------+-------------------------|
 | 149     5       3       | 7       14      2       | 8       6       49      |
 | 24789   2467    4679    | 3       48      469     | 2479    5       1       |
 | 124789  2467    4679    | 68      5       1469    | 2479    3       479     |
 |-------------------------+-------------------------+-------------------------|
 | 249     3       469     |*68      7       146     |*14569   249    *4589    |
 | 2479    2467    1       | 5       248     3       | 4679    2479    4789    |
 | 247     8       5       | 9       124    *146     |*1467    247     3       |
 *-----------------------------------------------------------------------------*


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Implication Chain/Stream: left-to-right

r7c4=6 => r7c9=8 => r7c7=5 => r9c7=1 => r9c6=6 => r7c4=8


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Inference Chain: bi-directional (w/ bivalue-cell information added)

(6=)[r7c4]=8=[r7c9]=5=[r7c7]=1=[r9c7]=6=[r9c6]-6-[r7c4]

Strong Link:  [cell_1]=a=[cell_2]  =>  if (cell_1 is not a) then (cell_2 is     a)
Weak   Link:  [cell_1]-a-[cell_2]  =>  if (cell_1 is     a) then (cell_2 is not a)


Q 1: Is this correct?

Q 2: To present a more complete picture of an Implication Chain/Stream, I'd like to place (l-r) in front of what appears to be an Implication Chain. Is this acceptable? Is there another way that already exists?

Finally, I'd like to present an alternate format for chain notation.

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Inference Chain: bi-directional, alternate format (w/ bivalue-cell information added)

(6=)[r7c4]-8=[r7c9]-5=[r7c7]-1=[r9c7]-6=[r9c6]=6-[r7c4]

Strong Link:  [cell_1]-a=[cell_2]  =>  if (cell_1 is not a) then (cell_2 is     a)
Weak   Link:  [cell_1]=a-[cell_2]  =>  if (cell_1 is     a) then (cell_2 is not a)


Q 3: Is there a case where the alternate format doesn't work? (Why do I have a feeling that I've asked this question before!)

[re'born]

Finally, I'd like to present an alternate format for chain notation.

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Inference Chain: bi-directional, alternate format (w/ bivalue-cell information added)

(6=)[r7c4]-8=[r7c9]-5=[r7c7]-1=[r9c7]-6=[r9c6]=6-[r7c4]

Strong Link:  [cell_1]-a=[cell_2]  =>  if (cell_1 is not a) then (cell_2 is     a)
Weak   Link:  [cell_1]=a-[cell_2]  =>  if (cell_1 is     a) then (cell_2 is not a)


Q 3: Is there a case where the alternate format doesn't work? (Why do I have a feeling that I've asked this question before!)

When using the nice loop notation, isn't it sometimes the case that one would write a link in the following way (think of a UR)

[r3c1]=4|3=[r3c8] (which means that if r3c1<>4 then r3c8=3 and if r3c8<>3 then r3c1 = 4)

In this case, I'm not sure how to write it in your notation. If I write

[r3c1]-4|3=[r3c8],

then I get r3c1 <> 4 => r3c8 = 3, but the other direction is lost (and is even incorrect).

[ronk]

Q 3: Is there a case where the alternate format doesn't work? (Why do I have a feeling that I've asked this question before!)

If you didn't someone else did ... and my answer is the same as before. For your notation, the inferences are incorrect when reading right-to-left.

[daj95376]

Q 3: Is there a case where the alternate format doesn't work? (Why do I have a feeling that I've asked this question before!)

If you didn't someone else did ... and my answer is the same as before. For your notation, the inferences are incorrect when reading right-to-left.

It was probably me. While out running errands, I realized that my notation wasn't bi-directional ... and that someone had told me so in the past. It was probably you in a pm ... and that's why I couldn't find it when I did a search of the forum.

I'm sorry for wasting your time ... AGAIN!!!

[daj95376]

Here is a finned X-Wing puzzle from Mike Barker's contributions to the zoo. It can be solved with Singles and any one of two Sashimi X-Wings.

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 6..........7...64.....92.1...4..79...3..1.42.......1.6..32....5.4.5......2.......

#                  Singles
#   c28   -  7     X-Wing (finned/Sashimi)   (note: [r7 c7]<>7)
# r67     -  7     X-Wing (finned/Sashimi)   (note: [r89c8]<>7)
 *-----------------------------------------------------------*
 | 6     1     2     | 347   37    34    | 5     8     9     |
 | 3     9     7     | 1     58    58    | 6     4     2     |
 | 4     5     8     | 6     9     2     | 37    1     37    |
 |-------------------+-------------------+-------------------|
 | 1     6     4     | 38    2     7     | 9     5     38    |
 | 78    3     5     | 9     1     6     | 4     2     78    |
 | 2     78    9     | 348   358   3458  | 1     37    6     |
 |-------------------+-------------------+-------------------|
 | 9     78    3     | 2     4     1     | 8-7   6     5     |
 | 78    4     6     | 5     378   389   | 2     39-7  1     |
 | 5     2     1     | 378   6     389   | 378   39-7  4     |
 *-----------------------------------------------------------*
#                  Singles


The two Sashimi X-Wings can be expressed as a chain or with grouped colors.

