I get to be first, with no miracle guesses this time!
Thanks to Afmob and Andrew for correcting typos!
Prelims:
a) N1: Two 13(2) no 1,2,3
b) N12: 6(3) no 4,5,6,7,8,9
c) N12: 14(2) no 1,2,3,4,7
d) N14: 14(4) no 9
e) N3: 8(3) no 6,7,8,9
f) N47: 20(3) no 1,2
g) N5: 32(5) no 1
h) N45 and N56: 6(2) no 3,6,7,8,9
i) N58: 7(3) no 3,5,6,7,8,9
j) N6: 19(3) no 1
k) N78: 29(4) no 1,2,3,4,6
l) N89: 15(2) no 1,2,3,4,5
m) N9: 7(2) no 7,8,9
n) N9: 8(2) no 4,8,9
Solving:
1) R1C234 6(3) = {123} locked for R1
2) N3: 8(3) 1 locked for N3.
3) R5: locked quad {1245} in the two 6(2) for R5.
4) R12: 2 innies R2C28 = 8 -> R2C2 = {567}, R2C8 = {123}
a) R3C2 = {678}
5) R89: 2 innies R8C28 = 5 -> R8C28 = {1234}
a) R7C8 = {3456}
6) N5: 4 innies R45C6 + R56C4 = 13.
a) R4C6 = {36} -> r3c56 NO 3,6,9
b) 1,4 locked into R5C46 and R6C4 for N5
7) N78: 29(4) {5789} locked
a) R8C56 no 5,7,8,9
8) C1: 4 innies: R3489C1 = 12 -> R3489C1 no 7,8,9
9) N3: 2 innies: R2C7+ R3C9 = 12 - > R2C7 and R3C9 no 2,6
10) N7: 2 innies R7C1 + R8C3 = 17 -> R7C1 and R8C3 = {89} locked for N7
a) Cleanup: R7C6 no 7 -> R7C7 no 8 because of the 29(4). R9C6 no 5,7.
11) R789: 2 innies and 1 outie R7C19 = R6C4 + 9 -> R7C9 = {12345}
12) 9 locked in N4 R56C2 n/e.
13) N47: 2 innies and 1 outie: R58C3 = R3C1 +10 -> R5C3 no 1 -> R5C4 no 5, R3C1 no 5,6
14) R567C4 = {124} triple locked for C4
a) Cleanup: R1C4 = 3
b) R1C23 no 3 -> {12} locked for N1
15) N1: 3 innies R23C3 + R3C1 = 16 -> R2C3 no 6,9
16) N12: 13(3) R2C3 no 8, R2C5 no 5,6,7,8,9
17) N89: 17(3) r8C7 = {789} R8C56 no 1,2. 6 locked into R8C56 for N8, R8. R8C7 no 9
a) Cleanup: R9C9 no 2, R7C7 no 9.
18) N8: Quad {5789} at R7C6 and R8C4 and R9C45 -> no 8,9 at R9C6
19) N89: 15(3) R9C78 no 1. 9 locked into R9C78 -> R9C78 no 3,6,7,8
20) N9: R8C7 = 8 since n/e.
a) Cleanup: R8C3 = 9
b) R7C1 = 8
c) R3C4 no 5
d) R12C1 no 5
e) R7C6 = 9
f) R56C1 = [75]
g) R12C1 = {49} locked for C1
h) R5C34 = {24} locked for R5
i) Remainder of puzzle continues to be cleanup, simple sums, hidden and naked singles.
421395768
965718324
378642159
182956473
794231586
536487912
847129635
219563847
653874291
Editted twice for typos.
Assassin 79
This one was special since it led to my shortest walkthrough I've written so far. Normally I need some hours to solve Ruud's Assassins but this time it took me about 40 minutes, but more like 2 hours 
since I've made mistakes somewhere and had to start over again twice.
Edit: Made a mistake in the beginning which led to a quicker solution. Thanks to Andrew, I corrected it. So after rewriting my walkthrough I still managed to make it my shortest one so far, but it's a bit longer than my first path.
Let's see how demanding the RP version is.
