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Hi,
not able to provide a V2 for A146. I will have a look to the WTs posted for that puzzle. Waiting for Tarek's puzzle, here is another one. Not planned for a future Assassin because this one is a blank cells killer. BTW, I would need to know if such puzzles can be accepted for Assassins ? I have never seen this kind of puzzle in our Assassins archive ; what is the position of the others participants ? Blank cells can offer some spices to killer puzzles.I feel much difficulties to make blank cells killers because either they are too hard, either the solving path is too apparent from the cages pattern.
For this one, I have chosen to make few blank cells ; with regard to the solving path, this puzzle is very similar to classical killer puzzles. I had to use technicals moves to solve it (much killer pairs) but it feel not to be so difficult....



J F F K 4

[edit to add new image - Ed]


Edit :Caution : r2c258 r5c258 r8c258 is not a 45(9) cage : digit can be repeated in this set of cells !

PS code :
3x3::k3840:3840:3330:3330:3332:3332:2310:3335:3335:3840:10:3083:4620:13:3332:2310:16:3335:3346:3083:3083:4620:4620:2327:2327:3609:3609:3346:3100:3100:1822:3871:3871:3871:5410:5410:3364:37:3100:1822:40:1833:3626:43:5410:3364:3364:5167:5167:5167:1833:3626:3626:1589:3126:3126:2104:2104:4410:4410:5692:5692:1589:4671:64:2881:2370:67:4410:5692:70:2375:4671:4671:2881:2370:2370:3149:3149:2375:2375:




SSscore : 1.65

Solution :

Your cage pattern reminded me of this. I think V1 Assassins should have no holes but otherwise you can do as you please on V2 or non-Assassin Killers as you can see in the Human Solvable series.

JFF 4 Walkthrough:

1. R789
a) Innies N7 = 4(2) = {13} locked for N7
b) 8(2) = [17/35]
c) 12(2) @ R7 = {48} locked for R7+N7 because {57} blocked by R7C4 = (57)
d) 8 locked in 12(2) @ R9 = {48} locked for R9
e) Innies N8 = 19(3) = 8{47/56} because R7C4 = (57) and R9C6 = (48) -> 8 locked for N8; R8C5 = (468)
f) Innies N9 = 14(3) = {149/158/248} <> 3,6,7 because R9C7 = (48) and R7C9 = (125)
g) 7 locked in 22(3) @ N9 = {679} locked for N9
h) 7,9 locked in R9C123 @ R9 for N7
i) Hidden pair (79) locked in R8C67 for R8 -> R8C67 = {79}

2. R789+N6
a) Innies+Outies R7: 14 = R8C67 - R7C9: R8C67 = {79} -> R7C9 = 2
b) Cage sum: R6C9 = 4
c) Innies N6 = 6(2) = {15} locked for N6
d) 14(3) = {239} locked for N6
e) 15(3) = 5{19/28/37/46} because R4C7 = (15) and {168} blocked by R4C89 = (678) -> 5 locked for R4

3. R456
a) 20(3) = 5{69/78} because {389} blocked by R6C78 = (239) -> 5 locked for R6
b) 13(3): R5C1 <> 6,7 since R6C12 <> 4,5
c) 7(2) @ R6: R5C6 <> 2,3
d) Outies R6 = 13(3) = {139/256/346} <> 8 because R5C6 = (1456) and R5C7 = (239)
e) Outies R6 = 13(3): R5C1 <> 1 because R5C6 <> 3,9
f) Outies R6 = 13(3) = {139/256/346} -> R5C6 = (16)
g) 7(2) @ R6 = {16} locked for C6+N5
h) Hidden Killer pair (16) in R6C123 for R6
i) 12(3) <> 5 because {156} blocked by Killer pair (16) of R6C123 and (345) is a Killer triple of (345) of 13(3)

