Easter Egg

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Easter Egg

Postby eleven » Sun Apr 01, 2018 12:41 am

Code: Select all
 +-------+-------+-------+
 | . . . | . 1 8 | 3 . . |
 | . . 9 | 5 . . | . 6 . |
 | . 2 3 | . . . | . . 9 |
 +-------+-------+-------+
 | 6 9 . | . . . | . . 8 |
 | 7 . . | . . . | . 3 5 |
 | 2 . . | . . . | . 9 4 |
 +-------+-------+-------+
 | 3 6 . | . . . | 1 8 . |
 | . 5 . | . . 7 | . . . |
 | . . 7 | 2 6 . | . . . |
 +-------+-------+-------+
eleven
 
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Re: Easter Egg

Postby Leren » Sun Apr 01, 2018 1:55 am

Code: Select all
*-------------------------------------*
| 5 4  6  | 9    1      8    | 3  7 2 |
| 8 7  9  | 5    23     23   | 4  6 1 |
| 1 2  3  | 67c a7-4aA b46bB | 8  5 9 |
|---------+------------------+--------|
| 6 9  45 | 37   23457  2345 | 27 1 8 |
| 7 1 e48 | 68d  2489F  2469 | 26 3 5 |
| 2 3 d58 | 1    578   c56C  | 67 9 4 |
|---------+------------------+--------|
| 3 6  2  | 4    59E    59D  | 1  8 7 |
| 4 5  1  | 38   38     7    | 9  2 6 |
| 9 8  7  | 2    6      1    | 5  4 3 |
*-------------------------------------*

Kraken Row 5 Digit 8: 

4 r3c5 - (4=6) r3c6 - (6=5) r6c6 - (5=8) r6c3                - 8 r5c3;

4 r3c5 - (4=6) r3c6 - r3c4 = 6 r5c4                          - 8 r5c4;

4 r3c5 - (4=6) r3c6 - (6=5) r6c6 - (5=9) r7c6 - r7c5 = 9 r5c5 -8 r5c5; => - 4 r3c5; stte

This egg was overcooked, the Yolk was hard :D .

Leren
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Re: Easter Egg

Postby pjb » Sun Apr 01, 2018 3:01 am

Code: Select all
 5       4       6      | 9      1      8      | 3      7      2     
 8       7       9      | 5     g23    f23     | 4      6      1     
 1       2       3      | 67     7-4   a46     | 8      5      9     
------------------------+----------------------+---------------------
 6       9       45     |d37    h23457 e235-4  | 27     1      8     
 7       1       48     | 68     2489   269-4  | 26     3      5     
 2       3      c58     | 1     c578   b56     | 67     9      4     
------------------------+----------------------+---------------------
 3       6       2      | 4      59     59     | 1      8      7     
 4       5       1      | 38     38     7      | 9      2      6     
 9       8       7      | 2      6      1      | 5      4      3     

(4=6)r3c6 - (6=5)r6c6* - (5=7)r6c35^ - (7=3)r4c4~ - r4c6 = r2c6 - (3=2)r2c5# - (2357=4)r4c5*^~# => -4 r3c5, r45c6; stte

Phil
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Re: Easter Egg

Postby eleven » Mon Apr 02, 2018 9:18 am

Code: Select all
 *--------------------------------------------------*
 |  5  4  6    |  9    1       8      |  3    7  2  |
 |  8  7  9    |  5    23      23     |  4    6  1  |
 |  1  2  3    |  67   47      46     |  8    5  9  |
 |-------------+----------------------+-------------|
 |  6  9  45   |  37   23457   2345   |  27   1  8  |
 |  7  1 b48   |  8-6  2489   a2469   | a26   3  5  |
 |  2  3 b58   |  1    578   ca56     |  67   9  4  |
 |-------------+----------------------+-------------|
 |  3  6  2    |  4    59     a59     |  1    8  7  |
 |  4  5  1    |  38   38      7      |  9    2  6  |
 |  9  8  7    |  2    6       1      |  5    4  3  |
 *--------------------------------------------------*
(6=2594)r567c6,r5c7 - (4=85)r56c3 - (5=6)r6c6 => -6r5c4, stte
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Re: Easter Egg

Postby Sudtyro2 » Mon Apr 02, 2018 11:33 am

eleven wrote: (6=2594)r567c6,r5c7 - (4=85)r56c3 - (5=6)r6c6 => -6r5c4, stte

Hi eleven,
Could you elaborate a bit about the first node? I understand it to form an ALS of sorts, but in two houses, as in the Mar 26 puzzle. In both cases, the exclusion digit is seen by all 6s in structure. Other than that, I wouldn't know how to spot such an animal. Are there alternate ways to write it?

