The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|.8.|
 |...|..1|.23|
 |..7|.5.|...|
 |---+---+---|
 |...|2..|.1.|
 |..5|.7.|4..|
 |.7.|..8|...|
 |---+---+---|
 |...|.4.|8..|
 |12.|6..|...|
 |.3.|...|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 234569  14569  b12       | 3479   c2369    234679   | 15679   8       145679   |
| 45689   45689   4689     | 4789    689     1        | 5679    2       3        |
| 234689  14689   7        | 3489    5       23469    | 169     469     1469     |
|--------------------------+--------------------------+--------------------------|
| 4689    4689    3        | 2       69      45       | 5679    1       56789    |
| 2689    1689    5        | 139     7       369      | 4       369     2689     |
| 2469    7      a2-1      | 45     e1369    8        | 23569   3569    2569     |
|--------------------------+--------------------------+--------------------------|
| 5679    569     69       | 13579   4       23579    | 8       35679   12569    |
| 1       2       489      | 6       389     3579     | 359     34579   459      |
| 456789  3       4689     | 15789  d289-1   2579     | 12569   45679   124569   |
*--------------------------------------------------------------------------------*

Skyscraper (2) with Strong link extensions on 1:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 => r6c3, r9c5 <> 1; stte

Leren

[eleven]

Code: Select all

 *---------------------------------------------------------------------*
 | 234569  14569  12    | 3479   2369  234679  | 15679  8      145679  |
 | 45689   45689  4689  | 4789   689   1       | 5679   2      3       |
 | 234689  14689  7     | 3489   5     23469   | 169    469    1469    |
 |----------------------+----------------------+-----------------------|
 | 4689    4689   3     | 2      69    45      | 5679   1      56789   |
 | 2689   #1689   5     |#139    7     369     | 4      369   *2689    |
 | 2469    7     *12    | 45    #1369  8       | 23569  3569   2569    |
 |----------------------+----------------------+-----------------------|
 | 5679    569    69    | 13579  4    *23579   | 8      35679 #12569   |
 | 1       2      489   | 6      389   3579    | 359    34579  459     |
 | 456789  3      4689  | 15789 #1289  2579    |#12569  45679 #124569  |
 *---------------------------------------------------------------------*

x-chain in 1 (marked #) -> 1r5c2=1r7c9
r5c2=1->r6c3=2->r5c9=2, r7c9=1->r7c6=2 => r7c9<>2

[pjb]

Similar short AIC:

(2=1)r6c3 - r6c5 = (1-2)r9c5 = r1c5; => r1c3 <> 2; stte

or fancier:

(1=2)r1c3 - r1c5 = (2-1)r9c5 = r6c5 - (1=2)r6c3 - (2=1)ALS: r4c12 r5c12 r6c1; => r13c2, r5c3 <> 1; stte

Phil

[ArkieTech]

Code: Select all

 after lcls
 *-----------------------------------------------------------------------------*
 | 234569  14569   12      | 3479    2369    234679  | 15679   8       145679  |
 | 45689   45689   4689    | 4789    689     1       | 5679    2       3       |
 | 234689  14689   7       | 3489    5       23469   | 169     469     1469    |
 |-------------------------+-------------------------+-------------------------|
 | 4689    4689    3       | 2       69      45      | 5679    1       56789   |
 | 2689    1689    5       | 139     7       369     | 4       369     2689    |
 | 2469    7      c12      | 45     b1369    8       |d23569   3569    2569    |
 |-------------------------+-------------------------+-------------------------|
 | 5679    569     69      | 13579   4       23579   | 8       35679   12569   |
 | 1       2       489     | 6       389     3579    | 359     34579   459     |
 | 456789  3       4689    | 15789  a189-2   2579    |e2569-1  45679   124569  |
 *-----------------------------------------------------------------------------*
s-wing
1r9c5=r6c5-(1=2)r6c3-r6c7=2r9c7 => -1r9c7 -2r9c5; stte

