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PostPosted: Thu Feb 25, 2016 10:16 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Assassin 331 X Flatfish 18s

I like the flatfish shape and it goes well with X. To limit the number of combinations I went for 18 and then went mad and tried to do all 18s. However there were two solutions so needed the 17 at r3c6. At this stage it was unsolvable, so I added some easier cages. Different cage combinations bounced the score between 1.1 and 2.3, but I eventually found this one which has an SS score of 1.5. JS uses six large fishes so it is not easy.

Image

JS Code:
3x3:d:k:4610:4610:4617:4617:4615:4121:26:4611:4611:4610:4610:4617:4617:4615:4121:27:4611:4611:28:4624:4610:4624:4615:4367:4611:4618:4618:29:30:4624:4624:4615:4367:4367:4618:4618:4614:4614:4614:4614:3859:4613:4613:4613:4613:4620:4620:4620:4620:4616:3859:4621:4621:4120:4622:4622:4612:5905:4616:4621:4609:4621:4120:4612:4612:4622:5905:4616:4619:4619:4609:4609:4612:4612:31:5905:4616:4619:4619:4609:4609:

Solution:
128537946
374169825
965284173
497318562
632795418
581426397
843671259
256943781
719852634


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PostPosted: Mon Mar 07, 2016 4:21 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for another Assassin! Yes, the flatfish 18(5) cages do go well with the diagonals.

This was a challenging puzzle; it took me a long time to solve it.

Here is my walkthrough for Assassin 331 X Flatfish 18s:
Prelims

a) R12C6 = {79}
b) R67C9 = {79}
c) 15(2) cage at R5C5 = {69/78}
d) 23(3) cage at R7C4 = {689}
e) 18(5) cage at R1C1 = {12348/12357/12456}, no 9
f) 18(5) cage at R1C8 = {12348/12357/12456}, no 9
g) 18(5) cage at R7C3 = {12348/12357/12456}, no 9
h) 18(5) cage at R7C7 = {12348/12357/12456}, no 9

1. 45 rule on R5/C5 1 innie R5C5 = 9 -> R6C6 = 6, placed for D\
1a. 45 rule on N7 1 innies R9C3 = 9
1b. 9 in N1 only in R3C12, locked for R3
1c. 9 in N3 only in R12C7, locked for C7

Steps resulting from Prelims
2a. Naked pair {79} in R12C6, locked for C6 and N2
2b. Naked pair {79} in R67C9, locked for C9
2c. R8C4 = 9 (hidden single in R8)
2d. Naked pair {68} in R79C4, locked for C4 and N8
2e. 18(5) cage at R1C1 = {12348/12357/12456}, 1,2 locked for N1
2f. 18(5) cage at R1C8 = {12348/12357/12456}, 1,2 locked for N3
2g. 18(5) cage at R7C3 = {12348/12357/12456}, 1,2 locked for N7
2h. 18(5) cage at R7C7 = {12348/12357/12456}, 1,2 locked for N9
2i. 7 in N8 only in R789C5, locked for C5

3. 17(3) cage at R3C6 = {278/368/458} (cannot be {467} because no 6,7 in R4C7), no 1
3a. 6,7 of {278/368} must be in R4C7 -> no 2,3 in R4C7

4. 18(3) cage at R7C1 = {378/468/567}
4a. 4 of {468} must be in R7C12 (R7C12 cannot be {68} which clashes with R7C4) -> no 4 in R8C3

5. 6 in N2 only in 18(4) cage at R1C5 = {1368/3456}, no 2, 3 locked for C5
5a. 18(4) cage at R6C5 = {1278/2457}
5b. 8 of {1278} must be in R6C5 -> no 1 in R6C5
5c. 3 in N8 only in R789C6, locked for C6
5d. 17(3) cage at R3C6 (step 3) = {278/458}, no 6

6. 45 rule on C89 6(2+4) outies R57C6 + R3567C7 = 16
6a. Min R3567C7 = 10 -> max R57C6 = 6, no 8 in R5C6
6b. Min R57C6 = 3 -> max R3567C7 = 13, no 8
6c. 8 in C6 only in R34C6, locked for 17(3) cage at R3C6 -> no 8 in R4C7

7. 45 rule on R1234 5(2+1+2) innies R12C7 + R3C1 + R4C12 = 39
7a. Max R12C7 + R3C1 = 17 + 9 -> min R4C12 = 13, no 1,2,3
7b. Max R3C1 + R4C12 = 9 + 17 -> min R12C7 = 13, no 3
7c. Max R12C7 + R4C12 = 17 + 17 -> min R3C1 = 5