4. C789 !
a) Outies C9 = 18(4) must have two of (1234) -> R19C8 = (1234)
b) 9(3) = {135} -> 5 locked for C9
c) 13(3) <> 7 because R12C9 <> 2,4
d) ! 9(2) @ R1 <> {27} since it's blocked by R568C7 = (2379)
e) 7 locked in Innies N3 = 9(2) = {27} locked for N3
f) 9(2) @ R3 = {27} locked for R3

5. ! C789+R3
a) Innies+Outies R3: 8 = R2C34 - R3C1 -> R2C23 <> 1,2 because R3C1 >= 4
b) 12(3) = {138/147/156/345} <> 9
c) ! Grouped Killer pair (13) in 12(3) @ N1 + R7C3+R8C2 for C23 -> 12(3) @ N4 can only have one of (13) -> 12(3) @ N4 <> 8
d) ! Innies N4 = 20(3) = {389/569/578} <> 1,2,4 since (479) is a Killer triple of 12(3) @ N4
e) 13(2) = [49/58/67]
f) Innies N1 = 18(3) <> 1,2 because R3C1 = (456)
g) 2 locked in 15(3) @ N1 = 2{49/58/67} <> 1,3
h) Hidden Single: R6C1 = 1 @ C1, R5C1 = 3 @ C1 -> R6C2 = 9
i) R6C6 = 6, R5C6 = 1, R5C8 = 5, R4C7 = 1

6. C456
a) 7(2) = {34} -> R5C4 = 4, R4C4 = 3
b) 15(3) = {159} -> 5,9 locked for N5
c) 2 locked in 9(3) @ N8 = {126} locked for N8
d) 17(3) = {359} -> R8C6 = 9; 3,5 locked for R7
e) R4C6 = 5, R7C6 = 3, R7C5 = 5
f) 13(3) = 2{38/47} because R12C6 = (2478) and 1{48} blocked by R9C6 -> 2 locked for N2
g) R3C6 = 7
h) 13(3) = {238} -> R1C5 = 3; 8 locked for C6+N2
i) 18(3) = {459} -> R3C5 = 4; 5,9 locked for N2
j) R1C4 = 6 -> R1C3 = 7

7. Rest is singles.

Rating: Hard 1.25 - Easy 1.5. I used some cage blockers and a Grouped Killer Pair.

I've got no problem with Assassins having blank cells provided they are in the right range of difficulty. Assassins have developed significantly since Ruud started them. Diagonally-linked cages and Killer-Xs started in variants and forum puzzles and are now accepted for Assassins.

I'll be interested to see what views other forum members have.


My solving path for JFFK4 started with it being another fun puzzle, then I got bogged down with nibbling away for a while, with some of this almost certainly not needed for the solving path, and then it became fun again when I found steps 25 and 26.

Afmob and I started in fairly similar ways but then our solving paths became very different. I'd spotted the outies in Afmob's step 4a but there were so many possible combinations that I didn't notice that they all contained two of 1,2,3,4. Afmob's step 5c is clever and, along with step 4d, the hardest.

I'll rate my walkthrough for JFFK4 at 1.5 because of step 11 and the whole of step 26. I'm not really sure how to rate step 26 but I feel it shouldn't be any higher than 1.5.

Here is my walkthrough. It would have been a lot shorter if I'd spotted step 26 earlier, which could have been done any time after step 15. Thanks Afmob for pointing out that my original step 11a was incorrect. I've re-worked parts of steps 11, 12 and 13 but resisted the temptation to move step 26 earlier; that would have made it a different walkthrough.

Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R12C7 = {18/27/36/45}, no 9
c) R34C1 = {49/58/67}, no 1,2,3
d) R3C67 = {18/27/36/45}, no 9
e) R3C89 = {59/68}
f) R45C4 = {16/25/34}, no 7,8,9
g) R56C6 = {16/25/34}, no 7,8,9
h) R67C9 = {15/24}
i) R7C12 = {39/48/57}, no 1,2,6
j) R7C34 = {17/26/35}, no 4,8,9
k) R78C3 = {29/38/47/56}, no 1
l) R9C78 = {39/48/57}, no 1,2,6
m) R6C345 = {389/479/569/578}, no 1,2
n) 21(3) cage in N6 = {489/579/678}, no 1,2,3
o) 22(3) cage in N9 = {589/679}, 9 locked for N9, clean-up: no 3 in R9C6
p) 9(3) cage in N8 = {126/135/234}, no 7,8,9
q) 9(3) cage in N9 = {126/135/234}, no 7,8

1. 45 rule on N3 2 innies R2C8 + R3C7 = 9 = {18/27/36/45}, no 9
1a. 45 rule on N3 1 innie R2C8 = 1 outie R3C6

2. 45 rule on N4 3 innies R4C1 + R5C2 + R6C3 = 20 = {389/479/569/578}, no 1,2

3. 45 rule on N6 3 innies R4C7 + R5C8 + R6C9 = 10 = {127/136/145/235}, no 8,9

4. 45 rule on N7 2 innies R7C3 + R8C2 = 4 = {13}, locked for N7, clean-up: no 9 in R7C12, no 1,2,3,6 in R7C4, no 8 in R89C3
4a. R7C12 = {48} (only remaining combination, cannot be {57} which clashes with R7C4), locked for R7 and N7, clean-up: no 2 in R6C9, no 7 in R89C3
4b. 8 in R9 locked in R9C78 = {48}, locked for R9
4c. 7 in R9 locked in R9C12, locked for N7
4d. 9 in R9 locked in R9C123, locked for N7, clean-up: no 2 in R9C3

5. 45 rule on N8 3 innies R7C4 + R8C5 + R9C6 = 19 = {478/568} (cannot be {289/469} because R7C4 only contains 5,7, cannot be {379} because R9C6 only contains 4,8), no 1,2,3,9, 8 locked for N8
5a. R7C4 = {57} -> no 5,7 in R8C5
5b. 9 in N8 locked in 17(3) cage = 9{17/26/35}, no 4

6. 45 rule on N9 3 innies R7C9 + R8C8 + R9C7 = 14 = {158/248} (cannot be {167/257/356} because R9C7 only contains 4,8, cannot be {347} because 3,7 only in R8C8), no 3,6,7, 8 locked for N9, clean-up: no 5 in 22(3) cage (prelim o)
6a. 2 of {248} must be in R7C9 -> no 2 in R8C8
6b. Naked triple {679} in 22(3) cage, locked for N9

7. 45 rule on R3 2 outies R2C34 = 1 innie R3C1 + 8
7a. Min R3C1 = 4 -> min R2C34 = 12, no 1,2

8. R8C67 = {79} (hidden pair in R8)
8a. 6 in N9 locked in R7C78, locked for R7
8b. 45 rule on R7 2 outies R8C67 = 1 innie R7C9 + 14 -> R7C9 = 2, R6C9 = 4, clean-up: no 3 in R5C6
8c. Naked triple {135} in 9(3) cage, locked for N9
8d. 5 in R7 locked in R7C456, locked for N8

9. R6C9 = 4 -> R4C7 + R5C8 (step 3) = {15}, locked for N6, clean-up: no 9 in 21(3) cage (prelim n)
9a. Naked triple {678} in 21(3) cage, locked for N6

10. R6C345 = {569/578} (cannot be {389} which clashes with 14(3) cage in N6), no 3, 5 locked for R6, clean-up: no 2 in R5C6
10a. Hidden killer pair 7,8 in R6C12 and R6C345 for R6, R6C345 must contain both or neither of 7,8, R6C12 cannot contain both of 7,8 -> R6C345 = {578}, locked for R6

11. R12C7 = {18/45} (cannot be {27/36} which clash with 2,3,6,7 in R5678C7), no 2,3,6,7
[I think this is an ALS block]
11a. Naked quad {1458} in R1249C7, locked for C7, clean-up: no 1,4,5,8 in R2C8 (step 1), no 1,4,5,8 in R3C6
11b. 9 in C9 locked in R123C9, locked for N3, clean-up: no 5 in R3C9