[daj95376]

Code: Select all

*--------------------------------------------------------------------------------*
| 234569  14569  b12       | 3479   c2369    234679   | 15679   8       145679   |
| 45689   45689   4689     | 4789    689     1        | 5679    2       3        |
| 234689  14689   7        | 3489    5       23469    | 169     469     1469     |
|--------------------------+--------------------------+--------------------------|
| 4689    4689    3        | 2       69      45       | 5679    1       56789    |
| 2689    1689    5        | 139     7       369      | 4       369     2689     |
| 2469    7      a2-1      | 45     e1369    8        | 23569   3569    2569     |
|--------------------------+--------------------------+--------------------------|
| 5679    569     69       | 13579   4       23579    | 8       35679   12569    |
| 1       2       489      | 6       389     3579     | 359     34579   459      |
| 456789  3       4689     | 15789  d289-1   2579     | 12569   45679   124569   |
*--------------------------------------------------------------------------------*

Skyscraper (2) with Strong link extensions on 1:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 => r6c3, r9c5 <> 1; stte

Leren

Hmmm!!! I don't see your second elimination; but, since the first elimination is sufficient, that's all that's important.

I've suggested in the past, when a chain starts with a weak inference, to make it into a discontinuous loop:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3

The elimination follows from the contradiction of the initial assumption, and does not need to be explicitly stated.

[DonM]

Code: Select all

*--------------------------------------------------------------------------------*
| 234569  14569  b12       | 3479   c2369    234679   | 15679   8       145679   |
| 45689   45689   4689     | 4789    689     1        | 5679    2       3        |
| 234689  14689   7        | 3489    5       23469    | 169     469     1469     |
|--------------------------+--------------------------+--------------------------|
| 4689    4689    3        | 2       69      45       | 5679    1       56789    |
| 2689    1689    5        | 139     7       369      | 4       369     2689     |
| 2469    7      a2-1      | 45     e1369    8        | 23569   3569    2569     |
|--------------------------+--------------------------+--------------------------|
| 5679    569     69       | 13579   4       23579    | 8       35679   12569    |
| 1       2       489      | 6       389     3579     | 359     34579   459      |
| 456789  3       4689     | 15789  d289-1   2579     | 12569   45679   124569   |
*--------------------------------------------------------------------------------*

Skyscraper (2) with Strong link extensions on 1:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 => r6c3, r9c5 <> 1; stte

Leren

Hmmm!!! I don't see your second elimination; but, since the first elimination is sufficient, that's all that's important.

I've suggested in the past, when a chain starts with a weak inference, to make it into a discontinuous loop:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3

The elimination follows from the contradiction of the initial assumption, and does not need to be explicitly stated.

Am I missing something? AICs are supposed to always be notated starting with the strong link. The discontinuous AIC will virtually always have the initial strong link 'seeing' the digit for elimination so, unless I have forgotten about an alternative, one could say that all discontinuous AICs start with a weak inference if one chooses to see them that way, but, following the rules of AIC notation, one doesn't notate the weak inference. I may be mistaking the point you're making, but it appears that you are suggesting the notation:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3
over:
(2)r6c3 = SS = (2-1) r9c5 = (1)r6c5

[ArkieTech]

Code: Select all

*--------------------------------------------------------------------------------*
| 234569  14569  b12       | 3479   c2369    234679   | 15679   8       145679   |
| 45689   45689   4689     | 4789    689     1        | 5679    2       3        |
| 234689  14689   7        | 3489    5       23469    | 169     469     1469     |
|--------------------------+--------------------------+--------------------------|
| 4689    4689    3        | 2       69      45       | 5679    1       56789    |
| 2689    1689    5        | 139     7       369      | 4       369     2689     |
| 2469    7      a2-1      | 45     e1369    8        | 23569   3569    2569     |
|--------------------------+--------------------------+--------------------------|
| 5679    569     69       | 13579   4       23579    | 8       35679   12569    |
| 1       2       489      | 6       389     3579     | 359     34579   459      |
| 456789  3       4689     | 15789  d289-1   2579     | 12569   45679   124569   |
*--------------------------------------------------------------------------------*

Skyscraper (2) with Strong link extensions on 1:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 => r6c3, r9c5 <> 1; stte

Leren

Hmmm!!! I don't see your second elimination; but, since the first elimination is sufficient, that's all that's important.

