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Please let me know if anything isn't clear or is wrong. Thanks Andrew for the corrections.

Prelims
i. 20(3)n1: no 1 or 2
ii. 8(2)n1: no 4, 8 or 9
iii. 9(3)n2: no 7, 8 or 9
iv. 13(2)n2: no 1, 2 or 3
v. 5(2)n2 = {14/23}
vi. 12(2)n2: no 1, 2 or 6
vii. 10(2)n3: no 5
viii. 12(2)n4: no 1, 2 or 6
ix. 13(2)n5: no 1, 2 or 3
x. 11(3)n6: no 9
xi. 10(2)n6: no 5
xii. 14(2)n8 = {59/68}
xiii. 12(2)n8: no 1, 2 or 6

1. "45" n478: r4c1 - 1 = r9c7
1a. = [54/65] = 5...
1b. no 5 in r4c7 or r9c1
1c. r4c1 = (56) -> r3c1 = (23)
1d. r9c7 = (45) -> r9c6 = (78)

2. "45" n9: r6c9 = r9c7 = (45)
Andrew has pointed out that combining step 1a and step 2 -> more CPEs for 5 in r4c9 and r6c123; of course the 5 in r4c9 is eliminated in step 3 and from r6c123 in step 5. Nice one Andrew! Wish I'd seen that.

3. 11(3)n6 = {128/137/146/236}(no 5) ({245} blocked by r6c9)

4. 12(2)n89 = [75/84] = [5/8..] -> [85] blocked from r5c67 in 13(2)n56

5. r6c9 = 5 (hsingle n6)
5a. r7c89 = 9 = {18/27/36}(no 4 or 9)

6. r9c7 = 5 (step 2)
6a. no 9 in r8c5

7. r4c1 = 6 (step 1)
7a. no 4 in r3c8
7b. r3c1 = 2
7c. no 8 in r4c8

8. "45" n1: r1c4 - 5 = r3c1 -> r1c4 = 7
8a. no 5 in r4c5
8b. no 6 in r23c4 (13(2)n2)
8c. r12c3 = 6 = {15}: both locked for n1 & c3

9. 20(3)n1 = {389/479}(no 6)
9a. = 9{..}: 9 locked for n1
9b. 17(3)n1 = 6{38/47}

10. r9c6 = 7 (cage sum)
10a. no 6 in r5c7

11. 5 in r3 only in n2: 5 locked for n2
11a. no 8 in r3c4
11b. 9(3)n2 = {126/234} = 2{16/34} = [1/3..]
11c. 2 locked for n2
11d. no 3 in r2c7
11e. if 1 is not in 9(3) it must be {234} -> r2c6 = 1
11f. -> 1 locked for n2 in r12c56

12. 1 in r3 only in n3: locked for n3
12a. no 4 in r2c6

13. Killer pair (13) in 9(2)n2 (step 11b) & r2c6: 3 locked for n2
13a. no 9 in r4c5

Looking around now for somewhere to make another big chunk
14. "45" n6: 3 innies r4c78 + r5c7 = h19(3): no 1
14a. no 9 in r3c8
14b. h19(3) = {289/379/478}

15. "45" n8: r789c4 = h9(3) = {126/135/234}(no 89) = [2/5..]
15a. 8 & 9 in n8 must be in 14(2) & 15(3) since they cannot both be in one
15b. 15(3) = {159/168/249/348} ({258} clashes with h9(3) step 15)

16. 15(3)n4 = {249/258/348/357}(no 1) ({159} not possible with 1 & 5 only in r4c2)

17. 1 in n4 only in r6: 1 locked for r6
17a. no 9 in 10(2)n6

18. 9 in n6 only in h19(3)(step 14) = 9{28/37}(no 4) = [2/3..]
18a. no 6 in r3c8
18b. no 9 in r5c6

19. "45" n5: 3 innies = h17(3)
19a. max. r4c5 + r5c6 = 14 -> min. r4c6 = 3
19b. h17(3) = {359/368/458/467}

20. "45" r1234: 4 innies r4c2349 = h16(4) & must have 1 for r4
20a. = 1{249/258/348/357} = [2/3..]

