December 29, 2019

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December 29, 2019

Postby tarek » Sun Dec 29, 2019 8:20 am

Code: Select all
+-------+-------+-------+
| . 6 . | 5 . 7 | . 3 . |
| . . 5 | . . . | 7 . . |
| 3 4 . | . 8 . | . 1 2 |
+-------+-------+-------+
| 4 . . | . . . | . . 1 |
| 5 2 . | . . . | . 8 6 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| 6 . . | . 9 . | . . 8 |
| . . . | 8 1 5 | . . . |
| . 5 . | . . . | . 4 . |
+-------+-------+-------+
.6.5.7.3...5...7..34..8..124.......152.....86...3.6...6...9...8...815....5.....4.


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Re: December 29, 2019

Postby Leren » Sun Dec 29, 2019 8:59 am

Code: Select all
*--------------------------------------------------*
| 129   6    Ed19-2e | 5   c24 7   | 8     3    49 |
| 289   89     5     | 124  3  124 | 7     6    49 |
| 3     4      7     | 6    8  9   | 5     1    2  |
|--------------------+-------------+---------------|
| 4     379    6     | 29   5  8   | 239   279  1  |
| 5     2      39    | 149  7  14  | 349   8    6  |
| 1789b 1789   189   | 3   b24 6   | 249 Aa279a 5  |
|--------------------+-------------+---------------|
| 6     137   D123d  | 47   9  34  | 12    5    8  |
|C279c  379    4     | 8    1  5   | 6    B29   37 |
| 189   5      189   | 27   6  23  | 19    4    37 |
*--------------------------------------------------*

Kraken Cell r6c8 :

2 r6c8 - r6c5 = r1c5              - 2 r1c3;

7 r6c8 - r6c1 = (7-2) r8c1 = r7c3 - 2 r1c3;

9 r6c8 - (9=2) r8c8 - r8c1 = r7c3 - 2 r1c3; => - 2 r1c3; stte

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Re: December 29, 2019

Postby totuan » Sun Dec 29, 2019 10:56 am

Code: Select all
 *-----------------------------------------------------------*
 | 129   6     129   | 5     24    7     | 8     3     49    |
 | 289   89    5     | 124   3     124   | 7     6     49    |
 | 3     4     7     | 6     8     9     | 5     1     2     |
 |-------------------+-------------------+-------------------|
 | 4     379   6     | 29    5     8     | 239   279   1     |
 | 5     2     39    | 149   7     14    | 349   8     6     |
 | 1789  1789  189   | 3     24    6     | 249   279   5     |
 |-------------------+-------------------+-------------------|
 | 6     137   123   | 47    9     34    | 12    5     8     |
 | 279   379   4     | 8     1     5     | 6     29    37    |
 | 189   5     189   | 27    6     23    | 19    4     37    |
 *-----------------------------------------------------------*

My path for this one - an almost coloring 2’s (kite or others name – I’m not sure :D).
Look at, if r4c8<>2 then:
1- (2)r7c3=r7c7-r4c7=r4c4-r6c5=r1c5 => r1c3<>2, r7c3=2
or
2- (2)r7c3=r1c3-r1c5=r6c5-r6c8=r8c8 => r7c7<>2, r7c3=2
or

…………

(2)r7c3=(2-7)r8c1=r6c1-r4c2=r4c8-{almost coloring 2’s: (2)r4c8=[(2)r7c3=r1c3-r1c5=r6c5-r6c8=r8c8]} => r7c7<>2, stte

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Re: December 29, 2019

Postby Mauriès Robert » Sun Dec 29, 2019 11:35 am

Hi all,
Congratulations to Leren for his very simple resolution, but which is btte and we stte.
I have more trouble understanding Totuan's one.
Here is another different one, made with TDP and two conjugated tracks from the 2r8 pair. (See diagram and puzzle)
P(2r8c1) : 2r8c1-> --- ->2r9c6
P(2r8c8) : 2r8c8-> --- ->2r9c6
=> r9c6=2, stte.

