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Swordfish challenges

 
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Sun Nov 04, 2012 10:36 pm    Post subject: Swordfish challenges Reply with quote

Keith suggested posting puzzles that seemed to need a swordish:
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?p=31626&sid=3efa30cb40f3a2f3285828d231a16763#31626

This is Menneske 6912567.
Code:

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

Play this puzzle online at the Daily Sudoku site

In case you prefer your grid post-basics:
Code:

+------------------+-------------------+-----------------+
| 357  13457 12347 | 124578 2457 6     | 9    237  12378 |
| 57   1457  9     | 124578 3    12457 | 1258 6    1278  |
| 6    8     1237  | 12579  257  12579 | 1235 237  4     |
+------------------+-------------------+-----------------+
| 379  347   347   | 2479   1    23479 | 6    8    5     |
| 3579 34567 3467  | 479    47   8     | 234  1    239   |
| 1    2     8     | 4569   456  3459  | 7    349  39    |
+------------------+-------------------+-----------------+
| 4    9     137   | 127    8    127   | 123  5    6     |
| 2    1367  1367  | 14567  9    1457  | 1348 347  1378  |
| 8    167   5     | 3      2467 1247  | 124  2479 1279  |
+------------------+-------------------+-----------------+

Play this puzzle online at the Daily Sudoku site

Challenge 1. I couldn't crack this puzzle without using the swordfish. Can you?
(You can achieve the same deletions as the swordfish with a loop as is sometimes (often?) the case:-
(2)r9c8 = r13c8 - r2c79 = r2c46 - r13c5 = r9c5 - loop
But that doesn't seem any easier and so doesn't count!)

Challenge 2. The swordfish merely made a little dent in the puzzle, though just enough. But it still required many moves. Can anyone see a killer move or two that makes the solution not too long?
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JC Van Hay



Joined: 13 Jun 2010
Posts: 364
Location: Charleroi, Belgium

PostPosted: Mon Nov 05, 2012 1:21 pm    Post subject: Reply with quote

The Swordfish, rather than its elimination(s), shows the path ...

#1. "basics"

5 Singles : r6c1=1, r2c8=6, r4c8=8=r9c1, r7c2=9

1-fish(2B6) : 2r5c7=2r5c9 :=> -2r5c45
3-fish(2C358) : 2r3c3=2r1c3-2r1c58=XWing[2r3c5=2r3c8-2r9c8=2r9c5] Loop :=> -2r139c4679
2-fish(3R37) : no elimination
1-fish(5B4) : 5r5c1=5r5c2 :=> -5r5c45
1-fish(6B4) : 6r5c2=6r5c3 :=> -6r5c45

#2. Analysis of the B/B-Plot shows that the strongest digits are 2 and 6. Furthermore, they are weakly coupled in r9c5 ...

Fortunately, r9c5=2->contradiction, while r9c8=2->solution, using only singles.

Correspondingly, a chain[15] not requiring the Swordfish may be written as :

Code:
+---------------------+---------------------------+-----------------------+
| 357   13457  12347  | 124578    2457     6      | 9       237    12378  |
| 57    1457   9      | 124578    3        12457  | 1258    6      1278   |
| 6     8      127(3) | 12579     257      12579  | 125(3)  27(3)  4      |
+---------------------+---------------------------+-----------------------+
| 379   347    347    | 2479      1        23479  | 6       8      5      |
| 3579  34567  3467   | 479       47       8      | 4(23)   1      (239)  |
| 1     2      8      | -9(56-4)  (456)    39(45) | 7       (349)  (39)   |
+---------------------+---------------------------+-----------------------+
| 4     9      17(3)  | 17(2)     8        17(2)  | 1(23)   5      6      |
| 2     1367   1367   | 17(456)   9        17(45) | 1348    (347)  1378   |
| 8     167    5      | 3         7-2(46)  127(4) | (124)   2479   (1279) |
+---------------------+---------------------------+-----------------------+
15 Truths = {3R3 2R5 456R6 23R7 5R8 8N8 9N79 39B6 46B8}
22 Links = {24r9 2c7 3c378 4c68 5c6 6c5 9c9 5n9 6n4589 8n46 9n5 2b8 17b9}
3 Eliminations --> [r6c4<>49 : not required], r9c5<>2

