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very extreme I

 
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
PostPosted: Tue Aug 15, 2017 8:54 pm    Post subject: very extreme I Reply with quote
Hi everyone

Code:

+-------+-------+-------+
| . . . | . . 1 | . 4 . |
| . . . | 6 . . | 8 . . |
| . . 3 | . 2 . | . . 9 |
+-------+-------+-------+
| . 5 . | . 7 . | . . 2 |
| . . . | . . 4 | . 6 . |
| . . . | 8 . . | 1 . . |
+-------+-------+-------+
| . 7 6 | . 3 . | . . . |
| 9 3 . | . . . | . . 5 |
| 4 . 5 | . . . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Ciao a Tutti

Paolo
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
PostPosted: Thu Aug 17, 2017 10:42 am    Post subject: Reply with quote
Hi everyone


Code:

+------------------+------------------+--------------------+
| 25678 2689 2789  | 3579  589  1     | 23567 4      367   |
| 1257  1249 12479 | 6     459  3579  | 8     12357  137   |
| 15678 1468 3     | 457   2    578   | 567   157    9     |
+------------------+------------------+--------------------+
| 1368  5    1489  | 139   7    369   | 349   389    2     |
| 12378 1289 12789 | 12359 159  4     | 3579  6      378   |
| 2367  2469 2479  | 8     569  23569 | 1     3579   347   |
+------------------+------------------+--------------------+
| 128   7    6     | 12459 3    2589  | 249   1289   148   |
| 9     3    128   | 1247  1468 2678  | 2467  1278   5     |
| 4     128  5     | 1279  1689 26789 | 23679 123789 13678 |
+------------------+------------------+--------------------+

Play this puzzle online at the Daily Sudoku site



Found Multi-Fish pattern with base set of 1,4,6 and 8

18 Truths = {1468R3, 1468R4, 148R7, 1468R8, 168R9
11 Eliminations: r3c1≠5, r3c1≠7, r4c1≠3, r4c3≠9, r9c5≠9, r9c9≠3, r9c9≠7, r1c7≠6, r2c8≠1, r5c4≠1, r6c6≠6.

When each of the 1s in pair r2c9, r3c8 are made true in turn, and then the 3 at r6c8 is made true, there is a contradiction, so 3 can be removed.

When each of the 1s in pair r2c9, r3c8 are made true in turn, and then the 5 at r1c4 is made true, there is a contradiction with 1 in R3C8 while with 1 in R2C9 => solution stte.


Ciao a Tutti
Paolo
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Thu Aug 17, 2017 5:22 pm    Post subject: Reply with quote
The following Symmetric Pigeonhole Matrix :
Code:
+---------------------+-----------------------+------------------------+
| 25678   2689  2789  | 3579    (589)  1      | 2357-6  4       (367)  |
| 1257    1249  12479 | 6       (459)  3579   | 8       2357-1  (137)  |
| 168-57  1468  3     | (457)   2      (578)  | (567)   (157)   9      |
+---------------------+-----------------------+------------------------+
| 168-3   5     148-9 | (139)   7      (369)  | (349)   (389)   2      |
| 12378   1289  12789 | 2359-1  (159)  4      | 3579    6       (378)  |
| 2367    2469  2479  | 8       (569)  2359-6 | 1       3579    (347)  |
+---------------------+-----------------------+------------------------+
| 128     7     6     | 12459   3      2589   | 249     1289    148    |
| 9       3     128   | 1247    1468   2678   | 2467    1278    5      |
| 4       128   5     | 1279    168-9  26789  | 23679   123789  168-37 |
+---------------------+-----------------------+------------------------+
5r1c5 9r1c5 8r1c5
5r2c5 9r2c5       4r2c5
            8r3c6       5r3c6 7r3c6
                  4r3c5 5r3c5 7r3c5
                        5r3c7 7r3c7 6r3c7
                        5r3c8 7r3c8       1r3c8
                                    6r1c9       3r1c9 7r1c9
                                          1r2c9 3r2c9 7r2c9
                                                3r5c9 7r5c9 8r5c9
                                                3r6c9 7r6c9       4r6c9
                                                            8r4c8       3r4c8 9r4c8
                                                                  4r4c7 3r4c7 9r4c7
                                                                        3r4c4 9r4c4 1r4c4
                                                                        3r4c6 9r4c6       6r4c6
5r5c5 9r5c5                                                                         1r5c5
5r6c5 9r6c5                                                                               6r6c5
shows that the 16 constraints P={r1256c59, r34c4678} is a subset of the 16 constraints {(16)B35, (48)B26, (57)R3, (39)R4; (59)C5, (37)C9} => -{1r2c8, 1r5c4, 6r1c7, 6r6c6, (57)r3c1, 3r4c1, 9r4c3, 9r9c5, (37)r9c9} [sk-loop]

Note:
Belt 1 : (48)r12c5 -> (16)r3c78 -> (48)r56c9 -> (16)r4c46 -> (48)r12c5
Belt 2 : (48)r3c46 -> (16)r56c5 -> (48)r4c78 -> (16)r12c9 -> (48)r3c45

Solving P from (16)B35, (48)B26} :
1. (48)r12c5 or (48)r3c46 -> 0 solution => Belts 1&2 are false
2a. (48)r1c5.r3c4 + 1r4c4 + 1r2c9 + (59)r25c5 -> 0 solution
2b. (48)r1c5.r3c4 + 1r4c4 + 1r3c8 -> 0 solution
2c. (48)r1c5.r3c4 + 1r5c5 + (59)r25c5 -> 0 solution; r2c5=r3c2=4, r3c6=8
3. 1r4c4 -> 0 solution via the 5s, 8s, 3s and 7s; r5c5=1, r4c6=6
4. 1r3c8 + (59)r16c5 -> 0 solution; r2c9=1 and 1 unique solution via the 5s
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