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[ArkieTech]

Code: Select all

 *-----------*
 |..7|3.5|...|
 |653|...|..4|
 |8.1|..2|.6.|
 |---+---+---|
 |..8|9..|...|
 |1..|.4.|..2|
 |...|..1|6..|
 |---+---+---|
 |.1.|8..|4.7|
 |4..|...|856|
 |...|6.4|1..|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 2       4       7      | 3      6      5      | 9      1      8     
 6       5       3      | 1      89     89     | 2      7      4     
 8       9       1      | 4      7      2      | 35     6      35     
------------------------+----------------------+---------------------
a35      267     8      | 9      23     367    |b357    4      1     
 1       67      9-5    |d57     4      3678   |c357    389    2     
 359     27      4      | 257    238    1      | 6      389    359   
------------------------+----------------------+---------------------
 59      1       6      | 8      2359   39     | 4      239    7     
 4       3       29     | 27     1      79     | 8      5      6     
 7       8       259    | 6      2359   4      | 1      239    39     


(5)r4c1 = (5-7)r4c7 = r5c7 - (7=5)r5c4 => -5 r5c3; stte

Phil

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 2     4     7     |  3     6     5     | 9     1     8     |
 | 6     5     3     |  1     89    89    | 2     7     4     |
 | 8     9     1     |  4     7     2     | 35    6     35    |
 *-------------------+--------------------+-------------------|
 | 35    267   8     |  9     23    367   | 357   4     1     |
 | 1     67   a9-5   |ad57    4     3678  |a357  b389   2     |
 | 359   27    4     | c257   238   1     | 6    b389  b359   |
 *-------------------+--------------------+-------------------|
 | 59    1     6     |  8     2359  39    | 4     239   7     |
 | 4     3     29    |  27    1     79    | 8     5     6     |
 | 7     8     259   |  6     2359  4     | 1     239   39    |
 *------------------------------------------------------------*


(9=573)r5c347 - (3=895)b6p589 - (5)r6c4 = (5)r5c4 => -5 r5c3 ; stte

[bat999]

Code: Select all

.-----------------.-------------------.-----------------.
|  2    4     7   |  3     6     5    |  9     1    8   |
|  6    5     3   |  1     89    89   |  2     7    4   |
|  8    9     1   |  4     7     2    |  35    6    35  |
:-----------------+-------------------+-----------------:
| b35   267   8   |  9    c23    367  | b357   4    1   |
| 1     67   g59  | h57    4     3678 | a35-7  389  2   |
| 359   27    4   |  257   238   1    |  6     389  359 |
:-----------------+-------------------+-----------------:
| 59    1     6   |  8    d2359  39   |  4     239  7   |
| 4     3    f29  | e27    1     79   |  8     5    6   |
| 7     8     259 |  6    d2359  4    |  1     239  39  |
'-----------------'-------------------'-----------------'

AIC: (7)r5c7 - (7=35)r4c17 - (3=2)r4c5 - (2)r79c5 = r8c4 - (2=9)r8c3 - (9=5)r5c3 - (5=7)r5c4 - (7)r5c7 => -7 r5c7; stte

[SteveG48]

AIC: (7)r5c7 - (7=35)r4c17 - (3=2)r4c5 - (2)r79c5 = r8c4 - (2=9)r8c3 - (9=5)r5c3 - (5=7)r5c4 - (7)r5c7 => -7 r5c7; stte

Good one, Bat, but notice that if you drop the first and last terms you get:

(7=35)r4c17 - (3=2)r4c5 - (2)r79c5 = r8c4 - (2=9)r8c3 - (9=5)r5c3 - (5=7)r5c4 => -7 r5c7

You get the same elimination with a pincer attack, and your chain is a bit more compact.

[bat999]

... a pincer attack...

You saw a pincer.
I saw a Type 1 Discontinuous Nice Loop and expressed it as an AIC.

[SteveG48]

... a pincer attack...

You saw a pincer.
I saw a Type 1 Discontinuous Nice Loop and expressed it as an AIC.

Indeed you did. (The shortened solution is also an AIC.) I just think that it's always nice to look at your solution and see if there's a way to make it shorter and/or simpler. If nothing else, you learn alternate ways of doing things, and that's always a good thing.

[daj95376]

I saw a Type 1 Discontinuous Nice Loop and expressed it as an AIC.

Be aware that Type 1 and Type 2 Discontinuous Loops can be expressed using Eureka notation, but most people choose to express the eliminations using shorter/equivalent Eureka notation for an AIC.

Code: Select all

 +--------------------------------------------------------------+
 |  2     4     7     |  3     6     5     |  9     1     8     |
 |  6     5     3     |  1     89    89    |  2     7     4     |
 |  8     9     1     |  4     7     2     |  35    6     35    |
 |--------------------+--------------------+--------------------|
 |  35    267   8     |  9     23    367   |  357   4     1     |
 |  1     67    59    |  57    4     3678  |  357   389   2     |
 |  359   27    4     |  257   238   1     |  6     389   359   |
 |--------------------+--------------------+--------------------|
 |  59    1     6     |  8     2359  39    |  4     239   7     |
 |  4     3     29    |  27    1     79    |  8     5     6     |
 |  7     8     259   |  6     2359  4     |  1     239   39    |
 +--------------------------------------------------------------+
 # 51 eliminations remain


Code: Select all

 Type 1 Discontinuous Loop: 5r7c1 - 5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1 - 5r7c1

 equivalent AIC:                    5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1  =>  -5 r7c1


Code: Select all

 Type 2 Discontinuous Loop:         5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1 - r7c1 = 5r9c3

 shorter AIC:                       5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1  =>  -5 r7c1


Here, both the Type 1 and Type 2 Discontinuous Loops were replaced by the same AIC. In the case of the Type 2 Discontinuous Loop, the assignment =5r9c3 was replaced with the elimination -5r7c1.