or

6r9c5=6r8c4
      5r8c4=5r8c6
4r9c5=4r8c4=4r8c6=4r9c6----------------------------------------------------------------------AAHS(456)B8
2r9c7=============4r9c7=1r9c7
      6r6c4===================6r6c5
            5r6c6=============5r6c5=5r6c4
                  4r6c6=======4r6c5=4r6c4=4r6c8----------------------------------------------AAHS(456)R6
                                          9r6c8=9r56c9
2r9c9===================1r9c9===================9r9c9==7r9c9
                                          4r8c8========7r8c8=3r8c8
                                                             3r7c7=3r7c3
                                                             3r3c8=3r3c3=3r3c7---------------FXW(3R37)
                                                             3r6c8=======3r5c7=3r56c9
                                          9r6c8================================9r56c9--------HP(39)r56c9
                                                                               2r5c9==2r5c7
2r7c46================================================================================2r7c7
 
=> 4r9c5=6r9c5=2r9c79=2r7c46 :=> -2r9c5

If the Swordfish isn't done first, what remains of it then leads to : 2-fish(2r13c35) :=> r9c8=2; Singles to the end


Alternatively, for example, but after some hard work :

#2. Chain[3] : 4r5c7=(4-9)r6c8=(9-2)r9c8=2r7c7 :=> r5c9=2; 1-fish(9B6) :=> -9r646
#3. Chain[8] : Kraken (347)r8c8 => 3r3c7=3r7c7=4r5c7 :=> -3r5c7; 6 Singles
Code:
+----------------------+-----------------------+---------------------+
| 357   13457   12347  | 14578   2457    6     | 9      237     1378 |
| 57    1457    9      | 124578  3       12457 | 1258   6       178  |
| 6     8       127(3) | 1579    257     1579  | 15(3)  27(3)   4    |
+----------------------+-----------------------+---------------------+
| 379   347     347    | 2479    1       23479 | 6      8       5    |
| 3579  34567   3467   | 479     47      8     | -3(4)  1       2    |
| 1     2       8      | 456     456     345   | 7      3(49)   39   |
+----------------------+-----------------------+---------------------+
| 4     9       1(37)  | 127     8       127   | 12(3)  5       6    |
| 2     136(7)  136(7) | 14567   9       1457  | 1348   (347)   1378 |
| 8     1(67)   5      | 3       47(26)  147   | 14     47(29)  179  |
+----------------------+-----------------------+---------------------+
8 Truths = {2R9 3R37 6R9 9C8 8N8 4B6 7B7}
11 Links = {7r8 3c378 4c8 5n7 6n8 7n3 9n258}
1 Elimination --> r5c7<>3

or

3r8c8-3r3c8=*XWing[3r3c7=*3r3c3-3r7c3=3r7c7]
||
4r3c8-4r6c8=4r5c7
||
7r8c8-7r8c23=*[3r7c7=(3-7)r7c3=*(7-6)r9c2=(6-2)r9c5=(2-9)r9c8=(9-4)r6c8=4r5c7]

#4. 2-fish(1R3C2) : 1r3c4=1r3c3-1r12c2=1r8c2 :=> -1r8c4
#5. Loop[3] : 2r2c6=(2-5)r2c7=5r3c7-(5=2)r3c5 :=> -8r2c7,-5r3c4,-2r1c5; 1-fish and Locked Subsets to the end.
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ffred



Joined: 29 Oct 2012
Posts: 19
Location: Kent, Egland

PostPosted: Tue Nov 06, 2012 8:51 pm    Post subject: Reply with quote

JC, as I said in another post, that's seriously clever.

I'm going to work through your solutions, though they're at or beyond my limit of understanding. Anyway, thanks!
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