21. hidden Killer pair (23) in h16(4)(step 20) & r4c78 in h19(3)n6 (step 18)
[edit: Discussion with Andrew (by PM) about this one. I think of it as "hidden" because the 2 cages do not completely share a house.]
21a. 3 locked for r4
21b. no 9 in r3c5

22. h17(3)n5 = {458/467}(no 9) = [7/8..]
22a. = 4{58/67}: 4 locked for n5

23. "45" r6789: r6c456 = h18(3) = {279/369}(no 8) ({378} clashes with h17(3)n5 step 22)
23a. 9 locked for n5 & r6

24. split-cage 10(3) at r4c4 + r5c45 must have 1 = {127/136}(no 5, 8)

25. h17(3)n5 must have all of 4, 5 & 8 for n5: hidden triple (no 6, 7)
25a. no 7 in r5c7
25b. no 5 in r3c5
25c. 8 locked for r4
25d. 5 locked for c6

26. r3c4 = 5(hsingle r3)
26a. r2c4 = 8

27. r34c5 = [48]

28. r89c5 = [59] (last permutation)

29. r3c6 = 9 (hsingle n2) -> no 9 elsewhere in 31(5)n3

30. 9(3)n2 = {126} (last combination): 1 locked for n2

31. r2c67 = [32]

32. h19(3)n6 must have 3/7 for r4c7 = {379}
32a. r5c7 = 9, 3 & 7 locked for r4

33. r5c6 = 4 (cage sum) -> r4c6 = 5 (no 5 in r2c8)

34. 12(2)n4 = {57} last combination; 7 locked for r5 & n4

35. r6c5 = 7 (hsingle r6) -> r6c46 = [92] (h18(3)r6)

36. r4c4 = 1, r1c5 = 2 (hsingle n2), r1c8 = 5 (hsingle n3), r8c8 = 9 (hsingle c8)
36a. r78c7 = 4 = {13}: both locked for n9 & c7

37. 19(5)n478 must have 1: only in r6c2

38. 10(2)n6 = {46}: both locked for n6 & r6

39. r4c7 = 7 -> 10(2)n3 = [73]

40. 14(3)n69 = [5][27] (last permutation)

41. naked triple {468} in n3: all locked for n3

Looks like I lost the last few steps.
Cheers
Ed

Assassin 108 v2 walkthrough: (9 major steps)


0. Preliminary work

5/2 @ r2c6={14|23}
8/2 @ r3c1={17|26|35}
12/2 @ r3c5,r5c1,r9c6={39|48|57}
13/2 @ r2c4,r5c6={49|58|67}
14/2 @ r8c5={59|68}
9/3 @ r1c5={126|135|234}


1. Gentle crackdown #1: n1, n478

Innies @ n478: r4c1+r9c6=13=[58|67]
=> r34c1=[26|35], r9c67=[75|84]
Outies @ n1: r1c4+r4c1=13=[85|76]
=> r1c4=r9c6=7|8
Innies @ n1: r12c3+r3c1=8=[{14}3|{15}2]
=> 1 @ c3,n1 locked @ r12c3


2. Gentle crackdown #2: n5, c4

Innies @ c1234: r456c4=16
Outies @ r6789: r45c4+r5c5=10
=> r6c4-r5c5=16-10=6 => r5c5+r6c6=[17|28|39]
=> r1c4,r23c4,r6c4 form killer NT {789} @ c4
=> r45c4+r5c5=10=[{16|25}3|{35}2|{36|45}1]
But 13/2 @ r2c4 has 4|5|7
=> r456c4=16 can't be [{45}7]
=> r45c4+r5c5 can't be [{45}1]
=> r45c4+r5c5={136|235} with 3 @ n5 locked
=> 12/2 @ r3c5=[39|48|57|75|84]


