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Here is something quite hard, so this one might be '' Just For a Frightful Killer!'' for some people, which explains the "F" .
However, I have tried to keep a similar concept as Assassin 152 : a X-killer with many Innies and outies.
It is still solvable without using too heavy moves, but the cracking step I have used for this one was not easy to find for me.
On the other hand, it then could be solved quite (?) straightforwardly if you find the good trick ! See by yourself ...




J F F K 6






PScode :3x3:d:k:3840:1793:1793:6147:6147:6147:3590:3590:2824:3840:3840:2315:2315:4109:6147:3590:2824:2577:5906:5906:2324:4109:4109:3607:3607:2577:794:2587:5906:5906:2324:4127:3607:3873:3873:794:2587:4901:4901:4901:4127:3113:3113:3113:3116:2093:2094:2094:2352:4127:2610:4915:4915:3116:2093:3383:2352:2352:4666:4666:2610:4915:4915:3383:3136:3137:5186:4666:2116:2116:4934:4934:3136:3137:3137:5186:5186:5186:2638:2638:4934:

Solution :

SSscore : 2.75

Edit : There was a trouble (thanks Afmob) with the PS-code (there was a "broken" cage). I apologize for that problem, everything is OK now !

I tried to tackle this Killer a week ago but I didn't come far, so I stopped and deleted my partial wt since I thought vast T & E was needed because of SudokuSolver's score. Today I tried it again and it fell quite fast.

My rating is not "just" 1.25 because the Hidden Cage I used seems useless at first and one normally looks for other Hidden Cages first.

JFF 6 Walkthrough:

1. R1234
a) Innies N3 = 10(2) = [91/82]
b) 11(2) <> {29} because it's a Killer pair of Innies N3
c) Outies N3 = 7(2+1) <> 6,7,8,9; R3C6 <> 3 since it sees R4C6
d) Innies N2 = 5(2) = [14/32/41]
e) 9(2) = [54/63/81]
f) Outies R12 = 16(3) must have one of (1234)

2. R1234 !
a) ! Innies N1 = 23(4) <> 49{28/37} since R3C123 can only have one of (1234) because of Killer quad (1234) in Outies R12 + R3C69
b) ! Innies N1 = 23(4) <> 56{39/48} because they're blocked by Killer triples (356,456) of 7(2)
-> Innies N1 = 23(4) = {1589/1679/2579/2678/3578} <> 4
c) ! Hidden Killer pair (56) locked in Innies N1 + Outies R12 for R3 since none of them can have both
-> Innies N1 = 23(4): R2C3 <> 5,6
d) R2C3 = 8 -> R2C4 = 1
e) Innie N2 = R3C6 = 4
f) 14(3) = 4[82/91]
g) Innies R12 = 10(2) = [37/64/73]
h) 10(2) @ N3 = [37/46/73]
i) 11(2) <> {47} since it's a Killer pair of 11(2)

3. R456
a) Naked pair (12) locked in R4C69 for R4
b) Innies R1234 = 10(2) = {37/46}
c) 9(2): R4C4 <> 5
d) 5 locked in R4C23 @ R4 for N4+23(4)
e) 10(2) @ N4 = {37/46}
f) 8 locked in R45C2 @ N4 for C2
g) 8(2) @ R6C2 <> 3
h) Killer pair (67) locked in 10(2) + 8(2) @ R6C2 for N4
i) 8(2) @ C1: R7C1 = (567)

4. R789
a) Outies R89 = 22(3) = 9{58/67} -> 9 locked for R7
b) Innies N7 = 8(2): R7C3 = (123)
c) 4 locked in Innies N89 = 15(4) @ R7 = 4{128/137/236} <> 5
d) 9(3): R7C4 <> 6 because [216] blocked by R4C6 = (12)
e) Innies N8 = 7(2) = [25/43]
f) 8(2) = {35} locked for R8
g) Innies R89 = 9(2) = [72/81]
h) 13(2) = [58/67]
i) 12(2) = [48/93] since (57) is a Killer pair of 12(2)

5. D\/
a) 11(2) = {56} locked for N3+D/ because {38} blocked by R9C1 = (38)
b) 9(3) = {234} -> 4 locked for C4
c) 9(2) <> 5

6. C456
a) 5 locked in 16(3) @ R3 = {358} because R2C5 = (367) -> R2C5 = 3; 5,8 locked for R3+N2
b) R3C7 = 9 -> R4C6 = 1, R8C2 = 4 -> R9C1 = 8, R8C1 = 7 -> R7C2 = 6
c) R7C1 = 5 -> R6C1 = 3, R6C4 = 2, R7C3 = 3
d) 16(3) @ N5 = {457} -> R5C5 = 7, R4C5 = 4, R6C5 = 5

7. Rest is singles.

Rating: Hard 1.25. I used a Killer quad and a Hidden Killer pair.

