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[tarek]

Code: Select all

+-------+-------+-------+
| 8 . . | . . . | . . 4 |
| . 9 . | . . . | . 8 . |
| . 1 . | 3 . 7 | . 6 . |
+-------+-------+-------+
| 3 . . | . . . | . . 5 |
| 2 . 7 | 5 . 8 | 9 . 1 |
| . . 1 | . . . | 6 . . |
+-------+-------+-------+
| . . . | . 3 . | . . . |
| . . . | 1 . 6 | . . . |
| . . 2 | . 4 . | 5 . . |
+-------+-------+-------+
8.......4.9.....8..1.3.7.6.3.......52.75.89.1..1...6......3.......1.6.....2.4.5..


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[SpAce]

Code: Select all

.-----------------.-------------------.--------------------.
| 8     2    3    |  6     9     1    | 7      5      4    |
| 7     9    6    | b24    25   b245  | 1      8      3    |
| 45    1    45   |  3     8     7    | 2      6      9    |
:-----------------+-------------------+--------------------:
| 3     6    89   |  2479  1   ab2[4] | 8-4    247    5    |
| 2     4    7    |  5     6     8    | 9      3      1    |
| 59    58   1    |  2479  27    3    | 6      247    278  |
:-----------------+-------------------+--------------------:
| 16   c578  4589 | c278   3    c25   | c8(4)  12479  2678 |
| 459   578  4589 |  1     257   6    |  3     2479   278  |
| 16    3    2    |  78    4     9    |  5     17     678  |
'-----------------'-------------------'--------------------'

(4)r4c6 = (4,2)r2c64,(2)r4c6 - (2=5784)r7c2467 => -4 r4c7; stte

7x7 PM: Show

Code: Select all

 4r4c6 2r4c6
       2r7c6 5r7c6
 4r4c6 ........... 4r2c6
                   4r2c4 2r2c4
 4r7c7 ....................... 8r7c7
             5r7c2 ........... 8r7c2 7r7c2
                         2r7c4 8r7c4 7r7c4
==========================================
-4r4c7

[Cenoman]

Code: Select all

 +---------------------+---------------------+----------------------+
 |  8     2     3      |  6      9     1     |  7    5       4      |
 |  7     9     6      | b24     25   c245   |  1    8       3      |
 |  45    1     45     |  3      8     7     |  2    6       9      |
 +---------------------+---------------------+----------------------+
 |  3     6     89     |  2479   1   Bd24    |  8-4  247     5      |
 |  2     4     7      |  5      6     8     |  9    3       1      |
 |  59    58    1      |  2479   27    3     |  6    247     278    |
 +---------------------+---------------------+----------------------+
 |  16   z578   4589   |za278    3   zA25    | z48   12479   2678   |
 |  459   578   4589   |  1     y257   6     |  3    2479    278    |
 |  16    3     2      |  78     4     9     |  5    17      678    |
 +---------------------+---------------------+----------------------+

Kraken box (2)b8p135
(2)r7c4 - (2=4)r2c4 - r2c6 = (4)r4c6
(2)r7c6 - (2=4)r4c6
(2)r8c5 - (2=5784)r7c2467
=> -4 r4c7; ste

Comparison to SpAce's solution:

Hidden Text: Show

At the moment of posting my solution, I wandered how similar it was to SpAce's.
To compare, I draw the matrix 8x8 TM (or PM)

Code: Select all

4r4c6 4r2c6
      4r2c4 2r2c4
4r4c6             2r4c6
            2r7c4 2r7c6 2r8c5
                        2r7c6 5r7c6
4r7c7                               8r7c7
                              5r7c2 8r7c2 7r7c2
                        2r7c4       8r7c4 7r7c4

in which the last three rows can be condensed to:

4r7c7                                8r7c7
                        2r7c4 5r7c2 78r7c24

Same condensation can be made on SpAce's matrix, showing that his solution could be written as a Kraken AALS (2578)r7c24, or an almost-almost naked pair:
(78)r7c24 - (8=4)r7c7
(2)r7C4 - (2=4)r2c4 - r2c6 = (4)r4c6
(5)r7c2 - (5=2)r7c6 - (2=4)r4c6
=> -4 r4c7

[SpAce]

Hi Cenoman,

Nice variant and good analysis! This is indeed an interesting puzzle. Even though there probably aren't many reasonable possibilities for totally different solutions, there are still several ways to see it, as you just demonstrated. For example, I do consider your solution distinct from mine, and a perfectly good one too, because it's definitely a different and valid way to spot it.