Code: Select all
2r8c1->2r1c3->2r6c5->7r6c8->7r4c2->3r8c2->3r9c9->2r9c6
  \                 /            /
    - - - - - - - - - - - - - - -

                            - - - - - - - - - - - - - -
                          /                             \
2r8c8-1r7c7->(18r9c13->2r7c3)->3r5c3->3r4c7->2r6c7->2r4c4->2r9c6
  \                  /                    /
    - - - - - - - - - - - - - - - - - - -


puzzle: Show
Image

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Re: December 29, 2019

Postby eleven » Sun Dec 29, 2019 3:15 pm

Code: Select all
 *--------------------------------------------------------------*
 |  129    6      129   |  5     24   7     |  8     3     49   |
 |  289    89     5     |  124   3    124   |  7     6     49   |
 |  3      4      7     |  6     8    9     |  5     1     2    |
 |----------------------+-------------------+-------------------|
 |  4    ba379    6     |  2-9   5    8     | b239  a279   1    |
 |  5      2      39    |  149   7    14    |  349   8     6    |
 |  1789   1789   189   |  3     24   6     |  249   279   5    |
 |----------------------+-------------------+-------------------|
 |  6     *137   A123   |  47    9    34    | B12    5     8    |
 | B279   *379    4     |  8     1    5     |  6    A29    37   |
 |  189    5      189   |  27    6    23    |  19    4     37   |
 *--------------------------------------------------------------*

A: 2r8c8 & 23b8p325 - (3|2=79)r4c28
B: 2r7c7 & 27b8p425 - (7|2=39)r4c27
=> 9r4c4, stte

In a line:
(39=2|7)r4c72 - 2r7c7 & 27b8p425 = 2r8c8 & 23b8p325 - (3|2=79)r4c28 => -9r4c4, stte
[Edit: corrected typo - thanks Robert]
Last edited by eleven on Sun Dec 29, 2019 7:52 pm, edited 2 times in total.
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Re: December 29, 2019

Postby Mauriès Robert » Sun Dec 29, 2019 4:59 pm

Whoops ... I hadn't seen the triplet 237r9c469 !
So my resolution becomes simpler obviously (see diagram).
P(2r8c1) : 2r8c1-> --- ->2r4c4
P(2r8c8) : 2r8c8-> --- ->2r4c4
=> r4c4=2 (so r9c6=2), stte

Code: Select all
        >7r6c1->39r4c2
       /              \
2r8c1->                 ->2r4c4
       \              /
         >2r7c7->39r4c7


2r8c8->2r7c3->3r5c3->79r4c2->2r4c4
       \                   /
        >79r4c8  - - - - -

So it's the same resolution as Eleven. (Attention Eleven you have some typing errors)
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Re: December 29, 2019

Postby Cenoman » Sun Dec 29, 2019 8:04 pm

Code: Select all
 +----------------------+-------------------+-------------------+
 | a129#   6      129*  |  5     24*  7     |  8     3     49   |
 |  289    89     5     |  124   3    124   |  7     6     49   |
 |  3      4      7     |  6     8    9     |  5     1     2    |
 +----------------------+-------------------+-------------------+
 |  4     B379    6     |  29    5    8     |  239  A279#  1    |
 |  5      2      39    |  149   7    14    |  349   8     6    |
 | C1789   1789   189   |  3     24*  6     | x249#  279*  5    |
 +----------------------+-------------------+-------------------+
 |  6      137    123*  |  47    9    34    | y12*   5     8    |
 | D79-2   379    4     |  8     1    5     |  6    z29*   37   |
 |  189    5      189   |  27    6    23    |  19    4     37   |
 +----------------------+-------------------+-------------------+

7-link oddagon (2)r167, c468, b9 having three guardians
(2)r1c1
(2-7)r4c8 = r4c2 - r6c1 = (7)r8c1
(2)r6c7 - r7c7 = (2)r8c8
=> -2 r8c1; ste
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Re: December 29, 2019

Postby SpAce » Mon Dec 30, 2019 2:09 am

Hi totuan and Robert,

totuan wrote:My path for this one - an almost coloring 2’s (kite or others name – I’m not sure :D).

Nice move! Not that it matters one bit, but if you're interested, I'd call it Almost X-Chain (or Almost Finned Swordfish with fish notation). "Almost Coloring" is not incorrect, but it's not very specific as it could mean anything (Simple Coloring, Multi-Coloring, X-Coloring, 3D Medusa, GEM, Full Tagging...). In this case Simple Coloring would not work (not all conjugate links), so you'd need at least Multi-Coloring or X-Coloring.

