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Prelims
i. 12,11(2+2) at r1c3: no 1
ii. 8,7(2+2) at r1c9: no 8,9
iii. 13,11(2+2) at r3c2: no 1
iv. 14,11(2+2) at r3c6: no 1
v. 11,5(3+2) at r4c7: no 9
vi. 15,11(2+2) at r5c9: no 1
vii. 9,8(2+2) at r7c2: no 9
viii. 9,7(2+2) at r8c5: no 9
ix. 12,12(2+2) at r8c7: no 1,2

1. "45" on n9: 7 outies!! r56c9 + r6c8 + r6c56 + r79c6 = 52
1a. max. r6c8 + r79c6 = 26 (9+8+9) -> r56c9 + r6c56 min. 26
1b. -> must be 15(2) + 14(2) to make it to min. 26
1c. 15(2) at r56c9 = {69/78}
1d. 14(2) at r6c56 = {59/68}
1e. -> 3 remaining outies n9 = 23
1f. max. r79c6 = 17 -> min. r6c8 = 6
1g. max. r6c8 = 9 -> min. r79c6 = 14 (no 1..4)
1h. r7c67 = 10(2)(no 5), max. r7c7 = 4
1i. r67c8 = 11(2), max. r7c8 = 5

2. 11,5(5) at r4c7 must be 5(2) since min. any 3 cells is 6
2a. 5(2) must be at r5c56 = {14/23}
2b. 11(3) at r456c7

3. "45" on n6: 1 remaining outie r3c9 + 2 = 1 remaining innie r6c8
3a. but [68/79] clashes with 15(2) at r56c9 -> = [46/57]
3b. r3c9 = (45), r6c8 = (67)
3c. r7c8 = (45) (11(2) permutations)

A fun one, don't think it's needed.
4. "45" on n6: 2 remaining outies r3c9 + r7c8 = 9 = {45}
4a. 4 and 5 locked in common peers at r123c8 and r789c9

5. "45" on n9: 1 outie r9c6 - 2 = 2 innie r7c78
5a. max. 2 innies = 7 -> max. r7c7 = 2
5b. min. 2 innies = 5 -> min. r9c6 = 7
5c. r7c6 = (89) (10(2) cage)

6. Killer pair 6,7 in 15(2) at r5c9 and r6c8: both locked for n6

7. 11(3) at r4c7 = {245} only ({128} blocked by r7c7): all locked for c7 & n6

It's cracked from now so only essential clean-up done.
8. r7c7 = 1 -> r7c6 = 9 (10(2) cage)

9. r34c9 can only be 6(2) since no 6 nor 7 are available in r4c9 for an 11(2)
9a. r34c9 = [51]
9b. -> r6c8 = 7 (step 3a) and r7c8 = 4 (11(2) cage)

10. r7c78 = 5 -> r9c6 = 7 (i/o n9)

11. 15(2) at r5c9 = {69}: both locked for c9 & n6

12. r45c8 = {38}: both locked for c8

13. "45" on r89: 2 outies r7c29 = 12(2)
13a. ->r7c29 = [57] (last permutation)

14. r9c67 can only be a 13(2) cage since no 5 is in r9c7 for a 12(2)
14a. r9c7 = 6

15. r8c78 = 12(2) = [39] (only permutation)

16. r78c9 must be 9(2) cage since no 6 in r8c9
16a. -> r8c9 = 2
16b. r9c89 = [58]

17. "45" on c89: 1 remaining innie r1c8 = 1

Continue along in similiar vein with a couple of killer pairs thrown in. The only thing to watch is that the 12,6(4) at r4c4 must have a 6(1)