8. 45 rule on N3 2 innies R12C7 = 2 outies R4C89 + 9, max R12C7 = 17 -> max R4C89 = 8, no 8,9
8a. 9 in R4 only in R4C12, locked for N4

9. 9 in C8 only in R67C8 -> 18(4) cage at R6C7 = {1269/1359/2349}, no 7,8
9a. 8 in N6 only in R5C89, locked for R5

10. 18(4) cage at R6C5 (step 5a) = {1278/2457}, 18(4) cage at R6C7 (step 9) = {1269/1359/2349}
10a. 9 in R6 only in R6C89
10b. 45 rule on R6 4 innies R6C5789 = 21 contains 9 = {1389/1479/2379/3459}
10c. 2 of {2379} must be in R6C5 -> no 2 in R6C78
10d. Consider combinations for R6C5789
R6C5789 = {1389/2379/3459} => 3 in R6C78 => 18(4) cage at R6C7 = {1359/2349}
or R6C5789 = {1479} = [4197] => 18(4) cage at R6C5 = 4{257}, 2 locked for N8 => 18(4) cage at R6C7 = {1359}
-> 18(4) cage at R6C7 = {1359/2349}, no 6
10e. 2 of {2349} must be in R7C6 -> no 4 in R7C6
10f. 2 of {2349} in R7C6 => R6C5 = 2 (hidden single in C5) => R6C5789 = [2397] -> no 4 in R6C78
10g. 4 of R6C5789 = {3459} must be in R6C5 -> no 5 in R6C5

11. 18(4) cage at R6C5 (step 5a) = {1278/2457}, R6C5789 (step 10b) = {1389/1479/2379/3459}
11a. Max R4C89 = 8 (step 8) -> R4C89 must contain at least one of 1,2,3
11b. Consider combinations for 17(3) cage at R3C6 (step 5d) = {278/458}
17(3) cage = {278} = [287], 8 placed for N5
or 17(3) cage = {278} = [827] => R4C89 must contain at least one of 1,3 => R6C5789 cannot be {1389) = 8{13}9
or 17(3) cage = {458} => 1,2 in C6 only in R5789C6 => R789C6 must contain at least one of 1,2 => 18(4) cage at R6C5 cannot be {1278} = 8{127}
-> no 8 in R6C5
11c. 18(4) cage at R6C5 = {2457} (only remaining combination), locked for C5, 5 also locked for N8
11d. 8 in N5 only in R4C56, locked for R4
11e. 1 in N8 only in R789C6, locked for C6

12. R12C7 + R3C1 + R4C12 (step 7) = 39
12a. Max R3C1 + R4C12 = 9 + 16 -> min R12C7 = 14, no 4 in R12C7
12b. Max R12C7 + R4C12 = 17 + 16 -> min R3C1 = 6

13. 17(3) cage at R3C6 (step 5d) = {278/458}
13a. R57C6 + R3567C7 = 16 (step 6)
13b. Consider combinations for R3567C7
R3567C7 = 10 = {1234}, locked for R7 => R34C6 = {28/48} => R57C6 cannot be [42]
or R3567C7 = 11,12,13 => R57C6 = 5,4,3 => no 2 in R7C6
-> no 2 in R7C6
13c. 18(4) cage at R6C7 (step 10d) = {1359} (only remaining combination), no 4 in R7C8
13d. 18(4) cage at R6C7 = {1359}, CPE no 5 in R45C8

14. R6C5789 (step 10b) = {1479/2379/3459}, 18(4) cage at R6C7 = {1359} -> R6C5789 + R7C68 = [4197][35]/[2397][15]/[4{35}9][19] -> no 3 in R7C8

15. 45 rule on N9 4 innies R7C89 + R89C7 = 27 = {5679} (only possible combination, cannot be {3789} because 18(4) cage at R8C6 cannot be {34}{38}, cannot be {4689} because 4,6,8 only in R89C7), locked for N9, 6 also locked for C7

16. 8 in R5 only in 18(4) cage at R5C6 = {1278/1458/2358} (cannot be {1368} because R5C6 only contains 2,4,5), no 6
16a. 6 in N6 only in R4C89, locked for R4 and 18(4) cage at R3C8, no 6 in R3C89

17. R12C7 = {89} (hidden pair in C7), locked for N3
17a. 45 rule on N3 4 innies R12C7 + R3C89 = 27, R12C7 = 17 -> R3C89 = 10 = [73]
17b. R3C89 = 10 -> R4C89 = 8 = {26}, locked for R4 and N6