Thanks Afmob for having taken time with this puzzle.
This is not so much difficult (by the way, all the puzzles I post on this forum are solvable using logic, without vast T_E steps whereas I am not completely against some short contradiction move : trust me,I solve each of them several times).

Here is the way I solve this killer :


Walkthough JFFK 6




PS : A strange fact : without the diagonal condition, the puzzle is still solvable and SSscore is 2.23 < 2.75 ! However, I have kept this condition since it seems to me more interesting to solve.

Another from my backlog of unfinished puzzles.

I also came back to it but, in my case, just over a year and a half later.

Thanks manu for an interesting Killer. Nice solving paths by both Afmob and manu! I also used a hidden cage for my breakthrough but a very different one, the 22(5) one on D/, so thanks manu for deciding to post this puzzle as a Killer-X.

As can be seen from my walkthrough, when I came back to this puzzle I found that I had been very close to solving it at the time; my key breakthrough was only two steps later, immediately after finding the hidden cage which Afmob used for his breakthrough.

I seem to have been good at spotting innies for this puzzle but not as good at seeing outies. I either missed several of them or saw them but didn't realise their importance. I don't know now which of those categories 3 outies for R12 R3C458 = 16 fits into. That was a key step in both Afmob's and manu's walkthroughs.


Here is my walkthrough for JF"F"K6.

Prelims

a) R1C23 = {16/25/34}, no 7,8,9
b) 11(2) cage in N3 = {29/38/47/56}, no 1
c) R2C34 = {18/27/36/45}, no 9
d) 10(2) cage in N3 = {19/28/37/46}, no 5
e) 9(2) cage at R3C3 = {18/27/36/45}, no 9
f) R34C9 = {12}
g) R45C1 = {19/28/37/46}, no 5
h) R4C78 = {69/78}
i) R56C9 = {39/48/57}, no 1,2,6
j) R67C1 = {17/26/35}, no 4,8,9
k) R6C23 = {17/26/35}, no 4,8,9
l) 10(2) cage at R6C6 = {19/28/37/46}, no 5
m) 13(2) cage in N7 = {49/58/67}, no 1,2,3
n) 12(2) cage in N7 = {39/48/57}, no 1,2,6
o) R8C67 = {17/26/35}, no 4,8,9
p) R9C78 = {19/28/37/46}, no 5
q) 19(3) cage at R5C2 = {289/379/469/478/568}, no 1
r) 9(3) cage at R6C4 = {126/135/234}, no 7,8,9
s) 19(3) cage in N9 = {289/379/469/478/568}, no 1

1. Naked pair {12} in R34C9, locked for C9, clean-up: no 9 in R2C8, no 8,9 in R3C8

2. 45 rule on N2 2 innies R2C4 + R3C6 = 5 = {14/23}, clean-up: no 1,2,3,4 in R2C3

3. 45 rule on N3 2 innies R3C79 = 10 = [82/91]
3a. Min R3C67 = 9 -> max R4C6 = 5
3b. 11(2) cage in N3 = {38/47/56} (cannot be [92] which clashes with R3C79), no 2,9
3c. R3C79 = 10 -> R3C67 cannot be 10 (CCC) -> no 4 in R4C6

4. 45 rule on N7 2 innies R7C13 = 8 = {26/35}/[71], no 1 in R7C1, no 4 in R7C3, clean-up: no 7 in R6C1
4a. R7C13 = 8 -> R7C34 cannot be 8 (CCC) -> no 1 in R6C4

5. 45 rule on N8 2 innies R7C4 + R8C6 = 7 = {16/25}/[43], no 3 in R7C4, no 7 in R8C6, clean-up: no 1 in R8C7

6. 45 rule on R12 2 innies R2C59 = 10 = [19/28]/{37/46}, no 5,8,9 in R2C5

7. 45 rule on R89 2 innies R8C15 = 9 = [45/54/63/72/81], no 9 in R8C1, no 6,7,8,9 in R8C5, clean-up: no 4 in R7C2
7a. Max R8C5 = 5 -> min R7C56 = 13, no 1,2,3 in R7C56

