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Another extreme multifish

 
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
PostPosted: Fri May 19, 2017 9:56 pm    Post subject: Another extreme multifish Reply with quote
Code:

+--------------------+------------------+--------------------+
| 7     1     269    | 2458  5689  3    | 289    2469  468   |
| 8     2369  2369   | 1247  1679  2469 | 12379  5     13467 |
| 2369  5     4      | 1278  16789 2689 | 123789 12679 13678 |
+--------------------+------------------+--------------------+
| 23469 7     23569  | 235   356   1    | 359    8     345   |
| 1239  2389  123589 | 23578 4     258  | 6      179   1357  |
| 1346  3468  13568  | 9     35678 568  | 1357   147   2     |
+--------------------+------------------+--------------------+
| 1239  2389  123789 | 6     13589 589  | 4      127   1578  |
| 1346  3468  13678  | 13458 2     458  | 1578   167   9     |
| 5     24689 12689  | 148   189   7    | 128    3     168   |
+--------------------+------------------+--------------------+
Ciao a tutti Paolo
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
PostPosted: Sat May 20, 2017 10:15 am    Post subject: Reply with quote
Code:

+----------------+----------------+----------------+
| 7     1    269 | 2458 5689 3    | 289  2469 468  |
| 8     269  3   | 1247 1679 2469 | 1279 5    1467 |
| 269   5    4   | 178  178  269  | 1378 1269 1378 |
+----------------+----------------+----------------+
| 23469 7    269 | 235  356  1    | 359  8    345  |
| 1239  2389 158 | 3578 4    258  | 6    179  1357 |
| 1346  3468 158 | 9    3578 568  | 1357 147  2    |
+----------------+----------------+----------------+
| 1239  2389 178 | 6    1358 589  | 4    127  1578 |
| 1346  3468 178 | 1358 2    458  | 1578 167  9    |
| 5     2469 269 | 148  189  7    | 128  3    168  |
+----------------+----------------+----------------+
After Multi-Fish pattern with base set of 2,4,6 and 9
16 Truths = {2469R1, 2469R2, 2469R4, 2469R9}
16 Links = {269c3, 24c4, 69c5, 29c7, 46c9,R1C8,R2C2,R2C6,R4C1,R9C2}
19 Eliminations: R2C2<>3,R4C1<>3,R9C2<>8,R3C4<>2,R3C5<>6,R3C5<>9,R3C7<>2,R3C7<>9,R3C9<>6, R5C3<>2,R5C3<>9,R5C4<>2,R6C3<>6,R6C5<>6,R7C3<>2,R7C3<>9,R7C5<>9,R8C3<>6,R8C4<4>
Naked-quads of-1378 at r3c4579=> -1 r3c8, -3 r3c1, -7 r3c8, -8 r3c6
Naked quads of 1578 at r5678c3 => -1 r9c3, -5 r4c3, -8 r9c3

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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Sat May 20, 2017 1:30 pm    Post subject: Reply with quote
Code:
+------------------------+-----------------------+-----------------------+
| 7       1       269    | 2458    5689    3     | 289     2469    468   |
| 8       2369    2369   | 1247    1679    2469  | 12379   5       13467 |
| 2369    5       4      | 1278    16789   269-8 | 123789  269-17  13678 |
+------------------------+-----------------------+-----------------------+
| 2469-3  7       269-35 | (235)   (356)   1     | (359)   8       (345) |
| 1239    2389    123589 | 3578-2  4       (258) | 6       (179)   1357  |
| 1346    3468    13568  | 9       3578-6  (568) | 1357    (147)   2     |
+------------------------+-----------------------+-----------------------+
| 1239    2389    123789 | 6       1358-9  (589) | 4       (127)   1578  |
| 1346    3468    13678  | 1358-4  2       (458) | 1578    (167)   9     |
| 5       2469-8  269-18 | (148)   (189)   7     | (128)   3       (168) |
+------------------------+-----------------------+-----------------------+
Continuous All Cell Loop :
The 16 cells P={R49C4579, R5678C68} is a proper valid subset of
the 16 constraints C={(35)R4, (49)B6, (17)C8, (26)B9, (18)R9, (49)B8, (58)C6, (26)B5}.
Therefore, the set C-P={3r4c1, (35)r4c3, (17)r3c8, 8r9c2, (18)r9c3, 4r8c4, 9r7c5, 8r3c6, 2r5c4, 6r6c5} of 13 candidates is excluded.