18. 3,7 on D/ only in R6C4 and 18(5) cage at R7C3 -> 18(5) cage must contain at least one of 3,7 = {12348/12357}, no 6, 3 locked for N7
18a. 6 on D/ only in R1C9 + R2C8, locked for N3

19. 5,7 on D\ only in 18(5) cage at R1C1 and R4C4 -> 18(5) cage must contain at least one of 5,7 = {12357/12456}, no 8, 5 locked for N1
19a. 8 on D\ only in R8C8 + R9C9, locked for N9

20. 45 rule on N1 4 innies R12C3 + R3C12 = 27 = {4689} (only possible combination, cannot be {3789} because 18(4) cage at R1C3 cannot be {37}{35}), locked for N1
20a. 18(4) cage at R1C3 = {1368/1458/3456} (cannot be {2358} because R12C3 only contain 4,6,8) -> R12C4 = {13/15/35}, no 2,4
20b. R3C46 = {24} (hidden pair in N3), locked for R3
20c. 4 in N1 only in R12C3, locked for C3
20d. 5 in N2 only in R12C4, locked for C4

21. 17(3) cage at R3C6 (step 5d) = {278/458} -> R4C6 = 8, placed for D/, R4C7 = {57}
21a. Naked triple {567} in R489C7, locked for C7 -> R3C7 = 1, placed for D/, R3C3 = 5, R56C7 = [43], R7C7 = 2, placed for D\, R7C6 = 1
21b. Naked pair {59} in R67C8, locked for C8
21c. 1,2 in C3 only in R456C3, locked for N4

22. R5C6 = 5 (hidden single in C6)
22a. Naked pair {18} in R5C89, locked for R5
22b. Naked triple {246} in R124C8, locked for C8, 4 also locked for N3

23. 18(4) cage at R3C2 = {1278/1467/2349/2367} (cannot be {1269/1368} because 6,8,9 only in R3C2)
23a. 17(3) cage at R3C6 (step 5d) = {278/458} = [287/485]
23b. 18(4) cage = {1278/2349/2367} (cannot be {1467} = [64]{17} which clashes with 17(3) cage) -> R3C4 = 2, R3C6 = 4, R4C7 = 5 (cage sum)
23c. R5C3 = 2 (hidden single in R5)

24. R6C5 = 2 (hidden single in R6), R7C8 = 5 (hidden single in N9)
24a. 18(3) cage at R7C1 (step 4) = {468}, locked for N7, 4 also locked for R7
24b. 18(4) cage at R6C1 = {1458} (only possible combination) -> R6C3 = 1, R6C4 = 4, placed for D/

25. R12C7 + R3C1 + R4C12 = 39 (step 7)
25a. R12C7 = {89} = 17, R4C12 = {49} (hidden pair in R4) = 13 -> R3C1 = 9

26. R9C9 = 4 (hidden single on D\), R8C9 = 1, R9C8 = 3, R8C8 = 8, R8C3 = 6
26a. R7C35 = [37], R3C3 = 7, R3C2 = 6 (hidden single in N1) -> R4C4 = 3 (cage sum), placed for D\

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough for A331X at Hard 1.5. I used three forcing chains. I went for Hard 1.5, rather than just 1.5, because of the difficulty in finding some of my steps.


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PostPosted: Sat Mar 12, 2016 11:19 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks HATMAN. I too find this quite tough. My WT is not how I originally did it. I found some quicker steps on my second go through.

Assassin 331 X Flatfish 18s WT:
1. Innies c5 -> r5c5 = 9
-> r6c6 = 6
-> Remaining innies c6789 -> r12c7 = +17(2) = {89}
Outies n3 -> r4c89 = +8(2) (No 8,9)
-> 9 in c8 in r67c8
-> 8 in n6 in r5c89
Also 8 in n9 in r89c89
-> 18(5)n9 = {12348}

2. 16(2)c9 = {79}
-> 9 locked in r6c89 and in r7c89
Innies n7 -> r9c3 = 9
-> 23(3)n8 = {689}
-> r8c4 = 9
16(2)n2 = {79}
-> 9 locked in r3c12 and in r4c12
Also remaining innies c1234 -> r3c1 + r4c12 = +22(3) and includes a 9 in r4c12
-> Either 9 in r3c1 -> r4c12 = [49]
Or 9 in r4c1 puts r3c1,r4c2 = {58} or {67}

