Ed wrote:
JFFC (Just For a Frightful Challenge)
I did several steps before I ground to a halt. Then a comment made to me by Manu about Just For Fun 3 made me wonder whether a similar step could be used in this puzzle. It is probably essential to solve this puzzle without extreme difficulty, whereas for Just For Fun 3 it only made the solution slightly shorter while, at the same time, increasing the rating of any walkthrough that used it.
After that the fun returned to this puzzle although I did get stuck later, taking some time to find the important combination elimination in step 20.
I'll rate JFFK1 at 1.5 to Hard 1.5 the way I solved it; it's hard to know what rating to give the first step which is the technically hardest one. Afmob's alternative start using more standard steps may be technically slightly easier so the rating for this puzzle should probably be 1.5.
Here is my walkthrough. I started again with the key breakthrough step before using some of my previous steps.
Prelims
a) R1C34 = {18/27/36/45}, no 9
b) R23C6 = {59/68}
c) R23C9 = {29/38/47/56}, no 1
d) R34C2 = {29/38/47/56}, no 1
e) R45C3 = {19/28/37/46}, no 5
f) R5C56 = {69/78}
g) R89C1 = {15/24}
h) R8C56 = {49/58/67}, no 1,2,3
i) R9C56 = {49/58/67}, no 1,2,3
j) 8(3) cage in N1 = {125/134}, 1 locked for N1, clean-up: no 8 in R1C4
k) R1C789 = {389/479/569/578}, no 1,2
l) 9(3) cage in N6 = {126/135/234}, no 7,8,9
m) R567C9 = {389/479/569/578}, no 1,2
n) 14(4) cage in N3 = {1238/1247/1256/1346/2345}, no 9
o) 41(8) cage at R3C3 = {12356789}, no 4
1. 45 rule on C123 2 outies R19C4 = 1 innie R3C3 (I had this part before)
1a. R9C4 “sees” all cells of 41(8) cage at R3C3 except for R3C3, R9C4 not equal to R3C3 (because R19C4 = R3C3) -> R9C4 not equal to any cell in 41(8) cage -> R9C4 = 4, clean-up: no 5 in R1C3, no 2 in R8C1, no 9 in R8C56, no 9 in R9C56
1b. R19C4 = R3C3 -> R3C3 = R1C4 + 4, no 6,7 in R1C4, no 2,3,8 in R3C3, clean-up: no 2,3 in R1C3
2. Naked quad {5678} in R89C56, locked for N8
2a. Naked quint {56789} in R23589C6, locked for C6
2b. 9 in N8 locked in R7C45 + R8C4, locked for 41(8) cage at R3C3, clean-up: no 5 in R1C4 (step 1b), no 4 in R1C3
3. 45 rule on C1234 1 innie R2C4 = 1 outie R7C5 + 4, R2C4 = {567}, no 9 in R7C5
4. 45 rule on N7 2 remaining outies R6C13 = 8 = {17/26/35}, no 4,8,9
4a. R6C13 = 8 -> R7C123 = 18
5. 45 rule on N9 1 innie R7C9 = 1 outie R7C6 + 6 -> R7C9 = {789}
6. 45 rule on R9 3 outies R8C123 = 11 = {128/137/146} (cannot be {236} because R8C1 only contains 1,4,5, cannot be {245} which clashes with R89C1 because no 4 in R8C23), no 5,9, 1 locked for R8 and N7
6a. 1 in R9 locked in R9C789, locked for N9
6b. R9C789 = {129/138/156}, no 7
7. 45 rule on R9 3 remaining innies R9C123 = 16 = {259/268/358} (cannot be {367} because R9C1 only contains 2,5), no 7
7a. 7 in R9 locked in R9C56 = {67}, locked for R9 and N8, clean-up: no 5 in R9C789 (step 6b)
7b. Naked pair {58} in R8C56, locked for R8, clean-up: no 2 in R8C23 (step 6)
7c. 5 in R9 locked in R9C123, locked for N7
8. Killer pair 5,8 in R23C6 and R8C6, locked for C6, clean-up: no 7 in R5C5
9. 1 in C9 locked in R49C9
9a. 45 rule on N9 4 innies R1489C9 = 14 = {1238/1247/1256/1346}, no 9
10. 45 rule on C789 4(3+1) outies R467C6 + R6C5 = 10
10a. R1467C6 = {1234} = 10 -> R1C6 = R6C5 -> R467C6 + R6C5 = {1234}, 4 locked for N5
10b. R6C5678 cannot contain more than two of 1,2,3,4 -> no 1,2,3,4 in R6C78
11. 25(4) cage at R8C2 = {14569/23479} (cannot be {13489} because R9C123 only contains one of 8,9 (step 7), cannot be {14578} which clashes with combinations for R8C123 and R9C123, cannot be {24568} because 2,5,8 only in R9C23, cannot be {34567} because R8C123 cannot contain both of 6,7), no 8
11a. 8 in R9 locked in R9C789, locked for N9, clean-up: no 2 in R7C6 (step 5)
11b. R9C789 (step 6b) = {138} (only remaining combination), locked for R9 and N9
11c. Naked triple {259} in R9C123, locked for N7
11d. 2 in N8 locked in R7C45 + R8C4, locked for 41(8) cage at R3C3