I've suggested in the past, when a chain starts with a weak inference, to make it into a discontinuous loop:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3

The elimination follows from the contradiction of the initial assumption, and does not need to be explicitly stated.

Am I missing something? AICs are supposed to always be notated starting with the strong link. The discontinuous AIC will virtually always have the initial strong link 'seeing' the digit for elimination so, unless I have forgotten about an alternative, one could say that all discontinuous AICs start with a weak inference if one chooses to see them that way, but, following the rules of AIC notation, one doesn't notate the weak inference. I may be mistaking the point you're making, but it appears that you are suggesting the notation:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3
over:
(2)r6c3 = SS = (2-1) r9c5 = (1)r6c5

or:

1r6c5=(1-2)r9c5=r1c5-r1c3=(2-1)r6c3=1r6c5 => 1r6c5; stte

[daj95376]

I've suggested in the past, when a chain starts with a weak inference, to make it into a discontinuous loop:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3

The elimination follows from the contradiction of the initial assumption, and does not need to be explicitly stated.

Am I missing something? AICs are supposed to always be notated starting with the strong link. The discontinuous AIC will virtually always have the initial strong link 'seeing' the digit for elimination so, unless I have forgotten about an alternative, one could say that all discontinuous AICs start with a weak inference if one chooses to see them that way, but, following the rules of AIC notation, one doesn't notate the weak inference. I may be mistaking the point you're making, but it appears that you are suggesting the notation:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 - (1)r6c3
over:
(2)r6c3 = SS = (2-1) r9c5 = (1)r6c5

DonM, you're "preaching to the choir".

I argued a long time ago that Myth Jellies' definition for an AIC states that it must start and end with a strong inference (followed by a conclusion). However, others argued that it was acceptable to call it an AIC when it starts and ends with a weak inference ... a discontinuous loop. The best I could do was insist that including a conclusion was redundant. That is my point here!

[aran]

Am I missing something? AICs are supposed to always be notated starting with the strong link. The discontinuous AIC will virtually always have the initial strong link 'seeing' the digit for elimination so, unless I have forgotten about an alternative, one could say that all discontinuous AICs start with a weak inference if one chooses to see them that way, but, following the rules of AIC notation, one doesn't notate the weak inference.

DonM, you're "preaching to the choir".

I argued a long time ago that Myth Jellies' definition for an AIC states that it must start and end with a strong inference (followed by a conclusion). However, others argued that it was acceptable to call it an AIC when it starts and ends with a weak inference ... a discontinuous loop. The best I could do was insist that including a conclusion was redundant. That is my point here!

The standard AIC has the form x=......=x (call that x=x)
A "non-standard" AIC has the form x-......=x (call that x-=x)
With x=x, there is an endpoint truth x.
With x-=x, there is....nothing...unless the endpoints share a house, in which case there is a contradiction.
In the case of discontinuous loops, the x=x version is usually truncated to x=y where x and y share a house, hence <y> in the starting cell
The x-=y version, where x and y share a house, produces nothing : there is neither endpoint truth nor contradiction.
An inexperienced solver might miss this point.
Example : suppose r1c1=127, and 7r1c1-.......=2r9c1 : wrong conclusion <2>r1c1.
Consequently there are good grounds for regarding the "standard" form as the norm.
Contradictions chains are easily converted into the norm as Don points out, becoming discontinuous loops ie x-....x becomes z=x-.....=x (z : candidates which if false make x true).
Which said, norms are norms and not dogma.