The similarity becomes apparent only when you write it into a matrix like you did. Then it's possible to see that you could freely remove the 2b8 matrix row and adjust the columns accordingly to end up with an equivalent to my matrix. So, from that point of view they are equivalent, but only after such an optimization, which would obviously make it different from how it was originally seen or intended.

Btw, I don't really like the way I wrote my matrix originally. This might be easier to follow:

7x7 PM: Show

Code: Select all

 4r4c6 4r2c6
       4r2c4 2r2c4
 4r7c7 ........... 8r7c7
             2r7c4 8r7c4 7r7c4
                   8r7c2 7r7c2 5r7c2
                               5r7c6 2r7c6
 4r4c6 ............................. 2r4c6
==========================================
-4r4c7

Your point about the Kraken AALS is also interesting.

Same condensation can be made on SpAce's matrix, showing that his solution could be written as a Kraken AALS (2578)r7c24, or an almost-almost naked pair:
(78)r7c24 - (8=4)r7c7
(2)r7c4 - (2=4)r2c4 - r2c6 = (4)r4c6
(5)r7c2 - (5=2)r7c6 - (2=4)r4c6
=> -4 r4c7

Indeed. That's another valid way to see it. Another (and closer to my original) is to see it directly as a Kraken ALS (2578)r7c246 or (25784)r7c2467:

(5784)r7c2467
(2)r7c4 - (2=4)r2c4 - r2c6 = (4)r4c6
(2)r7c6 - (2=4)r4c6
=> -4 r4c7

as an AIC with an embedded chain fragment: Show

(4)r4c6 = (2r4c6 & [+4r2c6 - (4=2)r2c4]) - (2=5784)r7c2467 => -4 r4c7; stte

Yours would be the same if you changed the last line of your kraken a bit. Btw, that's an interesting case of an ALS, because it's actually used much more like an AALS, since both instances of the digit 2 must be handled separately. I'm pretty sure it still must be called ALS because it has +1 digits than cells (unlike your real AALS that has +2).

One variant that hasn't been mentioned is the Death Blossom with (257)r8c5 as the stem cell. I didn't spot it but Hodoku did. I was actually expecting you to use that since you're typically good at spotting DBs (I'm not):

Death Blossom (found by Hodoku):

(2)r8c5 - (2=5784)r7c2467
(5)r8c5 - (5=24)r74c6
(7)r8c5 - (7=24)b5p83
=> -4 r7c7; stte

That's a pretty neat one. The matrix is the same size but a TM instead of a PM (unlike yours and mine). Not really sure if it makes a difference, but I've been thinking that anything writable as a PM is more like a "pure" AIC/kraken, while a TM is a bit (or sometimes much) more nettish. The difference is that TMs have "triplets" in Allan Barker's terminology; in this case two: 2r4c6 and 5r7c6. Would you agree with that assessment?

(My point is that the PM/TM label could be used as an indication of the complexity of a move. PMs seem inherently simpler because they have a single cover set per column (except the first one, unless they're also symmetric, i.e. Rank 0), which makes at least rank calculations much more straight-forward. Added: I guess that's not entirely true, since there can still be base triplets, as in my solution: 4r4c6 = 2r4c4 & 4r2c6.)

Death Blossom: 7x7 TM: Show

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 4r4c6 2r4c6
       2r7c6 5r7c6
       2r6c5 ..... 7r6c5
             5r8c5 7r8c5 2r8c5
 4r7c7 ....................... 8r7c7
                         2r7c4 8r7c4 7r7c4
             5r7c2 ........... 8r7c2 7r7c2
==========================================
-4r4c7