A79 Walkthrough:
1. R789
a) Innies R89 = 5(2) = {14/23}
b) 29(4) = {5789} locked between R8+N8 -> R8C56 <> 5,7,8,9
c) 17(3): R8C7 = (789) because R8C56 <= 10
d) 6 locked in 17(3) = 6{29/38/47} for R8+N8 because (789) only possible @ R8C7
e) 7(2): R7C8 <> 1,2
f) 8(2): R9C9 <> 2
g) Innies N7 = 17(2) = {89} locked for N7
h) 29(4) = {5789} -> 5,7 locked for N8
i) Naked pair (89) locked in R7C16 for R7
2. R789 !
a) ! 15(3) must have 8 xor 9 because it's only possible there and @ R8C7 for N3
-> R8C7 = (89)
b) 17(3) = 6{29/38}
c) Killer pair (23) of 17(3) blocks {23} of Innies R89 = 5(2)
d) Innies R89 = 5(2) = {14} locked for R8
e) 7(2) = [34/61]
f) 8(2): R9C9 <> 7
g) Innies N9 = 30(5) = 89{157/247/256}, {34689} blocked by Killer pair (36) of 7(2)
h) Innies N9 must have 6 xor 7 and R7C7 = (67) -> R7C9+R9C78 <> 6,7
3. R123
a) Innies N3 = 12(2) <> 1,2,6
b) 6 locked in 25(4) @ N3 = 6{289/379/478}
c) Innies R12 = 8(2) = [53/62/71]
d) 13(2): R3C2 <> 4,5,9
4. N4
a) Outies N4 = 13(2+1): R3C1+R5C4 <> 5,6,7,8,9 because R7C1 >= 8
b) 6(2) @ N4: R5C3 <> 1
5. C1234
a) Naked triple (124) locked in R567C4 for C4
b) 6(3) = {123} -> R1C4 = 3, {12} locked for N1+R1
c) Outies N4 = 13(2+1): R5C4 <> 4 because R37C1 >= 11
d) 6(2) = [42/51]
e) 9 locked in R56C2 for N4
f) 18(3) = 9{18/27/36} because {459} blocked by R5C3 = (45)
6. N36
a) Outies N6 = 15(2+1): R3C9 <> 3,4,5 because R5C6+R7C9 <= 10 and {55}+5 impossible
b) Innies N3 = 12(2) = [39/48/57]
7. R456 !
a) ! Innies+Outies R123: -6 = R4C6 - R3C19
-> R4C6 <> 1,2,3 because R3C19 >= 10
b) 3 locked in 32(5) = {35789} locked for N5
c) Hidden Single: R4C6 = 6 @ N5, R8C5 = 6 @ N8
d) 12(3) = 6{15/24}
8. R123 !
a) ! Killer pair (45) locked in 12(3)+8(3) for R3
b) 14(2) = {68} locked for R3
c) R3C2 = 7 -> R2C2 = 6, R3C3 = 8
d) 13(2) = {49} locked for C1+N1
e) Innies N3 = 12(2) = [39] -> R3C9 = 9, R2C7 = 3
f) 25(4) @ N2 = {3589}, {589} locked for N2
9. N45
a) 20(3) = {578} -> R7C1 = 8, {57} locked for C1+N4
b) R5C3 = 4 -> R5C4 = 2
c) R5C6 = 1 -> R5C7 = 5
10. N69
a) Outies N6 = 15(2+1) -> R7C9 = 5
b) R7C6 = 9 -> R7C7 = 6
c) 8(2) = {17} -> R9C9 = 1, R8C9 = 7
d) 18(3) = {369} -> R4C9 = 3, R5C9 = 6
11. Rest is singles.
Rating: 1.0
since I've made mistakes somewhere and had to start over again twice.Edit: Made a mistake in the beginning which led to a quicker solution. Thanks to Andrew, I corrected it. So after rewriting my walkthrough I still managed to make it my shortest one so far, but it's a bit longer than my first path.
Let's see how demanding the RP version is.
