3x3::k:3840:3840:3840:0000:3330:4867:4867:4867:4867:6678:0000:0000:0000:3330:4357:3078:4359:4359:6678:6678:0000:4357:4357:4357:3078:4359:2824:6678:5897:5897:5897:3338:3083:3083:4108:2824:6678:5897:5897:3853:3338:3083:4108:4108:3854:4367:4367:5897:3853:3853:3853:7696:3601:3854:6674:6674:6674:7696:1811:1811:7696:3601:3601:1044:6674:6165:7696:7696:7696:7696:3588:3588:1044:6165:6165:6165:5633:5633:5633:5633:3588:

Prelims

a) R12C5 = {49/58/67}, no 1,2,3
b) R23C7 = {39/48/57}, no 1,2,6
c) R34C9 = {29/38/47/56}, no 1
d) R45C5 = {49/58/67}, no 1,2,3
e) R56C9 = {69/78}
f) R6C12 = {89}
g) R7C56 = {16/25/34}, no 7,8,9
h) R89C1 = {13}
i) 26(4) cage at R7C1 = {2789/3689/4589/4679/5678}, no 1
j) 23(6) cage at R4C2 = {123458/123467}, no 9

Steps resulting from Prelims and Initial Placement
1a. Naked pair {89} in R6C12, locked for R6 and N4, clean-up: no 6,7 in R5C9
1b. Naked pair {13} in R89C1, locked for C1 and N7
1c. 45 rule on N7 1 outie R9C4 = 9

2. 45 rule on N5 1 innie R4C4 = 1 outie R4C7 + 5 -> R4C4 = {678}, R4C7 = {123}
2a. 23(6) cage at R4C2 = {123458/123467}, 2,4 locked for N4
2b. 45 rule on N4 2 innies R45C1 = 1 outie R4C4 + 5, IOU no 5 in R5C1

3a. 45 rule on N89 2 outies R6C78 = 6 = {15/24}
3b. 45 rule on N689 2 innies R4C79 = 8 = [17/26/35], R4C7 = {123} -> R4C9 = {567}, R3C9 = {456}
3c. Killer pair 6,7 in R34C9 and R6C9, locked for C9, 7 also locked for N6
3d. 45 rule on N3 2(1+1) outies R1C6 + R4C9 = 14 = [77/86/95], R4C9 = {567} -> R1C6 = {789}
3e. 45 rule on N2 3 innies R1C46 + R2C4 = 15 which can only contain one of 7,8,9 -> no 7,8 in R12C4
3f. 15(4) cage at R5C4 cannot be 7{125}/7{134}/8{124} which clash with R6C78 -> no 7,8 in R5C4

4. 15(4) cage at R5C4 = {1257/1347/1356/2346}
4a. 45 rule on N5 3 innies R4C46 + R5C6 = 17 = {179/269/278/368} (cannot be {359/458/467} which clash with 15(4) cage), no 4,5 in R45C6
4b. 6 of {269/368} must be in R4C4 (R4C46 + R5C6 cannot be 8{36} because 12(3) cage at R4C6 cannot be {36}3), no 6 in R45C6
4c. R45C5 = {49/58} (cannot be {67} which clashes with R4C46 + R6C5), no 6,7

5. 26(5) cage at R2C1 = {14579/14678/23579/23678/24569/24578/34568} (cannot be {13589/13679} because 1,3 only in R3C2, cannot be {12689/23489} because must contain two of 5,6,7 for R45C1)
5a. 26(5) cage only contains two of 5,6,7 which must be in R45C1 -> no 5,6,7 in R2C1 + R3C12

6. 16(3) cage at R4C8 = {169/349/358} (cannot be {259} which clash with R6C78, cannot be {268} which clashes with R56C9), no 2

7. 45 rule on R9 2 outies R8C13 = 1 innie R9C9 + 5
7a. Max R8C13 = 11 -> no 8 in max R9C9
7b. Min R8C13 = 6 -> no 2 in R8C3

