The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|6..|.42|
 |..2|5..|3.7|
 |.4.|7..|6..|
 |---+---+---|
 |...|.8.|.6.|
 |13.|...|.94|
 |.6.|.4.|...|
 |---+---+---|
 |..6|..3|.7.|
 |9.7|..5|4..|
 |31.|..2|...|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.------------------.---------------.------------------.
|d57(8)  579-8 1   | 6     3   89  | 589    4    2    |
| 6      9-8   2   | 5     19  4   | 3      18   7    |
|d5(8)   4     3   | 7     2   189 | 6      158  589  |
:------------------+---------------+------------------:
| 2457   257   459 | 139   8   179 | 125    6    135  |
| 1      3     8   | 2     5   6   | 7      9    4    |
|d257    6     59  | 139   4   179 | 1258  c23   1358 |
:------------------+---------------+------------------:
| 245-8  258   6   | 1489  19  3   | 12589  7    1589 |
| 9     a2(8)  7   | 18    6   5   | 4     b23   138  |
| 3      1     45  | 489   7   2   | 589    58   6    |
'------------------'---------------'------------------'


(8=2)r8c2 - r8c8 = r6c8 - (2=578)r136c1 => -8 r12c2, r7c1; stte

[Cenoman]

Code: Select all

 +-----------------------+--------------------+-----------------------+
 | b578     579-8  1     |  6      3    89    |  589     4     2      |
 |  6       9-8    2     |  5      19   4     |  3       18    7      |
 | b58      4      3     |  7      2    189   |  6       158   589    |
 +-----------------------+--------------------+-----------------------+
 | a2457#   257    459   |  139    8    179   |  125     6     135    |
 |  1       3      8     |  2      5    6     |  7       9     4      |
 | b257*    6      59    |  139    4    179   | a1258#   23*   1358   |
 +-----------------------+--------------------+-----------------------+
 |  245-8* A258#   6     |  1489   19   3     |  12589   7     1589   |
 |  9      B28*    7     |  18     6    5     |  4       23*   138    |
 |  3       1      45    |  489    7    2     |  589     58    6      |
 +-----------------------+--------------------+-----------------------+

5-links oddagon in the 2's (*) with three guardians (#)
(2)r4c1,r6c7 - (257=8)r136c1
(2)r7c2 -(2=8)r8c2
=> -8 r12c2,r7c1; ste

[SpAce]

5-links oddagon in the 2's (*) with three guardians (#)
(2)r4c1,r6c7 - (257=8)r136c1
(2)r7c2 -(2=8)r8c2
=> -8 r12c2,r7c1; ste

I love seeing Oddagon solutions, because I've never spotted one myself. Could it be written as an AIC:

(8=2)r8c2 - r7c2 =[Oddagon]= (r4c1|r6c7) - (257=8)r136c1 => -8 r12c2, r7c1

?

[Cenoman]

I love seeing Oddagon solutions, because I've never spotted one myself. Could it be written as an AIC:

(8=2)r8c2 - r7c2 =[Oddagon]= (r4c1|r6c7) - (257=8)r136c1 => -8 r12c2, r7c1

?

At first I have to give many thanks to SteveC, who made me aware of the oddagon pattern, and made me learn it.

Back to your question. Yes for this particular puzzle, you can write your AIC (similar to UR-AIC)
or (8=2)r8c2 - r7c2 == (r4c1|r6c7) - (257=8)r136c1 => -8 r12c2, r7c1 with symbol "==" meaning "derived strong link". (I'm reluctant to introduce in a logical expression a term that is not a logical variable, since its only value is FALSE).
I said "for this particular puzzle" because the guardians can be grouped into two nodes. When there are three or more guardians, you may need three chains (or more), then the kraken presentation is the clearest. Same concern for URs, DPs, BUGs, BUG-lite's

Anyhow, as often said on this forum, the important is substance. Choose your prefered presententation, provided it is legible and logically robust.

[SpAce]

At first I have to give many thanks to SteveC, who made me aware of the oddagon pattern, and made me learn it.

Well, thanks to both of you then! It's an interesting technique. I just tried my hand at constructing some variants of yours. It seems that there are (in this case) several ways of forming the deadly loop but only one way to place the guardians. Is that generally true? Here's two with 5-links and one with 7-links:

Code: Select all

.-----------------.---------------.------------------.
| 578   5789  1   | 6     3   89  | 589    4    2    |
| 6     89    2   | 5     19  4   | 3      18   7    |
| 58    4     3   | 7     2   189 | 6      158  589  |
:-----------------+---------------+------------------:
| 2457# 257*  459 | 139   8   179 | 125*   6    135  |
| 1     3     8   | 2     5   6   | 7      9    4    |
| 257   6     59  | 139   4   179 | 1258#  23*  1358 |
:-----------------+---------------+------------------:
| 2458  258#  6   | 1489  19  3   | 12589  7    1589 |
| 9     28*   7   | 18    6   5   | 4      23*  138  |
| 3     1     45  | 489   7   2   | 589    58   6    |
'-----------------'---------------'------------------'