Mauriès Robert wrote:I have more trouble understanding Totuan's one.

Let me try to explain. It's a nice example of using a nested AIC (in this case an X-Chain) as a node within an AIC. Below I've changed the colors for demonstration purposes:

totuan wrote:(2)r7c3=(2-7)r8c1=r6c1-r4c2=r4c8-{almost coloring 2’s: (2)r4c8=[(2)r7c3=r1c3-r1c5=r6c5-r6c8=r8c8]} => r7c7<>2, stte

If it weren't for the spoiler 2r4c8 we'd have an X-Chain with end points 2r7c3 and 2r8c8, which would eliminate 2r7c7 (and 2r8c1). In other words it's an Almost X-Chain with the strong link: [X-Chain]=2r4c8. To make it eliminate something both sides must prove the same eliminations, as usual. The green part does it for the spoiler side. It's perhaps a bit clearer if reversed:

[(2)r7c3 = r1c3 - r1c5 = r6c5 - r6c8 = (2)r8c8] = (2-7)r4c8 = r4c2 - r6c1 = (7-2)r8c1 = (2)r7c3 => -2 r7c7,r8c1; stte

Note that the nested X-Chain as a whole is the first node of the outer AIC. The second node is the strongly linked spoiler 2r4c8. One or the other must be true. Without the [brackets] we'd have a violation of AIC rules because of two adjacent strong links (=). Now we don't because the bracketed part is a single boolean node (true or false), despite being an AIC internally.

As a matrix (the first three rows forming the Almost X-Chain):

6x6 TM: Show
Code: Select all
 2r7c3 2r1c3
       2r1c5 2r6c5
 2r8c8       2r6c8 2r4c8
                   7r4c8 7r4c2
                         7r6c1 7r8c1
 2r7c3                         2r8c1
------------------------------------
-2r7c7,
-2r8c1

Note that the end-points also get -2 r8c1. In fact, we could shorten the chain to get just that:

[(2)r7c3 = r1c3 - r1c5 = r6c5 - r6c8 = (2)r8c8] = (2-7)r4c8 = r4c2 - r6c1 = (7)r8c1 => -2 r8c1; stte

Or if one likes it really short, it could be written as an Almost Finned Swordfish:

(2)C358\r16[r8b7] = (2-7)r4c8 = r4c2 - r6c1 = (7)r8c1 => -2 r8c1; stte

5x5 TM: Show
Code: Select all
 2r7c3 2r1c3
       2r1c5 2r6c5
 2r8c8       2r6c8 2r4c8
                   7r4c8 7r4c2
 7r8c1                   7r6c1
------------------------------
-2r8c1

From the matrix it's easy to see that it could also be written as a Kraken Column (2C8):

(2-7)r4c8 = r4c2 - r6c1 = (7)r8c1
||
(2)r6c8 - r6c5 = r1c5 - r1c3 = (2)r7c3
||
(2)r8c8


And from that it's easy to see that there are two other ways to split it as an Almost-AIC:

[(2)r7c3 = r1c3 - r1c5 = r6c5 - r6c8 = (2-7)r4c8 = r4c2 - r6c1 = (7)r8c1] = (2)r8c8 => -2 r8c1

[(2)r8c8 = (2-7)r4c8 = r4c2 - r6c1 = (7)r8c1] = (2)r6c8 - r6c5 = r1c5 - r1c3 = (2)r7c3 => -2 r8c1

The latter could be called Almost L2-Wing.

Hope this helped to get an idea how Almost-AICs work. Note that an Almost-AIC is the strongly linked combo [AIC]=Spoiler, i.e. the pattern that exists in the grid. The complete outer chain that contains an Almost-AIC is still an AIC. Similarly the nested [AIC] node is an actual AIC (within the context of the outer chain, not in the grid). Of course, if the pattern works without any further chaining, like with the spoiler 2r8c8 above, then it's both an Almost-AIC and an AIC (kind of like a finned fish where the fin sees the elimination directly).
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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