12. Killer pair 5,8 in R12C7 and R3C89, locked for N3
12a. 13(3) cage in N3 = {139/346} (cannot be {247} because 2,4 only in R1C8), no 2,7
12b. 4 of {346} must be in R1C8 -> no 6 in R1C8
12c. 5 in C9 locked in R89C9, locked for N9

13. Hidden pair {27} in R2C8 + R3C7, clean-up: R3C6 = {27}
13a. Naked pair {27} in R3C67, locked for R3, clean-up: no 6 in R4C1
13b. R7C7 = 6 (hidden single in C7)
13c. 3 in C7 locked in R45C7, locked for N6
13d. 7 in C9 locked in R45C9, locked for N6

14. 13(3) cage in N4 = {139/238/256/346} (cannot be {148/157/247} because 4,5,7,8 only in R5C1), no 7
14a. 4,5 of {256/346} must be in R5C1 -> no 6 in R5C1
14b. 1 of {139} must be in R6C12 (R6C12 cannot be {39} which clashes with R6C78), no 1 in R5C1
14c. 8 of {238} must be in R6C12 (R6C12 cannot be {23} which clashes with R6C78), no 8 in R5C1

15. 45 rule on R6 3 outies R5C167 = 13 = {139/256/346}
15a. 1,6 only in R5C6 -> R5C6 = {16}, clean-up: no 2,3 in R6C6
15b. 5 of {256} must be in R5C1 -> no 2 in R5C1
15c. Naked pair {16} in R56C6, locked for C6 and N5

16. R4C567 = {159/258/357} (cannot be {249/348} because R4C7 only contains 1,5), no 4, 5 locked for R4, clean-up: no 8 in R3C1, no 2 in R5C4

17. 12(3) cage in N4 = {129/138/147/156/246} (cannot be {237/345} which clash with 13(3) cage)
17a. 8 of {138} must be in R45C3 (R45C3 cannot be {13} which clashes with R7C3), no 8 in R4C2

18. 12(3) cage in N1 = {138/147/156/345}, no 9, clean-up: no 3 in R2C4 (step 7)
18a. 8 of {138} must be in R23C3 (R23C3 cannot be [31] which clashes with R7C3), no 8 in R3C2
18b. 45 rule on N1 3 innies R1C3 + R2C2 + R3C1 = 18 = {189/279/369/459/567} (cannot be {378} because R3C1 only contains 4,5,6,9, cannot be {468} which clashes with 12(3) cage)
18c. 1 in {189} must be in R2C2 -> no 8 in R2C2
18d. 15(3) cage in N1 = {168/249/258/267/348/456} (cannot be {159/357} which clash with 12(3) cage)
18e. 3 of {348} must be in R12C1 (R12C1 cannot be {48} which clashes with R7C1), no 3 in R1C2

19. 45 rule on N2 3 innies R1C4 + R2C5 + R3C6 = 14 = {167/239/248/257/347} (cannot be {149/158/356} because R3C6 only contains 2,7)
19a. 1,3 of {167/239} must be in R2C5 -> no 6,9 in R2C5
19b. 13(3) cage in N2 = {139/157/238/256/346} (cannot be {148} which clashes with R9C6, cannot be {247} which clashes with R1C4 + R2C5 + R3C6)
19c. 1,6 of {139/157/256/346} must be in R1C5 -> no 4,5,7,9 in R1C5
19d. 18(3) cage in N2 = {189/369/459/468} (cannot be {378} which clashes with R1C4 + R2C5 + R3C6, cannot be {567} which clashes with R3C89), no 7

20. 45 rule on C1 4 outies R1679C2 = 26 = {2789/3689/4589/4679/5678}, no 1

21. 2,5 in R8 locked in R8C1349
21a. 45 rule on R9 4 outies R8C1349 = 14 = {1256/2345}
21b. 4 of {2345} must be in R8C4 -> no 3 in R8C4

