September 8, 2016

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September 8, 2016

Postby ArkieTech » Wed Sep 07, 2016 11:24 pm

Code: Select all
 *-----------*
 |6.5|...|...|
 |3..|67.|8..|
 |82.|..5|..3|
 |---+---+---|
 |976|.2.|...|
 |...|...|...|
 |...|.1.|297|
 |---+---+---|
 |1..|7..|.58|
 |..4|.83|..2|
 |...|...|7.4|
 *-----------*


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dan
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Re: September 8, 2016

Postby Leren » Thu Sep 08, 2016 3:16 am

Best I can do is a two stepper, although today's single digit elimination stte list is at 12 sites : 4 r1c2, 8 r1c4, 2 r1c6, 1 r1c7, 4 r2c6, 8 r4c6, 8 r5c8, 2 r7c6, 2 r9c4, 1 r9c6 & 9 r9c6

None is easy to prove - good luck Steve and other stte fans.

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Re: September 8, 2016

Postby ArkieTech » Thu Sep 08, 2016 6:01 am

Hope someone can find an ste. :shock:

Code: Select all
 *--------------------------------------------------------------------*
 | 6      14     5      | 28     3      28     | 14     7      9      |
 | 3      149   e19     | 6      7     d14     | 8      2      5      |
 | 8      2      7      | 149    49     5      | 146    146    3      |
 |----------------------+----------------------+----------------------|
 | 9      7      6      | 3458   2      48     | 345    348    1      |
 | 245    1358  f138-2  | 34589  459    7      | 345    348    6      |
 | 45     358    38     | 3458   1      6      | 2      9      7      |
 |----------------------+----------------------+----------------------|
 | 1      369   a239    | 7      46    b249    | 369    5      8      |
 | 7      569    4      | 15     8      3      | 169    16     2      |
 | 25     35689  2389   | 125    56    c129    | 7      136    4      |
 *--------------------------------------------------------------------*
[2r7c3=(2-9)r7c6=(9-1)r9c6=r2c6-r2c3=1r5c3]-2r5c3; lclste
--or--
[(2=1)r2679-(1=8)r24c6-(8=2)r345689c4]-2r9c1; lclste
dan
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Re: September 8, 2016

Postby JC Van Hay » Thu Sep 08, 2016 10:58 am

The key of the puzlle is the hub cell (249)r7c6 strongly coupled to (2r7c3, 4r7c5, 9r9c6)
It leads immediately to Dan's solution!

The simplest(?) stte single-stepper :
Code: Select all
+---------------------+---------------------+---------------+
| 6    14      5      | 28        3    (28) | 14   7      9 |
| 3    149     (19)   | 6         7    (14) | 8    2      5 |
| 8    2       7      | 1(49)     49   5    | 146  16(4)  3 |
+---------------------+---------------------+---------------+
| 9    7       6      | 358(4)    2    (48) | 345  38(4)  1 |
| 245  135(8)  123(8) | 35(49-8)  459  7    | 345  3(48)  6 |
| 45   358     (38)   | 358(4)    1    6    | 2    9      7 |
+---------------------+---------------------+---------------+
| 1    369     (239)  | 7         46   49-2 | 369  5      8 |
| 7    569     4      | 15        8    3    | 169  16     2 |
| 25   35689   2389   | 125       56   129  | 7    136    4 |
+---------------------+---------------------+---------------+
[2r1c6==2r7c3]-2r7c6; stte
Proof :

The forbidding matrix : 2r7c6 => r7c3={}; stte
Code: Select all
2r7c6
2r1c6 8r1c6
      8r4c6 4r4c6               |
            4r456c4 4r3c4       | => [8r4c6==9r5c4]-8r5c4 [cannibalism]
                    9r3c4 9r5c4 |
            4r4c8   4r3c8       4r5c8
                          8r5c4 8r5c8 8r5c23
                                      8r6c3  3r6c3
            4r2c6                                  1r2c6
                                                   1r2c3 9r2c3
2r7c3                                        3r7c3       9r7c3
In other words, the solutions of the 10 constraints {4C48, 8R5, 9C4, R267C3, R124C6} => [2r1c6==2r7c3]-2r7c6 and optionally [8r4c6==9r5c4]-8r5c4; stte
This is to be compared with the 5 constraints of Dan's solution : {1C36, 9C6, 2R7} + {1B8}

The heavy Eureka notation :
[(8=4)r4c6-4r654c4=(4-9)r3c3=9r5c4]-8r5c4
(2=84)r14c6-XWing(4r3456,4r34c8)=(4-8)r5c8=8r5c23-(8=3)r6c3-3r7c3=*[(2=*9)r7c3-(9=14)r2c36-(4=82)r41c6] -> -2r7c6; stte
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Re: September 8, 2016

Postby ArkieTech » Thu Sep 08, 2016 11:56 am

JC Van Hay wrote:The simplest(?) stte single-stepper :


Thanks JC -- it is mind bending time for me
dan
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Re: September 8, 2016

Postby pjb » Thu Sep 08, 2016 1:04 pm

Code: Select all
 6      e14      5      | 28     3     a28     |f14     7      9     
 3      d149    d19     | 6      7     c14     | 8      2      5     
 8       2       7      | 149    49     5      | 146   g146    3     
------------------------+----------------------+---------------------
 9       7       6      | 3458   2     b48     | 345    348    1     
 245    k1358    1238   | 34589 i459    7      |j345  h348    6     
 45      358    l38     | 3458   1      6      | 2      9      7     
------------------------+----------------------+---------------------
 1       369    m239    | 7      469    49-2   | 369    5      8     
 7       569     4      | 159    8      3      | 169    16     2     
 25      35689   2389   | 1259   569    129    | 7      136    4     

(2=8)r1c6 - (8=4)r4c6 - (4=1)r2c6 - (1=4)r2c23^ - (4=1)r1c2* - (1=4)r1c7 - r3c8 = r5c8 - (49=5)r5c5# - (45=3)r5c7 - (135=8)r5c2#* - (8=3)r6c3 - (39=2)r7c3^ => -2 r7c6; stte
                 /   \
             r4c8    r456c4 = r3c4 - (4=9)r3c5 - r5c5


Just for fun, but on reflection it's similar to JC's
Phil
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Re: September 8, 2016

Postby SteveG48 » Thu Sep 08, 2016 4:31 pm

Leren wrote:Best I can do is a two stepper, although today's single digit elimination stte list is at 12 sites : 4 r1c2, 8 r1c4, 2 r1c6, 1 r1c7, 4 r2c6, 8 r4c6, 8 r5c8, 2 r7c6, 2 r9c4, 1 r9c6 & 9 r9c6

None is easy to prove - good luck Steve and other stte fans.

Leren


Thanks, but I threw in the towel last night.
Steve
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