A79 Walkthrough:
1. R789
a) Innies R89 = 5(2) = {14/23}
b) 29(4) = {5789} locked between R8+N8 -> R8C56 <> 5,7,8,9
c) 17(3): R8C7 = (789) because R8C56 <= 10
d) 6 locked in 17(3) = 6{29/38/47} for R8+N8 because (789) only possible @ R8C7
e) 7(2): R7C8 <> 1,2
f) 8(2): R9C9 <> 2
g) Innies N7 = 17(2) = {89} locked for N7
h) 29(4) = {5789} -> 5,7 locked for N8
i) Naked pair (89) locked in R7C16 for R7
2. R789 !
a) ! 15(3) must have 8 xor 9 because it's only possible there and @ R8C7 for N3
-> R8C7 = (89)
b) 17(3) = 6{29/38}
c) Killer pair (23) of 17(3) blocks {23} of Innies R89 = 5(2)
d) Innies R89 = 5(2) = {14} locked for R8
e) 7(2) = [34/61]
f) 8(2): R9C9 <> 7
g) Innies N9 = 30(5) = 89{157/247/256}, {34689} blocked by Killer pair (36) of 7(2)
h) Innies N9 must have 6 xor 7 and R7C7 = (67) -> R7C9+R9C78 <> 6,7
3. R123
a) Innies N3 = 12(2) <> 1,2,6
b) 6 locked in 25(4) @ N3 = 6{289/379/478}
c) Innies R12 = 8(2) = [53/62/71]
d) 13(2): R3C2 <> 4,5,9
4. N4
a) Outies N4 = 13(2+1): R3C1+R5C4 <> 5,6,7,8,9 because R7C1 >= 8
b) 6(2) @ N4: R5C3 <> 1
5. C1234
a) Naked triple (124) locked in R567C4 for C4
b) 6(3) = {123} -> R1C4 = 3, {12} locked for N1+R1
c) Outies N4 = 13(2+1): R5C4 <> 4 because R37C1 >= 11
d) 6(2) = [42/51]
e) 9 locked in R56C2 for N4
f) 18(3) = 9{18/27/36} because {459} blocked by R5C3 = (45)
6. N36
a) Outies N6 = 15(2+1): R3C9 <> 3,4,5 because R5C6+R7C9 <= 10 and {55}+5 impossible
b) Innies N3 = 12(2) = [39/48/57]
7. R456 !
a) ! Innies+Outies R123: -6 = R4C6 - R3C19
-> R4C6 <> 1,2,3 because R3C19 >= 10
b) 3 locked in 32(5) = {35789} locked for N5
c) Hidden Single: R4C6 = 6 @ N5, R8C5 = 6 @ N8
d) 12(3) = 6{15/24}
8. R123 !
a) ! Killer pair (45) locked in 12(3)+8(3) for R3
b) 14(2) = {68} locked for R3
c) R3C2 = 7 -> R2C2 = 6, R3C3 = 8
d) 13(2) = {49} locked for C1+N1
e) Innies N3 = 12(2) = [39] -> R3C9 = 9, R2C7 = 3
f) 25(4) @ N2 = {3589}, {589} locked for N2
9. N45
a) 20(3) = {578} -> R7C1 = 8, {57} locked for C1+N4
b) R5C3 = 4 -> R5C4 = 2
c) R5C6 = 1 -> R5C7 = 5
10. N69
a) Outies N6 = 15(2+1) -> R7C9 = 5
b) R7C6 = 9 -> R7C7 = 6
c) 8(2) = {17} -> R9C9 = 1, R8C9 = 7
d) 18(3) = {369} -> R4C9 = 3, R5C9 = 6
11. Rest is singles.
Rating: 1.0
Last edited by Afmob on Thu Dec 06, 2007 9:47 pm, edited 2 times in total.
Brain is back in gear! 
79
A nice one..no severe combo crunching needed.And a neat start possible...