22. 17(3) cage in N8 (step 5b) = {179/359}
22a. 1 of {179} must be in R7C5, 9 of {359} must be in R8C6 -> no 7,9 in R7C5

23. 13(3) cage in N4 (step 14) = {139/256/346}
23a. 1 of {139} must be in R6C1 -> no 9 in R6C1
23b. R4C1 + R5C2 + R6C3 (step 2) = {389/479/578} (cannot be {569} which clashes with 13(3) cage), no 6
23c. 12(3) cage in N4 (step 17) = {129/138/147/246} (cannot be {156} which clashes with 13(3) cage), no 5

24. 45 rule on R4 3 outies R5C349 = 1 innie R4C1 + 10, R4C1 = {4789} -> R5C349 = 14,17,18,19
24a. R5C349 cannot be {149} because R5C9 only contains 6,7,8, cannot be {158/167} which clash with R5C6 and R5C8 respectively, cannot be {179/189} because R5C4 only contains 3,4,5 -> no 1 in R5C3

25. 45 rule on N5 3 innies R5C5 + R6C45 = 1 outie R4C7 + 16
25a. R4C7 = {15} -> R5C5 + R6C45 = 17,21 = {278/458/579} (cannot be {359/489} because 3,4,9 only in R5C5)
25b. 2,4,9 only in R5C5 -> R5C5 = {249}

26. 5 in R4 locked in R4C567, 5 in R6 locked in R6C345
26a. 45 rule on N5 2 outies R4C7 + R6C3 = 1 innie R5C5 + 4
26b. R4C7 + R6C3 cannot be [55] because no 6 in R5C5 -> 5 locked in R4C56 + R6C45, locked for N5, clean-up: no 2 in R4C4

27. Naked pair {34} in R45C4, locked for C4 and N5, clean-up: no 9 in R1C3, no 7 in R4C56 (step 16), no 3 in R9C5 (prelim p)
27a. Naked triple {126} in 9(3) cage, locked for N8, clean-up: no 7 in 17(3) cage in N8 (step 22) -> R8C6 = 9, R8C7 = 7, R7C8 = 9, R3C67 = [72], R2C8 = 7, R6C8 = 2, clean-up: no 6 in R1C3
27b. Naked pair {35} in R7C56, locked for R7 -> R7C34 = [17], R8C2 = 3
27c. R6C5 = 7 (hidden single in C5)

28. R4C1 + R5C2 + R6C3 (step 23b) = {578} (only remaining combination, cannot be {479} because R6C3 only contains 5,8), locked for N4, clean-up: no 4,9 in R3C1
28a. Naked triple {678} in R4C189, locked for R4, clean-up: no 2 in R4C56 (step 16)
28b. R4C56 = [95], R4C7 = 1, R5C5 = 2, R5C8 = 5, R6C34 = [58], R7C56 = [53], clean-up: no 8 in R12C7, no 9 in R3C9, no 6 in R89C3
28c. R89C3 = [29]

29. Naked pair {45} in R12C7, locked for C7 and N3 -> R9C67 = [48], R8C58 = [84]
29a. Naked pair {68} in R3C89, locked for R3 and N3 -> R3C1 = 5, R89C1 = [67], R4C1 = 8, R4C89 = [67], R5C9 = 8, R3C89 = [86], R5C2 = 7, R7C12 = [48], R9C2 = 5, R8C4 = 1, R8C9 = 5, R9C45 = [26], R3C4 = 9, clean-up: no 4 in R1C3

30. R1C3 = 7 (hidden single in R1), R1C4 = 6

31. 13(3) cage in N4 (step 12) = {139} (only remaining combination) -> R6C2 = 9

32. R12C6 = {28} -> R1C5 = 3 (step 19b)

and the rest is naked singles