The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.8.|...|64.|
 |39.|...|7.8|
 |...|...|.32|
 |---+---+---|
 |..6|9.4|...|
 |.7.|..2|...|
 |15.|37.|...|
 |---+---+---|
 |.43|..1|.5.|
 |6..|.47|39.|
 |9..|2..|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*-------------------------------------------------*
|e257 8 127  | 17    123    39  | 6      4   d59  |
| 3   9 24   | 456   256    56  | 7      1    8   |
| 457 6 147  | 147  a1-8aA b89B |c59     3    2   |
|------------+------------------+-----------------|
|f28  3 6    | 9     158b   4   | 158F   278F 57  |
| 48  7 489  | 156D  1568D  2   | 14589  68E  3   |
| 1   5 2489 | 3     7      68C | 489    268  469 |
|------------+------------------+-----------------|
| 78  4 3    | 68    9      1   | 2      5    67  |
| 6   2 58   | 58    4      7   | 3      9    1   |
| 9   1 57   | 2     356    356 | 48     678  467 |
*-------------------------------------------------*

Kraken Row 4 Digit 8 (Read from right to left):

8 r3c5 - (8=9) r3c6 - (9=5) r3c7 - r1c9 = (5-2) r1c1 = 2 r4c1 - 8  r4c1;

8 r3c5                                                        - 8  r4c5;

8 r3c5 - r3c6 = (8-6) r6c6 = r5c45 - (6=8) r5c8               - 8 r4c78; => - 8 r3c5; stte

Leren

[SteveG48]

Code: Select all

 *---------------------------------------------------------------------*
 |d257    8      127    | 17     123    39     | 6       4      59     |
 | 3      9      24     | 456    256    56     | 7       1      8      |
 |e457    6      147    | 147    18    e89     |e59      3      2      |
 *----------------------+----------------------+-----------------------|
 |d28     3      6      | 9      158    4      | 158     278    57     |
 |c48     7     c489    | 15-6   158-6  2      | 14589 ab68     3      |
 | 1      5     c2489   | 3      7    bf68     | 489    b28-6  b49-6   |
 *----------------------+----------------------+-----------------------|
 | 78     4      3      | 68     9      1      | 2       5      67     |
 | 6      2      58     | 58     4      7      | 3       9      1      |
 | 9      1      57     | 2      356    356    | 48      678    467    |
 *---------------------------------------------------------------------*


6r5c8 = 8r5c8&(68)r6c689 - 8b4p469 = (82-5)r14c1 = (589)r4c167 - (8=6)r6c6 => -6 r5c45,r6c89 ; stte

[eleven]

Similar:

Code: Select all

 *---------------------------------------------------------------*
 |  257   8  127    |  17    123    39    |  6       4     59    |
 |  3     9  24     |  456   256    56    |  7       1     8     |
 |  457   6  147    |  147   18    d89    | c59      3     2     |
 |------------------+---------------------+----------------------|
 |  28    3  6      |  9     158    4     | b158     278   57    |
 | b48    7 b489    |  15-6  158-6  2     | b14589  a68    3     |
 |  1     5  2489   |  3     7     d68    |  489     28-6  49-6  |
 |------------------+---------------------+----------------------|
 |  78    4  3      |  68    9      1     |  2       5     67    |
 |  6     2  58     |  58    4      7     |  3       9     1     |
 |  9     1  57     |  2     356    356   |  48      678   467   |
 *---------------------------------------------------------------*

(6=8)r5c8 - (8=4915)r5c137,r4c7 - (5=9)r3c7 - (9=86)r6c6 => -6r5c45,r6c89; stte

[SpAce]

A follow-up example to the AIC vs Kraken discussion.

original: Show

Code: Select all

.----------------.-------------------.--------------------.
| bc257  8  127  | 17    123     39  |  6       4    c59  |
|   3    9  24   | 456   256     56  |  7       1     8   |
|   457  6  147  | 147   1-8   d(8)9 | d59      3     2   |
:----------------+-------------------+--------------------:
|  b28   3  6    | 9    a15[8]   4   | b158    b278   57  |
|   48   7  489  | 156   1568    2   |  14589  b68    3   |
|   1    5  2489 | 3     7      d6-8 |  489    c268  c469 |
:----------------+-------------------+--------------------:
|   78   4  3    | 68    9       1   |  2       5     67  |
|   6    2  58   | 58    4       7   |  3       9     1   |
|   9    1  57   | 2     356     356 |  48      678   467 |
'----------------'-------------------'--------------------'

AIC:

Code: Select all

(8)r4c5 = (82)r41c1|(86)b6p125 - (59)r1c19&(6)r6c89 = (9|6,8)r3c7,r63c6 => -8 r3c5,r6c6; stte

Kraken Row (8R4):

Code: Select all

(82-5)r41c1 = r1c9 - (5=98)r3c76
||
(8)r4c5
||
(86)b6p125 - r6c89 = (68)r63c6

=> -8 r3c5,r6c6; stte


Matrix (8x8 TM):

Code: Select all

 8r3c6 9r3c6
       9r3c7 9r1c9
             5r1c9 5r1c1
                   2r1c1 2r4c1
 8r4c5                   8r4c1 8r4c78
                               8r5c8  6r5c8
                                      6r6c89 6r6c6
 8r3c6                                       8r6c6
--------------------------------------------------
-8r3c5,r6c6