8. 45 rule on R1 2 innies R1C45 = 11 = [29/38/47]/{56}, no 1 in R1C4, no 4 in R1C5, clean-up: no 9 in R2C5
8a. 15(3) cage at R1C1 = {159/168/258/267/357/456} (cannot be {249/348} which clash with 26(5) cage at R5C1)
8b. R1C45 = [29/38/47] (cannot be {56} which clashes with 15(3) cage), no 5,6, clean-up: no 7,8 in R2C5
8c. R1C46 + R2C4 = 15 (step 3e) = {249/258/267/348/357} (cannot be {159/168} because R1C4 only contains 2,3,4, cannot be {456} because R1C6 only contains 7,8,9), no 1 in R2C4
8d. R1C45 = 11 -> R1C46 cannot be 11 (CCC) -> no 4 in R2C4
8e. R1C46 + R2C4 = {249/258/267/348} (cannot be {357} = [375] which clashes with R1C45 + R2C5 = [385])
8f. 4 of {348} must be in R1C4 -> no 3 in R1C4, clean-up: no 8 in R1C5, no 5 in R2C5

9. Consider placement for 8 in R1
9a. 8 in 15(3) cage at R1C1, locked for N1 => 26(5) cage at R2C1 (step 5) = {14579/23579/24569} => R4C1 = 5
or 8 in 19(4) cage at R1C7 which cannot contain both of 8,9 => no 9 in R1C6, no 5 in R4C9 (step 3d)
-> no 5 in R4C9, clean-up: no 9 in R1C6 (step 3d), no 6 in R3C9, no 3 in R4C7 (step 3b), no 8 in R4C4 (step 2)
[The first breakthrough, thanks to the elimination of 8 from R1C5 in step 8f.]
9b. Naked pair {67} in R4C49, locked for R4 -> R4C1 = 5, clean-up: no 8 in R5C5
9c. Naked pair {67} in R46C9, 6 locked for N6
9d. 3 in N6 only in 16(3) cage at R4C8 (step 6) = {349/358}, no 1
9e. R4C46 + R5C6 (step 4a) = {179/269/368} (cannot be {278} = 7{28} because 12(3) cage at R4C6 cannot be {28}2)
9f. 7 of {179} must be in R4C4 -> no 7 in R5C6
9g. R1C46 + R2C4 (step 8e) = {258/267/348}
9h. 2 of {258/267} must be in R1C4 -> no 2 in R2C4
9i. 19(4) cage at R1C6 = {1378/1468/1567/2368} (cannot be {1279} which clashes with R1C5, cannot be {2458/2467} which clash with R1C4, cannot be {1459/3457} which clash with R3C9, cannot be {1369/2359} because R1C6 only contains 7,8), no 9
9j. 15(3) cage at R1C1 (step 8a) = {159/357/456} (cannot be {168/258/267} which clash with 19(4) cage), no 2,8, 5 locked for R1 and N1
9k. 7,9 of {159} must be in R1C1 -> no 7,9 in R1C23
9l. R1C45 = 11 (step 8b) = [29/47], R12C5 = [76/94] -> R1C45 + R2C5 = [294/476], 4 locked for N2
9m. Killer triple 3,4,5 in 19(4) cage at R1C6, R23C7 and R3C9, locked for N3

