17Feb20

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17Feb20

Postby Yogi » Wed Feb 26, 2020 4:22 am

052300000000000760000000000600000480007020000000500000410000005700004000000060000

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Yogi
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Re: 17Feb20

Postby Ajò Dimonios » Wed Feb 26, 2020 4:56 pm

Code: Select all
+-------------+-------------+-----------------+
| 189  5   2  | 3   7   6   | 189   19   4    |
| 1389 389 4  | 2   189 5   | 7     6    1389 |
| 1389 7   6  | 4   189 19  | 25    25   1389 |
+-------------+-------------+-----------------+
| 6    39  5  | 19  139 7   | 4     8    2    |
| 389  4   7  | 6   2   389 | 1359  1359 19   |
| 2    389 1  | 5   4   389 | 39    7    6    |
+-------------+-------------+-----------------+
| 4    1   8  | 7   39  2   | 6     39   5    |
| 7    6   39 | 189 5   4   | 12389 1239 189  |
| 5    2   39 | 189 6   139 | 1389  4    7    |
+-------------+-------------+-----------------+



3r4c2=r4c5-(3=9)r7c5-9r23c5=(9-1)r3c6=(1-3)r9c6=3r56c6=>-3r4c5 + 4 insertions
Finned x-wing 9 (r1 and r5), fin r5c9=9 =>-9r6c7=>stte.
Note that the AIC is definitely a chain of contradiction, r4c5 = 3 is true and false in the same chain.


Paolo
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Re: 17Feb20

Postby Cenoman » Wed Feb 26, 2020 5:38 pm

Couldn't find a one stepper. In two steps:
Code: Select all
 +--------------------+--------------------+------------------------+
 |  189    5     2    |  3     7     6     |  189     19     4      |
 |  1389   389   4    |  2     189   5     |  7       6      1389   |
 |  1389   7     6    |  4     189   19    |  25      25     1389   |
 +--------------------+--------------------+------------------------+
 |  6      39    5    | b19   a19-3  7     |  4       8      2      |
 |  389    4     7    |  6     2     389   |  1359    1359   19     |
 |  2      389   1    |  5     4     389   |  39      7      6      |
 +--------------------+--------------------+------------------------+
 |  4      1     8    |  7    c39    2     |  6       39     5      |
 |  7      6     39   | c189   5     4     |  12389   1239   189    |
 |  5      2     39   | c189   6     139   |  1389    4      7      |
 +--------------------+--------------------+------------------------+

1. (1)r4c5 = r4c4 - (1=893)b8p247 => -3 r4c5; 4 placements & basics

Code: Select all
 +-----------------+-------------------+--------------------+
 |  89*  5    2    |  3     7     6    |  89*    1    4     |
 |  13   8-9  4    |  2     189   5    |  7      6    389   |
 |  13   7    6    |  4     189   19   |  25     25   389   |
 +-----------------+-------------------+--------------------+
 |  6    3    5    |  19    19    7    |  4      8    2     |
 |  8-9  4    7    |  6     2     38   |  1359   35   19    |
 |  2    89*  1    |  5     4     38   |  39*    7    6     |
 +-----------------+-------------------+--------------------+
 |  4    1    8    |  7     3     2    |  6      9    5     |
 |  7    6    39   |  189   5     4    |  1238   23   18    |
 |  5    2    39   |  189   6     19   |  138    4    7     |
 +-----------------+-------------------+--------------------+

2. Skyscraper (9)r1c1 = r1c7 - r6c7 = r6c2 => -9 r2c2, r5c1; ste
Cenoman
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Re: 17Feb20

Postby Cenoman » Wed Feb 26, 2020 5:55 pm

Ajò Dimonios wrote:3r4c2=r4c5-(3=9)r7c5-9r23c5=(9-1)r3c6=(1-3)r9c6=3r56c6=>-3r4c5 + 4 insertions
Finned x-wing 9 (r1 and r5), fin r5c9=9 =>-9r6c7=>stte.
Note that the AIC is definitely a chain of contradiction, r4c5 = 3 is true and false in the same chain.

Hi Paolo,

Your chain can be shortened. To demonstrate the elimination of 3r4c5, your first term is not needed:
(3=9)r7c5 - r23c5 = (9-1)r3c6 = (1-3)r9c6 = (3)r56c6 => -3 r4c5
Now, if you notice that 3r9c6 is in sight of 3r7c5, you can shorten the chain by the last term:
(3=9)r7c5 - r23c5 = (9-1)r3c6 = (1)r9c6 => -3 r9c6, not the same elimination but the same result: +3 r7c5.
And yes, it is a contradiction chain: 3r9c6 -> 1r3c6 -> 9r23c5 -> 3r7c5 => contradiction
Cenoman
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Re: 17Feb20

Postby Ajò Dimonios » Wed Feb 26, 2020 10:43 pm

Using the TDP technique I find two types of two-step solution that use the backdoors r6c2=9 and r5c6=3

P(3r5c6)=>backdoor;
P(3r4c5)=>contradiction;
P(3r6c6)=> contradiction=>solution
or
P(9r6c2)=>backdoor;
P(9r4c2)=>contradiction;
P(9r2c2)=> contradiction=>solution.

Paolo
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