SteveC
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Re: Easter Egg

Postby eleven » Mon Apr 02, 2018 12:06 pm

Hi Steve,

the bad news is, that the easy way to spot it is somewhat banned here:
The 6 in r5c4 directly implies 2r5c7 and 5r6c6, then 9r7c6 and 4r5c6. Thus you get the ALS (6=2594)r567c6,r5c7.

But of course, this is a t&e method ...
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Re: Easter Egg

Postby Cenoman » Tue Apr 03, 2018 4:56 pm

Sudtyro2 wrote:Are there alternate ways to write it?


Concern is the multi-sector "ALS".
(6=2594)r567c6,r5c7 - (4=85)r56c3 - (5=6)r6c6 => -6r5c4


eleven's logic can be written using only single-sector structures, several ways of writing may be viewed, but all using krakens. All suggestions below use exactly the same set of cells as eleven's solution

First, the most hated writing (though with the highest clarity):
Code: Select all
6r6c6 5r6c6
      5r6c3 8r6c3
            8r5c3 4r5c3
6r5c7                   2r5c7
6r5c6             4r5c6 2r5c6 9r5c6
      5r7c6                   9r7c6
=> -6 r5c4


This exactly the same writing the kraken cell r5c6:
(2)r5c6 - (2=6)r5c7
(4)r5c6 - (48=5)r56c3 -(5=6)r6c6
(6)r5c6
(9)r5c6 - (95=6)r67c6
=> -6 r5c4

Third idea, the almost-almost hidden pair (26)r5c67:
(26)r5c67
(4)r5c6 - (48=5)r56c3 -(5=6)r6c6
(9)r5c6 - (95=6)r67c6
=> -6 r5c4

or, similarly, the almost-almost hidden triple
(569)r567c6
(2)r5c6 - (2=6)r5c7
(4)r5c6 - (48=5)r56c3 -(5=6)r6c6
(my preference)

Note that
(569)r567c6
(2)r5c6 - (2=6)r5c7
(4)r5c6
is a demo of the derived strong link 4r5c6==6r56c6,r5c7 used in eleven's first node.

Other idea, the AALS r5c367. At least one digit must be True in any subset of three digits out of the AALS digits (kraken-AALS ?):
(6)r5c67
(8)r5c3 - (85=6)r6c36
(9)r5c6 - (95=6)r67c6
=> -6 r5c4

As I quite never used multisector structures, I have a question about naming the node (6=2594)r567c6,r5c7 an "ALS" as eleven did in his response to Steve:
Thus you get the ALS (6=2594)r567c6,r5c7.

To me, with an ALS you get a derived strong link with any two digits it contains. In this one, e.g. the strong links (2=4), (2=5), (4=5) do not exist. Is there a reference that I should read to have no longer doubts ?
Cenoman
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Re: Easter Egg

Postby eleven » Tue Apr 03, 2018 8:06 pm

Cenoman wrote:As I quite never used multisector structures, I have a question about naming the node (6=2594)r567c6,r5c7 an "ALS" as eleven did in his response to Steve:
Thus you get the ALS (6=2594)r567c6,r5c7.

To me, with an ALS you get a derived strong link with any two digits it contains. In this one, e.g. the strong links (2=4), (2=5), (4=5) do not exist. Is there a reference that I should read to have no longer doubts ?

Cenoman,

i agree, that "ALS" is a mistakable term here. Only the absence of the 6 "locks" it, while we are used to have the digits of an ALS in one unit (house, sector), where each 2 digits give a strong link.
On the other hand it defines a strong link (with the 6), and it should be allowed to use it in an AIC (or of course any other chain).

As you know, i am less interested in formulation and namings, but in logical correctness and the possibility to find (and follow) moves manually. So i will not call it ALS again and leave it to others to find a name or definition.
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