10. R1C6 + R4C9 (step 3d) = 14 = [77/86]
10a. R1C46 + R2C4 (step 9g) = {258/348} (cannot be {267} = [276] which clashes with R4C49 = [67], no 6,7
[The second breakthrough.]
10b. R1C6 = 8 -> R4C9 = 6, R3C9 = 5, R4C7 = 2 (step 3b), R4C4 = 7, R6C9 = 7 -> R5C9 = 8, clean-up: no 7 in R23C7, no 4 in R6C78 (step 3a)
10c. R4C7 = 2 -> R45C6 = 10 = {19}, locked for C6 and N5, clean-up: no 4 in R45C5, no 6 in R7C5
10d. R45C5 = [85], clean-up: no 2 in R7C6
10e. Naked pair {15} in R6C78, locked for R6 and N6
10f. 30(7) cage at R6C7 must contain 2, locked for N8, clean-up: no 5 in R7C6
10g. R7C56 = [16] (cannot be {34} because 30(7) cage at R6C7 must contain both of 3,4 and R7C56 ‘sees’ all its cells except for R68C7 and R6C7 only contains 1,5)
[I’d been aware of this type of ‘sees all except’ step for a while, realising that R678C7 had to contain one of 1,2,3, but this was the first time I found it useful.]
10h. 30(7) cage at R6C7 must contain 1 in R68C7, locked for C7

11. 8 in C4 only in 30(7) cage at R6C7 = {1234578}, no 6,9, no 8 in R78C7

12. R5C1 = 7 (hidden single in N4)
12a. 15(3) cage at R1C1 (step 9j) = {159/456}, no 3
12b. 3 in R1 only in R1C789, locked for N3, clean-up: no 9 in R23C7
12c. Naked pair {48} in R23C7, locked for C7 and N3
12d. R5C7 = 9 (hidden single in C7) -> naked pair {34} in R45C8, locked for C8, R45C6 = [91]
12e. 30(7) cage at R6C7 must contain 4, locked for N8
12f. 22(4) cage at R9C5 = {3568} (only possible combination, cannot be {1678/2578} because 1,2,8 only in R9C8) = [3568], R89C1 = [31]
12g. 7 in N8 only in R8C56, locked for R8 and 30(6) cage at R6C7
12h. Naked pair {15} in R68C7 -> R17C7 = [73]
12i. R1C67 = [87] = 15 -> R1C89 = 4 = [13], R1C5 = 9 -> R2C5 = 4, R1C4 = 2 (step 8b), R23C7 = [84], R6C78 = [15]
12j. Naked pair {37} in R23C6, locked for C6 and N2 -> R3C45 = [16]
12k. Naked pair {48} in R78C4, locked for N8 -> R8C56 = [72]
12l. Naked pair {29} in R2C29, locked for R2 -> R2C8 = 6
12m. R8C8 = 9 -> R89C9 = 5 = [14]
12n. Naked pair {27} in R9C23, locked for N7, R9C4 = 9 -> R8C3 = 6 (cage sum)

and the rest is naked singles.

I'll rate my walkthrough for A370 at 1.5 I only used one forcing chain, but my final key step was a 'sees all except' step.

Preliminaries from SukokuSolver
Cage 4(2) n7 - cells ={13}
Cage 17(2) n4 - cells ={89}
Cage 15(2) n6 - cells only uses 6789
Cage 7(2) n8 - cells do not use 789
Cage 12(2) n3 - cells do not use 126
Cage 13(2) n2 - cells do not use 123
Cage 13(2) n5 - cells do not use 123
Cage 11(2) n36 - cells do not use 1
Cage 26(4) n7 - cells do not use 1
Cage 23(6) n45 - cells do not use 9

NOTE: no clean-up done unless stated.
1. "45" on n7: 1 outie r9c4 = 9

2. 17(2)n4 = {89}: both locked for n4 and r6
2a. r5c9 = (89)

3. 4(2)n7 = {13}: both locked for c1 and n7

4. "45" on n3: 2 outies r1c6 + r4c9 = 14 (no 1,2,3,4: note, could be [77])

5. "45" on n6789: 2 innies r4c79 = 8 = [35/26/17](no 4,8,9); r4c7 = (123)
5a. no 5,6 in r1c6 (outiesn3=14)

6. "45" on n56789: 2 innies r4c49 = 13 = {67}/[85]
6a. r4c4 = (678)

7. 11(2)r3c9 = {56}/[47] = 6/7
7a. -> killer pair 6,7 with r6c9: both locked for c9 and 7 for n6