11e. 2 in R467C6 + R6C5 (step 10a) locked in R46C6 + R6C5, locked for N5
12. R7C123 = 18 (step 4a) = {378/468}
12a. R7C123 = {378} => R7C9 = 9 => R7C6 = 3 (step 5) clashes with R7C123 -> no {378} in R7C123
12b. R7C123 = {468}, locked for R7, N7 and 26(5) cage at R6C1 -> R8C1 = 1, R9C1 = 5, clean-up: no 2 in R6C1, no 2,3,7 in R6C3
12c. Naked pair {37} in R8C23, locked for R8
[I originally saw step 12a as that chain but later saw the simpler
R7C69 = [17/39] (using step 5)
R7C123 = {468} (cannot be {378} which clashes with R7C69)]
13. R34C2 = {38/47/56} (cannot be {29} which clashes with R9C2), no 2,9
13a. 9 in N1 locked in R123C1, locked for C1
14. 45 rule on C1 3 innies R567C1 = 16 = {367} (only remaining combination, cannot be {268} because R6C1 only contains 3,7) -> R7C1 = 6, R56C1 = {37}, locked for C1 and N4, clean-up: no 4,8 in R3C2
15. 45 rule on N47 2 remaining innies R4C12 = 10 = [28/46], clean-up: no 6,7 in R3C2
16. R13C3 = {67} (hidden pair in N1), locked for C3 -> R8C23 = [73], clean-up: no 1 in R1C4, no 4 in R45C3
[Alternatively, which I spotted first, killer pair 3,5 in 8(3) cage and R3C2, locked for N1]
16a. Killer pair 2,9 in R45C3 and R9C3, locked for C3
16b. 1 in C4 locked in R34567C4, locked for 41(8) cage at R3C3, clean-up: no 5 in R2C4 (step 3)
17. 45 rule on R6 3 remaining innies R6C249 = 18 = {189/279/369/459/468} (cannot be {378} which clashes with R6C1, cannot be {567} which clashes with R6C13)
17a. 5 of {459} must be in R6C4 -> no 5 in R6C29
17b. {279} must be [279] -> no 7 in R6C9
18. R567C9 = {389/479/569/578}
18a. 5 of {569} must be in R5C9 -> no 6 in R5C9
19. 1 in R1 locked in R1C256
19a. 45 rule on R1 4 innies R1C1256 = 16 = {1249/1258/1348/1456} (cannot be {1267} which clashes with R1C3, cannot be {1357} which clashes with R1C34), no 7
20. 17(3) cage in N4 = {179/278/359} (cannot be {269/458} because R5C1 only contains 3,7, cannot be {368} which clashes with R4C2, cannot be {467} which clashes with R47C2), no 4,6
21. R4C12 = [46] (hidden pair in N4), R3C2 = 5, clean-up: no 9 in R2C6, no 6 in R2C9
21a. Naked triple {289} in R123C1, locked for N1
22. Naked quad {1289} in R45C3 + R56C2, locked for N4 -> R6C3 = 5, R6C1 = 3 (step 4), R5C1 = 7, clean-up: no 3 in R1C6 (step 10a), no 8 in R5C5
[R6C3 is a hidden single but the naked quad was easier to see]
22a. Naked pair {69} in R5C56, locked for R5 and N5, clean-up: no 1 in R4C3
22b. R5C1 = 7 -> R56C2 = 10 = [19/28/82], no 1 in R6C2
22c. 1 in N4 locked in R5C23, locked for R5
22d. 1 in R6 locked in R6C456, locked for N5
23. R9C6 = 7 (hidden single in C6), R9C5 = 6, R5C56 = [96], clean-up: no 8 in R23C6
23a. R23C6 = [59], R8C56 = [58], clean-up: no 2 in R2C9, no 6 in R3C9
24. 29(6) cage at R1C5 = {134678} (only remaining combination), no 2
24a. R1C4 = 2 (hidden single in N2), R1C3 = 7, R3C3 = 6, R8C4 = 9, R2C4 = 6 (hidden single in C4), R7C5 = 2 (hidden single in N8)
25. 4 in N5 locked in R6C56, locked for R6
25a. R6C5678 = {1468/2467}, no 9, 6 locked in R6C78, locked for R6
26. 9(3) cage in N6 = {135/234}, 3 locked for N6
27. R567C9 = {479/578} -> R7C9 = 7, R7C6 = 1 (step 5), R7C4 = 3, R1C6 = 4, R6C6 = 2, R4C6 = 3, R6C5 = 4 (step 10a), clean-up: no 4 in R23C9
28. Naked pair {89} in R6C29, locked for R6
28a. R6C4 = 1 (hidden single in R6)
29. R5C8 = 3 (hidden single in N6), clean-up: no 2 in R4C89 (step 26)
29a. Naked pair {15} in R4C89, locked for R4 and N6, clean-up: no 8 in R45C9 (step 27)
29b. R56C9 = [49], R6C2 = 8, R5C2 = 2 (step 22b), R45C3 = [91], R2C3 = 4, R5C7 = 8, R5C4 = 5, R7C23 = [48], R9C23 = [92], clean-up: no 2 in R3C9
30. Naked pair {38} in R23C9, locked for C9 and N3 -> R9C9 = 1, R9C78 = [38], R4C89 = [15], R1C9 = 6, R8C9 = 2
31. Naked pair {59} in R1C78, locked for R1 -> R1C1 = 8, R23C1 = [92]
32. R4C7 = 2 (hidden single in R4), R2C8 = 2 (hidden single in R2)
33. 45 rule on N9 2 remaining innies R78C7 = 11 = [56]
and the rest is naked singles