3. 16(2)n2 = {79}
-> 7 in c5/n8 in r789c5
Also 6 in n2/c5 in r123c5
-> 18(4)r1c5 = {63(18|45)} and 18(4)r6c5 = {27(45|18)}

4! Given 18(5)n9 = {12348} -> 18(5)n1 cannot be {12348} (Would require 5 numbers in 6 spots on D\)
-> 18(5)n1 = {125} + {37} or {46}
-> 8 not in r4c2 (would put a 5 in r3c1)
Also 8 not in r4c3 (leaves no place for both 8 and 9 in n1)
-> 8 in r4 in r4c56
-> 8 not in 18(4)r6c5
-> 18(4)r6c5 = {2457}
-> 18(4)r1c5 = {1368}

5. (13) in n8 in r123c6
r89c7 = two from (567)
-> (13) cannot both go in r89c6
-> r7c6 from (13)
Also since one of (13) in r89c6 -> r89c7 cannot be {57}
-> r89c7 = {56} or {67}
-> 6 in n6 in r45c89
But 6 cannot be in r5c89 since 18(4)r5c6 cannot be [{13}{68}]
-> 6 in r4c89
-> r4c89 = {26}
-> r3c89 = [73]
-> 18(5)n3 = {12456}

6. 18(4)r6c7 contains a 9 and does not contain a 2
-> 18(4)r6c7 = {1359}
5 in n9 in r7c8 or r89c7
-> 5 in 18(4)r6c7 in r67c8
-> r67c8 = {59} and r6c7,r7c6 = {13}
-> r7c7 from (24)

7! Given r12c6 = {89} -> Outies r12 -> r3c357 + r4c5 = +15(4)
8 in r4 in r4c56
Trying 8 in r4c5 puts r3c357 = +7(3) = [214] or [412] ...
... but this contradicts r7c7 from (24)
-> r4c5 cannot be 8 -> r4c6 = 8
-> r4c5 from (13)
Given that and given r3c5 from (168) and that neither of r3c37 can be from (3679)
-> r34c5 from [81] or [63] and r3c37 = {15}

8. -> 5 in n2 in r12c4 and whichever of (13) is in r4c5 also goes in r12c4
Also r3c46 = {24}
-> r3c125 = {689} with 9 in r3c12
-> 18(5)n1 = {12357}
-> 4 in n1 in r12c3

9. Since r3c37 = {15} -> r7c3 cannot be 1
-> HS 1 in r7 -> r7c6 = 1
-> r6c7 = 3
Since 18(5)n3 = {12456} -> 18(5)n7 = {12348} or {12357}
-> HS 3 in r7 -> r7c3 = 3
Also since r3c37 = {15} -> (246) in n3 in r12c89
-> HS 2 in c7/n9 -> r7c7 = 2
-> 4 in n9 in r89c89
-> (since 17(3)r3c6 = [485] or [287]) -> HS 4 in c7 -> r5c7 = 4
-> 18(4)r5c6 = [54{18}]
-> 18(4)r5c1 = {2367}

10. Since 17(3)r3c6 = [485] or [287] r489c7 = {567}
-> r3c7 = 1
-> r3c3 = 5
1 in n1 in r12c12 and 1 in n7 in r89c12
-> HS 1 in r6 -> r6c3 = 1
3 in n4 in r5c12
-> HP r4c45 = {13}
-> 4 in n5 in r6c45
-> 4 in n4 in r4c12
-> r3c1,r4c12 = [949]
-> 5 in n4 in r6c12
-> HS 5 in r4 -> r4c7 = 5
-> r3c6 = 4
-> r3c4 = 2
Also HS 2 in n5 -> r6c5 = 2
-> r6c4 = 4
Also -> r789c5 = {457}
-> r89c6 = {23}
-> r89c7 = {67}
-> 16(2)c9 = [79]
-> r67c8 = [95]
-> 5 in n7 in r89c12
-> 18(5)n7 = {12357}
-> HS 7 in r7 -> r7c5 = 7
-> HS 4 in r7 -> r7c2 = 4
Also NS r5c4 = 7
Also HS 2 in c3 -> r5c3 = 2
-> NS r4c3 = 7
Also r5c12 = {36} and r6c12 = {58}
etc.

What I liked ...:
... was that my solution path jumped all over the place. I needed to make connections between different parts of the puzzle to solve it.

So my rating is ...:
... 1.5. Like Andrew says - the moves were hard to spot.

Now for the next one - the 12s. I solved it and will post a WT when I have time.


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