Key step to get anywhere. Like a big intersection.
8. "45" on n356789: 1 outie r1c6 - 1 = 1 innie r4c4 = [76/87/98]
8a. "45" on r1: 2 innies r1c45 = 11 (no 1: no 8 in r1c4)
8b. "45" on r1: 1 innie r1c4 + 2 = 1 outie r2c5
8c. "45" on c456789: 3 innies r124c4 = 14
8d. but [356] blocked by 5 in r2c5 (step 8b)
8e. but [536] blocked by 7 in both r1c6 and r2c5 (steps 8. & 8b)
8f. -> {356} blocked from h14(3)
8g. = {158/167/248/257/347}
8h. but {167} as [716], blocked by 7 in r1c6 (step 8.)
8i. and 1 in {167} must go in r2c4
8j. -> no 6 in r4c4 nor r2c4
8k. -> no 7 in r4c9 (h13(2))
8l. -> no 7 in r1c6 (outiesn3=14)
8m. and no 1 in r4c7 (h8(2)r4c79)

9. hidden single 7 in n6 -> r6c9 = 7, r5c9 = 8

10. 11(2)r3c9 = {56} only: 5 locked for c9

11. 23(6)r4c4 = {123458/123467}
11a. can't have both 7,8 -> no 7 in r45c23

12. 7 in n4 only in r45c1: 7 locked for c1 and no 7 in r3c2

13. "45" on n4: 1 outie r4c4 + 5 = 2 innies r45c1
13a. 1 outie = (78) -> 2 innies = 12/13 and must have 7 = {57/67}

Lots of combos involved here.
14. 26(5)r2c1: {13679} blocked by 1,3 only in r3c2
14a. must have 7 for r45c1 = {14579/14678/23579/23678/24578}
14b. can't have both 5 & 6, one of which must go in r45c1 -> no 5,6 in r23c1+r3c2

Took me a long time to look in this area.
15."45" on r4..9: 4 outies r2c1+r3c12 + r3c9 = 19
15a. 6 in r3c9 -> 3 outies in n1 = 13 = {28}[3]/{48}[1]
15b. note: must have 8 with r3c9 = 6
15c. "45" on n3: 1 outie r1c6 - 3 = 1 innie r3c9 = [85/96]: note: must have 8 with r3c9 = 5
15d. -> 8 in r1c6 or r23c1+r3c2 -> no 8 in r1c123

16. 19(4)r1c6 must have 8,9 for r1c6 -> max. other 3 = 11
16a. -> no 8,9 in r1c789 (note, can't be 8128)

17. 8 in r1 only in n2 in r1c56: locked for n2
17a. no 5 in r1c5, no 6 in r1c4 (h11(2)r1c45)

18. 8 in n2 in r1c6 -> 7 in r4c4 (iodn356789=-1) or 8 in n2 in r1c5 -> 3 in r1c4 (h11(2))
18a. -> h14(3)r124c4 must have 3 or 7
18b. = {167/257/347}(no 8)
18c. -> r4c4 = 7, r1c6 = 8, r34c9 = [56], r4c7=2 (1 innie n6789), r45c1 = [57]

19. "45" on n789: 2 outies r6c78 = 6 = {15} only: both locked for n6 and r6

20. 30(7)r6c7 = {1234569/1234578}
20a. must have 2 which is only in n8: 2 locked for n8
20a. must have both 3 & 4 which can't both go in r8c7
20b. ->{34} blocked from 7(2)n8
20c. -> 7(2)n8 = {16} only: both locked for n8 and r7

21. hidden single 6 in c1 -> r1c1 = 6

22. 19(4)r1c6 = [8]{137} only: 1,3,7 locked for r1 and n3

23. 12(2)n3 = {48} only: both locked for n3 and c7

24. r1c1 = 6 -> r1c23 = 9 = {45} only: both locked for r1 and n1
24a. r1c45 = [29], r2c5 = 4, r2c4 = 5 (h14(3))