.-----------------.---------------.------------------.
| 578   5789  1   | 6     3   89  | 589    4    2    |
| 6     89    2   | 5     19  4   | 3      18   7    |
| 58    4     3   | 7     2   189 | 6      158  589  |
:-----------------+---------------+------------------:
| 2457# 257*  459 | 139   8   179 | 125*   6    135  |
| 1     3     8   | 2     5   6   | 7      9    4    |
| 257*  6     59  | 139   4   179 | 1258#  23   1358 |
:-----------------+---------------+------------------:
| 2458* 258#  6   | 1489  19  3   | 12589* 7    1589 |
| 9     28    7   | 18    6   5   | 4      23   138  |
| 3     1     45  | 489   7   2   | 589    58   6    |
'-----------------'---------------'------------------'

.-----------------.---------------.------------------.
| 578   5789  1   | 6     3   89  | 589    4    2    |
| 6     89    2   | 5     19  4   | 3      18   7    |
| 58    4     3   | 7     2   189 | 6      158  589  |
:-----------------+---------------+------------------:
| 2457# 257*  459 | 139   8   179 | 125*   6    135  |
| 1     3     8   | 2     5   6   | 7      9    4    |
| 257*  6     59  | 139   4   179 | 1258#  23*  1358 |
:-----------------+---------------+------------------:
| 2458* 258#  6   | 1489  19  3   | 12589  7    1589 |
| 9     28*   7   | 18    6   5   | 4      23*  138  |
| 3     1     45  | 489   7   2   | 589    58   6    |
'-----------------'---------------'------------------'

Did I get them right?

Back to your question. Yes for this particular puzzle, you can write your AIC (similar to UR-AIC)
or (8=2)r8c2 - r7c2 == (r4c1|r6c7) - (257=8)r136c1 => -8 r12c2, r7c1 with symbol "==" meaning "derived strong link". (I'm reluctant to introduce in a logical expression a term that is not a logical variable, since its only value is FALSE).

I hear you. The point is to provide an inline explanation to the derived strong link, but I understand if it might cause confusion if there's no clearly defined standard for such. Sometimes it's also unclear what that explanation should be. For example, in the linked puzzle below I had first [BUG+2] because it was the starting pattern but then I changed it into [BUG+1] because it seemed more logical inside the chain (since we have either 1r6c6 or BUG+1)...

http://forum.enjoysudoku.com/august-15-2018-t34990.html#p269219

I guess similar logic would produce something like this here:

(8=2)r8c2 - r7c2 =[Oddagon+2]= (r4c1|r6c7) - (257=8)r136c1

Does that make more sense?

I said "for this particular puzzle" because the guardians can be grouped into two nodes. When there are three or more guardians, you may need three chains (or more), then the kraken presentation is the clearest. Same concern for URs, DPs, BUGs, BUG-lite's

I agree.

Anyhow, as often said on this forum, the important is substance. Choose your prefered presententation, provided it is legible and logically robust.

I agree.

[SpAce]

Experimenting with oddagons led me to this weirdo:

Code: Select all

.-------------------.---------------.-------------------.
| 578     5789  1   | 6     3   89  | 589    4     2    |
| 6      d89    2   | 5    d19  4   | 3     c(1)8  7    |
|e(5)8    4     3   | 7     2   189 | 6     f158!  589  |
:-------------------+---------------+-------------------:
|a457-2#  257  b459 | 139   8   179 | 125    6     135  |
| 1       3     8   | 2     5   6   | 7      9     4    |
| 257*    6     59  | 139   4   179 | 1258   3-2   1358 |
:-------------------+---------------+-------------------:
| 2458*   258   6   | 1489  19  3   | 12589  7     1589 |
| 9       28*   7   | 18    6   5   | 4      23*   138  |
| 3       1    b45  | 489   7   2   | 589   c5(8)  6    |
'-------------------'---------------'-------------------'

Kraken Finned 2-String Kite:


Kite:[(2)r6c1 = r7c1 - r8c2 = (2)r8c8] -> -2 r6c8
||
Fin:(2-4)r4c1=(4,5)r49c3-(5=8,1)r92c8*-(1=9,8)r2c52-(8=5)r3c1-*(8|1|5=0)r3c8 -> contradiction

 -> -2 r4c1

=> -2 r6c8, r4c1; stte

(I guess it's really two moves, but they were found as a combo as presented. I couldn't find a path for the fin to eliminate the target, but it decided to self-destruct instead, which works too.)