3. Gentle crackdown #3: n2, c5

Innies @ n2: r1c4+r2c6+r3c56=23
Max r1c4+r3c5=7+8=15 => Min r23c6=23-15=8
r2c6 from {1234} => r3c6 from {56789}
=> 1 @ r3,n3 locked @ r3c789
=> 5/2 @ r2c6=[14|23|32]
Max r1c4+r3c6=8+9=17 => Min r2c6+r3c5=6
=> r2c6 from {123} => r3c5 from {4578}
=> 12/2 @ r3c5={48|57}
=> r34c5,r89c5 form killer NP {58} @ c5


4. Powerful hammer #1: 28/6

Now consider 28/6 @ r4c4
r5c5+r6c4=[17|28|39], r45c4+r5c5=10
=> r6c456=28-10=18 => r45c4+r5c5+r6c456=
[{36}17{29}|{35}28{19|46}|{16}39{27|45}|{25}3918]
=> Either r45c4 has 6 or r6c46 has 8
=> Either r45c4 has 6 or r1c4=r9c6=7
=> 13/2 @ r2c4 can't be {67}
=> 13/2 @ r2c4 must be {49|58} with 5|9
=> r45c4+r5c5+r6c456 can't be [{25}3918], must be
[{36}17{29}|{35}28{19|46}|{16}39{27|45}]


5. Powerful hammer #2: c4

Now consider c4
r456c4=[{36}7|{35}8|{16}9] => r123456789c4=
[8{49}{36}7{125}|7{49}{35}8{126}|7{58}{16}9{234}]
=> Either r1c4=8 or r789c4={126} or r123c4=[7{58}]
=> Either r9c6=8 or r789c4={126} or 12/2 @ r3c5=[48]
=> 14/2 @ r8c5 can't be {68}, must be {59} (NP @ c5,n8)


6. Mop up #1: c5, n2

Now 12/2 @ r3c5={48} (NP @ c5)
=> r23c4,r3c5 form killer NP {48} @ n2
=> r1c4=7 => 12/2 @ r9c6=[75], 8/2 @ r3c1=[26]
=> 14/2 @ r8c5=[59], r12c3=13-7=6={15} (NP @ c3,n1)


7. Mop up #2: n5, n2

Innies @ n5: r4c56+r5c6=17 from {1245689}
r4c5 from {48} => r4c56+r5c6={458} (NT @ n5)
=> r6c4=9 => r5c5=3 => r4c45=[16], r6c56=[72]
=> 13/2 @ r2c4={58} (NP @ n2) => 12/2 @ r3c5=[48]
=> r23c6=23-7-4=12=[39] => r2c7=5-3=2


8. Mop up #3: n456

12/2 @ r5c1={48|57} has 5|8
=> 13/2 @ r5c6=[49] => r4c6=5
=> 12/2 @ r5c1={57} (NP @ r5,n4) => r5c89 from {128}
=> 11/3 @ r4c9=[2{18}] => r5c89={18} (NP @ r5,n6)
=> r5c3=2 => r4c23=15-2=13={49} (NP @ r4,n4)


9. Mop up #4: endgame

19/5 @ r6c2 from {12346789} can't be {12358}
=> it can't have 8 => r6c123=[813]
=> r78c4={24} (NP @ n8) => r7c3=19-1-3-2-4=9
=> r4c23=[94], r9c4=3 => r89c3=16-3=13=[76]
=> r3c3=8 => r23c2=17-8=9=[63] => r7c12=16-8=8=[35]
=> 10/2 @ r3c8=[73] => r4c7=7 => r2c8+r3c7=31-9-5-7=10=[46]


The rest is trivial.

941726853
765813249
238549671
694185732
572634918
813972465
359468127
487251396
126397584