25. r45c1 = 12 -> r2c1 + r3c12 = 14 = {29}[3] only: 2,9 locked for n1 and c1

26. hidden single 4 in c1 -> r7c1 = 4

27. 14(3)r6c8 = [572] only permutation

28. 8 in c4 only in 30(7)r6c7 -> = {1234578}(no 9)
28a. must have 2,4,7 which are only in n8 -> r8c456 = [4]{27}: 2 & 7 locked for r8 & n8
28b. r7c4 = 8

29. hidden single 9 in c7 -> r5c7 = 9

30. r4c7 = 2 -> r45c6 = 10 = [91/46] only

singles.

the interesting shape of the 30(7). E.g.,
First - if 7(2)n8 from {25}/{34} -> r68c7 = {25}/{34}
Second - if 30(7) = {1234569} -> r9c56 = {78} and r78c8 = {78}

1. Innies whole puzzle = uncaged cells in n12 = +23(5) (May have repeats).
Innies r1 -> r1c45 = +11(2)
4(3)r8c1 = {13}
Outies n7 -> r9c4 = 9
Outies r789 -> r6c78 = +6(2)
-> Remaining Innies n6 = r4c79 = +8(2)

2. 17(2)n4 = {89}
23(6)n4 = {1234(58|67)}
IOD n5 -> r4c4 = r4c7 + 5
-> r4c4 from (678), r4c7 from (123)

3. IOD n124 -> r1c6 = r4c4 + 1
-> r1c6 from (789)

5. Trying r4c4 = 8
Puts r45c1 = {67}
Also puts r1c6 = 9
Puts remaining Innies n2 = r12c4 = +6(2) (No 3)
-> puts 8 in r1 in r1c123
-> leaves no solution for 26(5)r2c1
-> r4c4 from (67)
-> r45c1 = [56] or [57] i.e., r4c1 = 5

6. Trying r4c4 = 6
Puts r1c6 = 7
Puts remaining innies n2 = r12c4 = +8(2)
-> puts r12c4 = {35}
-> puts 13(2)n2 = {49}
Which leaves no solution for r1c45 = +11(2)
-> r4c4 = 7

7. -> r45c1 = [57]
Also -> r4c7 = 2
-> r4c9 = 6
-> r3c9 = 5
Also -> 15(2)n6 = [87]
Also -> r6c78 = {15}
-> 16(3)n6 = {349}
Also r6c3456 = {2346}
-> 15(4)n5 = {2346}
-> 13(2)n5 = [85]
-> r45c6 = {19}
Also r1c6 = 8

8. 2 in r4c7 -> 2 in 30(7) in n8
-> 7(2)n8 not {25}
-> 12(2)n3 from {39} or {48}
-> At least one of (34) in 30(7) in n8
-> 7(2)n8 not {34}
-> 7(2)n8 = [16]

9. 26(5)n14 cannot contain all of (567)
-> HS 6 in c1 -> r1c1 = 6
-> 3 in r1 in n3
-> 19(4)r1 = [8{137}]
-> 12(2)n3 = {48}
-> 17(3)n2 = {269}
Also r1c45 = [29]
-> r2c45 = [54]
-> 17(4)n3 = {1367}
Also 12(2)n3 = [84]

10. Also 15(3)r1 = [6{45}
-> 26(5)n14 = [{29}357]
-> HS r7c1 = 4
Also 17(2)n4 = [89]
-> HS r7c3 = 9
Also HS r3c3 = 8
-> r2c23 = {17}

11. 8 in n8 in r78c4
-> 30(7) = {1234578}
-> 9 in n9 in r8c89
-> HS 9 in c7 -> r5c7 = 9
-> r45c6 = [91]
Also r45c8 = {34}

12. Only solution for 14(3)r6c8 is [572]
-> r6c7 = 1
-> 19(4)r1 = [8713]
Also 4 in 30(7) in r8c46
-> HS 4 in r9 -> r9c9 = 4
-> 14(3)n9 = [914]
etc.