[daj95376]

The standard AIC has the form x=......=x (call that x=x)
A "non-standard" AIC has the form x-......=x (call that x-=x)
With x=x, there is an endpoint truth x.
With x-=x, there is....nothing...unless the endpoints share a house, in which case there is a contradiction.
In the case of discontinuous loops, the x=x version is usually truncated to x=y where x and y share a house, hence <y> in the starting cell
The x-=y version, where x and y share a house, produces nothing : there is neither endpoint truth nor contradiction.
An inexperienced solver might miss this point.
Example : suppose r1c1=127, and 7r1c1-.......=2r9c1 : wrong conclusion <2>r1c1.
Consequently there are good grounds for regarding the "standard" form as the norm.
Contradictions chains are easily converted into the norm as Don points out, becoming discontinuous loops ie x-....x becomes z=x-.....=x (z : candidates which if false make x true).
Which said, norms are norms and not dogma.

I believe you missed the scenario where x-=x has endpoints in the same cell. The contradiction disappears and there is an apparent truth, but there are times when "x" is not true. I learned this the hard way while designing my chain routine. (ronk pointed out the flaw while reviewing my chain scenarios.)

[DonM]

Theory is interesting, but I hope the point is clear that the rule is that (Eureka) AIC notation starts with the strong inference. I believe that one of the important factors behind the active, innovative solving over a period of years on the Eureka forum was the establishment of a common notation standard.

It was the effectiveness of this standard in handling many of the newly 'discovered constructs that led to the preference over nice loop notation. I hope that the newer solvers here will try to adhere to that standard as much as possible.

End of broken-record rant.

[daj95376]

Addendum

When x-...=x is viewed from r-to-l, x=...-x, then it's more apparent that it's a (continuous) AIC loop, where nothing can be determined about the nature of "x".

[ronk]

Code: Select all

*--------------------------------------------------------------------------------*
| 234569  14569  b12       | 3479   c2369    234679   | 15679   8       145679   |
| 45689   45689   4689     | 4789    689     1        | 5679    2       3        |
| 234689  14689   7        | 3489    5       23469    | 169     469     1469     |
|--------------------------+--------------------------+--------------------------|
| 4689    4689    3        | 2       69      45       | 5679    1       56789    |
| 2689    1689    5        | 139     7       369      | 4       369     2689     |
| 2469    7      a2-1      | 45     e1369    8        | 23569   3569    2569     |
|--------------------------+--------------------------+--------------------------|
| 5679    569     69       | 13579   4       23579    | 8       35679   12569    |
| 1       2       489      | 6       389     3579     | 359     34579   459      |
| 456789  3       4689     | 15789  d289-1   2579     | 12569   45679   124569   |
*--------------------------------------------------------------------------------*

Skyscraper (2) with Strong link extensions on 1:

(1-2) r6c3 = SS = (2-1) r9c5 = r6c5 => r6c3, r9c5 <> 1; stte

IMO the proper "discontinuous AIC" for this deduction is:

(1)r6c5 = (1-2)r6c3 = (2)r1c3 - (2)r1c5 = (2-1r9c5 = (1)r6c5 ==> r6c5=1

IOW, for inclusions, the discontinuity should be part of the AIC expression.

[aran]

I believe you missed the scenario where x-=x has endpoints in the same cell. The contradiction disappears and there is an apparent truth, but there are times when "x" is not true. I learned this the hard way while designing my chain routine. (ronk pointed out the flaw while reviewing my chain scenarios.)

Yes a number of scenarios are in effect required to complete the picture :
x-=x where x share a cell : neither truth nor contradiction but a continuous loop (as you say in a later post). x may turn out to be true, but not by virtue of the logic alone
x=x where x share a house, hence x=x-x : continuous loop
x=x where x share a cell : x is true (technically a discontinuous loop but the basic logic - if x is false, then it's true, so it must be true, full stop - is enough)