HQ(1578)r5678c3; L2C3=3; HQ(1578)r3c4579

Solving P :
1. (26)r4c45 -> (26)r9c79 & r49c3=9!
2. (26)r56c6 -> (26)r78c8 & r3c68=9!
3a. 2r4c4 + 6r6c6 + 9r4c7 + 9r7c6 -> 0 solution via XWing{2C38}
3b. 2r4c4 + 6r6c6 + 9r4c7 + 9r9c5 -> 0 solution via XWing{1C18} -> NP(58)r5c36 -> Swordfish{5R148}
3c. 2r4c4 + 6r6c6 + 9r5c8 + 9r7c6 -> 0 solution via XWing{5R47}
3d. 2r4c4 + 6r6c6 + 9r5c8 + 9r9c5 -> 0 solution via NP(35)r4c57, NP(58)r57c6, Swordfish{6C258}
4a. 2r5c6 + 6r4c5 + 9r4c7 + 9r7c6 + 2L7C8 -> 0 solution
4b. 2r5c6 + 6r4c5 + 9r4c7 + 9r7c6 + 2L9C7 -> 0 solution via NP(69)r9c23, XYWing(358)r6c26.r4c4
4c. 2r5c6 + 6r4c5 + 9r4c7 + 9r9c5 -> 0 solution via XWing{5R47}
4d. 2r5c6 + 6r4c5 + 9r5c8 + 9r7c6 -> 0 solution via XWing{1C18} -> NP(58)r6c36 -> XWing{5C67}
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Ajò Dimonios



Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
PostPosted: Sun May 21, 2017 1:59 pm    Post subject: Reply with quote
I continue from my previous post.
When each of the 2s in pair r4c4, r5c6 are made true in turn, and then the 9 at r1c8 is made true, there is a contradiction, so 9 can be removed.
When each of the 2s in pair r7c8, r9c7 are made true in turn, and then the 5 at r7c5 is made true, there is a contradiction, so 5 can be removed.
If 5 is true in r5c6 then the 9 at r9c2 is both true and false, hence 5 is false and can be eliminated
If 6 is true in r4c1 then the 2 at r7c8 is both true and false, hence 6 is false and can be eliminated
When each of the 2s in pair r4c4, r5c6 are made true in turn, and then the 2 at r2c7 is made true, there is a contradiction, so 2 can be removed.
If 2 is true in r9c2 then the 9 at r1c5 is both true and false, hence 2 is false and can be eliminated

Similarly, contradiction is created by imposing values individually on the cells:
R1C3=2;R1C5=6; R1C8=6; R1C9=4; R1C5=8; R1C5=9; R1C9=8; R2C4=1; R2C7=1; R2C9=1; R2C4=7; R5C2=3; R5C4=3; R5C8=1 and R7C1=9. So these candidates can be eliminated. Solution with basic strategies

Code:

+---------------+----------------+---------------+
| 7    1    69  | 2458 5    3    | 289  24  6    |
| 8    269  3   | 24   1679 2469 | 79   5   467  |
| 269  5    4   | 1278 178  269  | 1378 269 1378 |
+---------------+----------------+---------------+
| 2469 7    269 | 35   356  1    | 359  8   345  |
| 1239 289  158 | 578  4    28   | 6    79  1357 |
| 1346 3468 158 | 9    3578 568  | 1357 147 2    |
+---------------+----------------+---------------+
| 123  2389 178 | 6    138  589  | 4    127 1578 |
| 1346 3468 178 | 1358 2    458  | 1578 167 9    |
| 5    469  269 | 148  189  7    | 128  3   168  |
+---------------+----------------+---------------+

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Ciao a tutti
Paolo
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