Two Type 3 Discontinuous Loops to get both eliminations from an AIC.

Code: Select all

 l-to-r:         2r4c2 = r4c5 - r6c4 = r8c4 - r8c3 = (2-5)r9c3 = r5c3 - r5c4 = (5-7)r6c4 = 7r6c2 - 7r4c2
 r-to-l: 2r6c2 - 2r4c2 = r4c5 - r6c4 = r8c4 - r8c3 = (2-5)r9c3 = r5c3 - r5c4 = (5-7)r6c4 = 7r6c2

 AIC:            2r4c2 = r4c5 - r6c4 = r8c4 - r8c3 = (2-5)r9c3 = r5c3 - r5c4 = (5-7)r6c4 = 7r6c2  =>  -2 r6c2 & -7 r4c2


_

[Marty R.]

Identical solution as Phil's.

[Leren]

Also same as Phil : M Wing Type 7B.

Leren

[bat999]

... but most people choose to express the eliminations using shorter/equivalent Eureka notation for an AIC...

Yes.

This shows the contradiction.
(7)r5c7 - (7=35)r4c17 - (3=2)r4c5 - (2)r79c5 = r8c4 - (2=9)r8c3 - (9=5)r5c3 - (5=7)r5c4 - (7)r5c7

This uses the forcing chain alalogy.
5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1

[Ngisa]

Code: Select all

+-------------+---------------+-------------+
| 2   4   7   | 3   6    5    | 9   1   8   |
| 6   5   3   | 1   89   89   | 2   7   4   |
| 8   9   1   | 4   7    2    | 35  6   35  |
+-------------+---------------+-------------+
| 35  b267 8   | 9   c23   367  | 357 4   1   |
| 1   6-7  g59  | h57  4    3678 | 357 389 2   |
| 359 a27  4   | 25-7 238  1    | 6   389 359 |
+-------------+---------------+-------------+
| 59  1   6   | 8   d2359 39   | 4   239 7   |
| 4   3   f29  | e27  1    79   | 8   5   6   |
| 7   8   259 | 6   d2359 4    | 1   239 39  |
+-------------+---------------+-------------+


(7=2)r6c2-r4c2=r4c5-r79c5=r8c4-(2=9)r8c3-(9=5)r5c3-(5=7)r5c4 => -7r5c2,r6c4; stte

Clement

[DonM]

... a pincer attack...

You saw a pincer.
I saw a Type 1 Discontinuous Nice Loop and expressed it as an AIC.

Indeed you did. (The shortened solution is also an AIC.) I just think that it's always nice to look at your solution and see if there's a way to make it shorter and/or simpler. If nothing else, you learn alternate ways of doing things, and that's always a good thing.

@Batt999
An important distinction is being missed here. There is Nice Loop notation and there is Eureka Alternating Inference Chain (AIC) notation. By the very name, Nice Loop Notation, you are always finding/notating a loop whether it is continuous or discontinuous. Alternating Inference Chain notation, by its name, will usually be expressed as a chain since most of the time you are dealing with discontinuities. However, it will be expressed as a loop only if the chain is continuous.

Therefore, with Eureka AIC notation, discontinuities are never expressed as a loop ie. the weak link at both ends of the chain are NOT notated. It is not discretionary to express them as a loop. And just for further clarity, there is no such thing as a Nice Loop in AIC notation; if there is a continuity, then there is just a loop.

[daj95376]

@Batt999
An important distinction is being missed here. There is Nice Loop notation and there is Eureka Alternating Inference Chain (AIC) notation. By the very name, Nice Loop Notation, you are always finding/notating a loop whether it is continuous or discontinuous. Alternating Inference Chain notation, by its name, will usually be expressed as a chain since most of the time you are dealing with discontinuities. However, it will be expressed as a loop only if the chain is continuous.

Therefore, with Eureka AIC notation, discontinuities are never expressed as a loop ie. the weak link at both ends of the chain are NOT notated. It is not discretionary to express them as a loop. And just for further clarity, there is no such thing as a Nice Loop in AIC notation; if there is a continuity, then there is just a loop.

Aack!!! I also thought this way, but found an exception. Consider my Type 2 Discontinuous Loop posted earlier in this thread.

Code: Select all

 Type 2 Discontinuous Loop: 5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1 - r7c1 = 5r9c3

 shorter AIC:               5r9c3 = r5c3 - (5=7)r5c4 - r5c7 = (7-5)r4c7 = 5r4c1  =>  -5 r7c1


I showed how it could be replaced by a shorter AIC, but there is nothing wrong with it being an AIC. All it needs is the conclusion: "=> -29 r9c3".

_

[bat999]

...Therefore, with Eureka AIC notation, discontinuities are never expressed as a loop ie. the weak link at both ends of the chain are NOT notated...

Hi
Sudopedia explains using Eureka notation with AICs here ---> http://sudopedia.enjoysudoku.com/Eureka.html
The final example on the page is:
(1)r5c4-(1=4)r5c8-(4)r9c8=(4-1)r7c7=(1)r7c4-(1)r5c4 => r5c4<>1