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    Blue    Green  Blue   Green  Blue  -Blue
(7) [r89c8]-[r6c8]=[r6c2]-[r7c2]=[r7c7]-[r89c8]


Did I do this right? I know it's not bi-directional, but I don't see a way around it.

[re'born]

Here is a finned X-Wing puzzle from Mike Barker's contributions to the zoo. It can be solved with Singles and any one of two Sashimi X-Wings.

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 6..........7...64.....92.1...4..79...3..1.42.......1.6..32....5.4.5......2.......

#                  Singles
#   c28   -  7     X-Wing (finned/Sashimi)   (note: [r7 c7]<>7)
# r67     -  7     X-Wing (finned/Sashimi)   (note: [r89c8]<>7)
 *-----------------------------------------------------------*
 | 6     1     2     | 347   37    34    | 5     8     9     |
 | 3     9     7     | 1     58    58    | 6     4     2     |
 | 4     5     8     | 6     9     2     | 37    1     37    |
 |-------------------+-------------------+-------------------|
 | 1     6     4     | 38    2     7     | 9     5     38    |
 | 78    3     5     | 9     1     6     | 4     2     78    |
 | 2     78    9     | 348   358   3458  | 1     37    6     |
 |-------------------+-------------------+-------------------|
 | 9     78    3     | 2     4     1     | 8-7   6     5     |
 | 78    4     6     | 5     378   389   | 2     39-7  1     |
 | 5     2     1     | 378   6     389   | 378   39-7  4     |
 *-----------------------------------------------------------*
#                  Singles


The two Sashimi X-Wings can be expressed as a chain or with grouped colors.

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    Blue    Green  Blue   Green  Blue  -Blue
(7) [r89c8]-[r6c8]=[r6c2]-[r7c2]=[r7c7]-[r89c8]


Did I do this right? I know it's not bi-directional, but I don't see a way around it.

This doesn't solve your problem, but how about this solution:

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 *-----------------------------------------------------------*
 | 6     1     2     | 347   37    34    | 5     8     9     |
 | 3     9     7     | 1     58    58    | 6     4     2     |
 | 4     5     8     | 6     9     2     | 37*   1     37*   |
 |-------------------+-------------------+-------------------|
 | 1     6     4     | 38    2     7     | 9     5     38    |
 | 78    3     5     | 9     1     6     | 4     2     78*   |
 | 2     78*   9     | 348   358   3458  | 1     37*   6     |
 |-------------------+-------------------+-------------------|
 | 9     78*   3     | 2     4     1     | 78*   6     5     |
 | 78    4     6     | 5     378   389   | 2     379   1     |
 | 5     2     1     | 378   6     389   | 378+  379   4     |
 *-----------------------------------------------------------*


r9c7 is the only guardian against a length 7 conjugate chain, and therefore r9c7=7.

[daj95376]

Hmmm! I thought my grouped conjugate chain of length 5 was sufficient. I included the Blue/Green notation because it could be interpreted as grouped Colors, which is akin to how Simple Sudoku handles the 7s.

I haven't implemented Colors (yet) in the new version of my solver that I'm writing. That's why the two Sashimi X-Wings in the solution above. While cross-checking it with chains, I couldn't decide on the best way to represent it as a chain.

Thanks for the alternate solution ... AND ... sorry about your losing all of your posts under your old account. It should have been my account because then there wouldn't have been any great loss!

[re'born]

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    Blue    Green  Blue   Green  Blue  -Blue
(7) [r89c8]-[r6c8]=[r6c2]-[r7c2]=[r7c7]-[r89c8]


Did I do this right? I know it's not bi-directional, but I don't see a way around it.

I suppose you could just break it up as two nice loops:

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1. [r89c8]-7-[r6c8]=7=[r6c2]-7-[r7c2]=7=[r7c7]-7-[r89c8], => r89c8<>7

2. [r7c7]-7-[r7c2]=7=[r6c2]-7-[r6c8]=7=[r89c8]-7-[r7c7], => r7c7<>7


Or you could combine everything if you use one of Carcul's famous TILA's

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7-[r9c7]-{TILA: [r7c7]-7-[r7c2]=7=[r6c2]-7-[r6c8]=7=[r89c8]-7-[r7c7]; [r7c7]=7=[r7c2]-7-[r6c2]=7=[r6c8]-7-[r89c8]=7=[r7c7]}, => r9c7=7


I like the idea of thinking of this as a grouped broken wing with r9c7 as the sole guardian.