Code: Select all

.----------------.--------------------.--------------------.
| bc257  8  127  | 17    123     39   |  6       4    c59  |
|   3    9  24   | 456   256     56   |  7       1     8   |
|   457  6  147  | 147   18    d(8)9  | d59      3     2   |
:----------------+--------------------+--------------------:
|  b28   3  6    | 9    a15[8]   4    | b158    b278   57  |
|   48   7  489  | 156   1568    2    |  14589  b68    3   |
|   1    5  2489 | 3     7     d(6)-8 |  489    c268  c469 |
:----------------+--------------------+--------------------:
|   78   4  3    | 68    9       1    |  2       5     67  |
|   6    2  58   | 58    4       7    |  3       9     1   |
|   9    1  57   | 2     356     356  |  48      678   467 |
'----------------'--------------------'--------------------'

AIC:

Code: Select all

(8)r4c5 = (82)r41c1|(86)b6p125 - (59)r1c19&(6)r6c89 = (98)r3c76|(6)r6c6 => -8 r6c6; stte

Kraken Row (8R4):

Code: Select all

(82-5)r41c1 = r1c9 - (5=98)r3c76
||
(8)r4c5
||
(86)b6p125 - r6c89 = (6)r6c6

=> -8 r6c6; stte


Matrix (7x7 TM):

Code: Select all

 8r3c6 9r3c6
       9r3c7 9r1c9
             5r1c9 5r1c1
                   2r1c1 2r4c1
 8r4c5                   8r4c1 8r4c78
                               8r5c8  6r5c8
 6r6c6                                6r6c89
--------------------------------------------
-8r6c6


Three different expressions for the same exact logic, ordered by increasing explicitness. In cases like this when the actual logic is pretty trivial, the most fun is in writing the AIC -- even if the end result is ugly like here. Whether it's easily understandable or not is secondary to me, because for that there are those other options (if need be, the kraken can of course be decompressed too). That should explain my notational philosophy.

PS. The most trivial Kraken -> AIC translation is of course a nested (almost) AIC:

Code: Select all

(#8)r4c5 = [(8=95)r3c67 - r1c9 = (52-8)r14c1 =#= (86)b6p125 - r6c89 = (6)r6c6] => -8 r6c6

...but I don't usually see much value in that option. It's just a kraken in a less readable format, though fitting on one line.

Edits: switched to a single, slightly simpler (and corrected) elimination.

[SpAce]

(6=8)r5c8 - (8=4915)r5c137,r4c7 - (5=9)r3c7 - (9=86)r36c6 => -6r5c45,r6c89; stte

Very pretty! Coming up with something like that is my goal in complex AIC writing. Usually I fail and end up with those horrible split-nodes.

From a pure readability pov, it might be slightly simpler to track if written:

Code: Select all

(6=849)r5c813 - (8|4|9=15)r45c7 - (5=98)r3c76 - (8=6)r6c6 => -6 r5c45,r6c89

That avoids the bent set in two houses, but the price is needing those ugly '|'s. The length is exactly the same.

But, I liked the original. Always nice to avoid the '|'. In fact, why not combine the first two nodes:

Code: Select all

(6=84915)r5c813,r45c7 - (5=98)r3c76 - (8=6)r6c6 => -6r5c45,r6c89

That almost begs to go all in:

Code: Select all

(6=84915)r5c813,r45c7 - (5=986)r3c76,r6c6 => -6r5c45,r6c89

PS. A minor typo in the last node.

[SteveG48]

From a pure readability pov, it might be slightly simpler to track if written:

Code: Select all

(6=849)r5c813 - (8|4|9=15)r45c7 - (5=98)r3c76 - (8=6)r6c6 => -6 r5c45,r6c89

That avoids the bent set in two houses, but the price is needing those ugly '|'s. The length is exactly the same.

Either way works for me, but I prefer your formulation. I don't see the |'s as ugly.

[SpAce]

Code: Select all

(6=849)r5c813 - (8|4|9=15)r45c7 - (5=98)r3c76 - (8=6)r6c6 => -6 r5c45,r6c89

That avoids the bent set in two houses, but the price is needing those ugly '|'s. The length is exactly the same.

Either way works for me, but I prefer your formulation. I don't see the |'s as ugly.

I agree that it's the least offending extra character in its normal use as a digit separator within parentheses (like above). ',' and '&' are already worse because they imply more complexity (split nodes, multi-house sets, ordered tuples, etc). Any other markings are more or less non-standard and best avoided (but not always avoidable). Extra symbols are a price I'm willing to pay for logically correct and compact expressions, but the fewer the better.

So, even though I freely use them all and even invent my own markers when needs arise, I don't particularly like them. To me the cleanest possible AIC doesn't have anything but digits, cells (and cell groups without commas), parentheses, and links -- and the '|' (as a digit separator) if need be. After those comes ',' (as a digit separator implying an ordered tuple), then any of the ',' or '|' or '&' as cell separators (implying split nodes or multi-house sets). I guess that ranking means I should prefer the above formulation too.

Added. Btw, your July 5 solution was an example of a really pretty AIC:

7r1c4 = (47)r78c4 - (4|7=189)b9p256 - (9=7)r3c8 => -7 r1c9,r3c5 ; stte

The expression is simple, yet the logic is non-trivial (the 4 and 7 working in parallel rows). The July 3 one was of course really nice for the same reasons (though a bit more complex), but that was already covered.