8. 45 rule on R1234 2 innies R4C15 = 10 = {19/28/37/46}, no 5 in R4C5

9. 45 rule on R6789 2 innies R6C59 = 14 = [59/68/95], clean-up: no 5,8,9 in R5C9

10. 45 rule on C1234 4 innies R1389C4 = 26 = {2789/3689/4589/4679/5678}, no 1

11. 45 rule on D/ 5 innies R3C7 + R4C6 + R5C5 + R6C4 + R7C3 = 22
11a. R3C7 = {89} -> no 8,9 in R5C5

12. 12(3) cage in N7 = {129/138/147/246} (cannot be {156/237} which clash with R7C13), cannot be {345} which clashes with 12(2) cage), no 5

13. 45 rule on N3 3(1+2) outies R3C6 + R4C69 = 7 = [151/232/412/421] (cannot be [322/331]), no 3 in R3C6, clean-up: no 2 in R2C4 (step 2), no 7 in R2C3

14. 45 rule on N6 5 innies R4C9 + R56C78 = 18 = {12348/12357/12456}, no 9
14a. 12(3) cage at R5C6 = {138/147/156/237/246/345} (cannot be {129} which clashes with R4C9), no 9

15. R45C1 = {19/28/46} (cannot be {37} because R67C1 and R6C23 cannot both be {26}), no 3,7, clean-up: no 3,7 in R4C5 (step 8)
15a. When R45C1 = {28/46} either R67C1 must be [17] or R6C23 must be {17}
-> 1 in N4 locked in R45C1 + R6C123, locked for N4

[The next step is in the spirit of many of manu’s puzzles and walkthroughs. When I first spotted it I couldn’t see how to use but when I came back to the puzzle I found that I was able to use it for a later step so I’ve numbered it, even though there aren’t any immediate eliminations.]

16. R4567C1 + R6C23 is effectively a 26(6) cage because, although R7C1 cannot “see” R6C23, R7C1 cannot be the same as one of R6C23 which would cause a clash between R6C1 and one of R6C23 because R67C1 and R6C23 are both 8(2) cages.
The only valid combinations for this 26(6) are {123569/123578/134567} (cannot be {123479/124568} because 4,8,9 are only in R45C1 and cannot have two of them in a 10(2) cage) -> only of the 8(2) cages must be {17/26} and the other {35}.

17. 45 rule on R5 3 innies R5C159 = 14 = {149/167/239/248/257/347/356} (cannot be {158} because R5C9 only contains 3,4,7)
17a. 4 of {149/248} must be in R5C9, 4 of {347} must be in R5C1 -> no 4 in R5C5

18. 1,2 on D/ only in R3C7 + R4C6 + R5C5 + R6C4 + R7C3 = 22 (step 11) = {12379/12469/12478/12568}
18a. 7 of {12379} must be in R5C5 -> no 3 in R5C5

19. 3 in R4 locked in R4C2346
19a. 45 rule on R123 5 outies R4C23469 = 20 = {12359/13457/23456} (cannot be {12368} which clashes with R4C78), no 8, clean-up: no 1 in R3C3

[This is how far I got when this puzzle first appeared.]

20. 45 rule on N1 4 innies R2C3 + R3C123 = 23 = {1589/1679/2678/3578} (cannot be {3479} because R2C3 only contains 5,6,8, cannot be {2489/2579} which clash with R3C79, cannot be {3569/4568} which clash with R1C23), no 4, clean-up: no 5 in R4C4

21. R3C7 + R4C6 + R5C5 + R6C4 + R7C3 (step 18) = {12379/12568} (cannot be {12469/12478} because 9(3) cage at R6C4 cannot contain both of 1,4 or both of 4,6 and R6C4 + R7C3 cannot be [42] because there’s no 3 in R7C4), no 4
[This is what I missed earlier.]
21a. 5 of {12568} must be in R4C6 + R5C5 (because 9(3) cage at R6C4 cannot contain both of 2,5 or both of 5,6 and R6C4 + R7C3 cannot be [51] because there’s no 3 in R7C4) -> no 5 in R6C4 + R7C3, clean-up: no 3 in R7C1 (step 4), no 5 in R6C1
21b. {12379} can only be [91723/91732/93721] (R3C7 + R4C6 cannot be [92] because no 3 in R3C6)
21c. 9(3) cage at R6C4 = {126/234} (cannot be {135} because R6C4 + R7C3 cannot be [31], step 21b), no 5 in R7C4, clean-up: no 2 in R8C6 (step 5), no 6 in R8C7

22. 11(2) cage in N3 (step 3b) = {47/56} (cannot be {38} which clashes with R3C7 + R4C6 + R5C5 + R6C4 + R7C3), no 3,8
22a. 10(2) cage in N3 = {37}/[82/91] (cannot be {46} which clashes with 11(2) cage), no 4,6, clean-up: no 4,6 in R2C5 (step 6)

23. 12(2) cage in N7 = {39/48} (cannot be {57} which clashes with R3C7 + R4C6 + R5C5 + R6C4 + R7C3), no 5,7
23a. 13(2) cage in N7 = {58/67} (cannot be [94] which clashes with 12(2) cage), no 4,9, clean-up: no 5 in R8C5 (step 7)
23b. 12(3) cage in N7 (step 12) = {129/147/246} (cannot be {138} which clashes with 12(2) cage), no 3,8

24. R4567C1 + R6C23 (step 16) = {123569/123578/134567}, 3 locked for R6 and N4, clean-up: no 7 in R7C7
24a. R6C23 = {17/35} (cannot be {26} which clashes with R6C4), no 2,6

25. 16(3) cage at R4C5 = {169/259/457} (cannot be {178} because R6C5 only contains 5,6,9, cannot be {268} which clashes with R6C4), no 8, clean-up: no 2 in R4C1 (step 8), no 8 in R5C1

26. Consider the placement for 3 in R6
R6C1 = 3
or R6C23 = {35} => R6C59 (step 9) = [68] => R6C4 = 2 => R6C1 = 1
-> R6C1 = {13}, clean-up: no 2,6 in R7C1, no 2,6 in R7C3 (step 4)
25a. Killer pair 1,3 in R6C1 and R6C23, locked for R6 and N4, clean-up: no 9 in R45C1, no 1,9 in R4C5 (step 8), no 9 in R7C7
25b. Killer pair 5,7 in R7C1 and 13(2) cage, locked for N7

27. 9(3) cage at R6C4 (step 21c) = {126/234}, 2 locked for C4, clean-up: no 7 in R3C3
27a. R7C3 = {13} -> no 1 in R7C4, clean-up: no 6 in R8C6 (step 5), no 2 in R8C7

28. 45 rule on D/ 2 outies R3C6 + R7C3 = 1 innie R5C5 + 1
28a. Min R3C6 + R7C3 = 3 -> min R5C5 = 2

29. 16(3) cage at R4C5 (step 25) = {259/457}, no 6, 5 locked for C5 and N5, clean-up: no 4 in R4C1 (step 8), no 6 in R5C1, no 8 in R6C9 (step 9), no 4 in R5C9
29a. Naked pair {59} in R6C59, locked for R6, clean-up: no 3 in R6C23, no 1 in R7C7
29b. Naked pair {17} in R6C23, locked for R6 and N4 -> R6C1 = 3, R7C1 = 5, R7C3 = 3 (step 4), placed for D/, clean-up: no 4 in R1C2, no 6 in R4C4, no 8 in 13(2) cage in N7, no 9 in 12(2) cage in N7, no 1,4 in R8C5 (step 7)

30. 9(3) cage at R6C4 (step 21c) = {234} (only remaining combination) -> R7C4 = 4, R6C4 = 2, R4C6 = 1, R34C9 = [12], R3C7 = 9 (step 3), R3C6 = 4 (cage sum), R2C4 = 1 (step 2), R2C3 = 8, R8C6 = 3 (step 5), R8C7 = 5, R4C5 = 4, R56C5 = {57} (step 29) -> R6C5 = 5, R5C5 = 7, placed for both diagonals, R56C9 = [39], R4C1 = 6 (step 8), R5C1 = 4, 13(2) cage in N7 = [67], R9C1 = 8, R8C2 = 4, placed for D/, R3C1 = 2, R12C1 = [19], R2C2 = 5 (cage sum),R4C4 = 3, R3C3 = 6, placed for D\, R6C6 = 8, placed for D\

and the rest is naked singles without using diagonals.