1.O-I N1245 -> R2C7+R7C1=R5C6+R6C4+6 and r7c1=8/9
2.I N5 =13/4 and this,together with constraints from the two 6(2) cages means that r5c6+r6c4=6 max (other combos impossible)
3.r2c7+8/9=12 max thus r2c7=3/4 (innies N3=12/2) r3c9=8/9
4.O-I N123 r3c19=r4c6+6
5.O-I N12 r3c1+6=r2c7+r4c6
6.Now only options for r4c6=3/6
6a if 3 -> r2c7=4 r3c1=1 and r3c9=8
6b now cannot complete 14(2) cage N12 and 8(3) cage N3
7.Thus r4c6=6
8.Thus r2c7=r3c1 (5. above) and also =r1c4
8a thus all these must=3 and r3c9=9
9. I r12 r2c28=8 -> 13(2) cage r23c2={67}
9a thus r3c4=6 r3c3=8 r8c3=9 r1c7=8
Mop up now
Regards
Gary
1.O-I N1245 -> R2C7+R7C1=R5C6+R6C4+6 and r7c1=8/9
2.I N5 =13/4 and this,together with constraints from the two 6(2) cages means that r5c6+r6c4=6 max (other combos impossible)
3.r2c7+8/9=12 max thus r2c7=3/4 (innies N3=12/2) r3c9=8/9
4.O-I N123 r3c19=r4c6+6
5.O-I N12 r3c1+6=r2c7+r4c6
6.Now only options for r4c6=3/6
6a if 3 -> r2c7=4 r3c1=1 and r3c9=8
6b now cannot complete 14(2) cage N12 and 8(3) cage N3
7.Thus r4c6=6
8.Thus r2c7=r3c1 (5. above) and also =r1c4
8a thus all these must=3 and r3c9=9
9. I r12 r2c28=8 -> 13(2) cage r23c2={67}
9a thus r3c4=6 r3c3=8 r8c3=9 r1c7=8
Mop up now
Regards
Gary
My solution seems to have taken a bit longer than some of the others. I missed a few things and was slow to spot others that I ought to have seen earlier, in particular I ought to have seen step 23, my breakthrough move, earlier.
I'll rate it as a moderate to harder 1.0.
Here is my A79 walkthrough.
Prelims
a) R12C1 = {49/58/67}, no 1,2,3
b) R23C2 = {49/58/67}, no 1,2,3
c) R3C34 = {59/68}
d) R5C34 = {15/24}
e) R5C67 = {15/24}
f) R7C67 = {69/78}
g) R78C8 = {16/25/34}, no 7,8,9
h) R89C9 = {17/26/35}, no 4,8,9
i) R1C234 = {123}, locked for R1
j) 8(3) cage in N3 = 1{25/34}, 1 locked for N3
k) 19(3) cage in N6 = {289/379/469/478/568}, no 1
l) R567C1 = {389/479/569/578}, no 1,2
m) 7(3) cage at R6C4 = {124}, CPE no 1 in R89C4
n) 14(4) cage at R3C1 = {1238/1247/1256/1346/2345}, no 9
o) 29(4) cage at R8C3 = {5789}, CPE no 5,7,8,9 in R8C56
p) 32(5) cage in N5 = {26789/35789/45689}, no 1, 8,9 locked for N5
1. Naked quad {1245} in R5C3467, locked for R5
2. 45 rule on R12 2 innies R2C28 = 8 = [53/62/71], clean-up: no 4,5,9 in R3C2
3. 45 rule on R89 2 innies R8C28 = 5 = {14/23}, clean-up: no 1,2 in R7C8
4. 45 rule on N7 2 innies R7C1 + R8C3 = 17 = {89}, locked for N7
4a. 5,7 of 29(5) cage locked in R8C4 + R9C45, locked for N8, clean-up: no 8 in R7C7
5. Killer pair 8,9 in R7C1 and R7C67, locked for R7
6. 45 rule on N3 2 innies R2C7 + R3C9 = 12 = {39/48/57}, no 2,6
7. R8C567 = {269/368/467} (cannot be {179/278/359/458} because 5,7,8,9 only in R8C7), no 1, 6 locked for R8C567, clean-up: no 2 in R9C9
7a. 7,8,9 only in R8C567 -> R8C7 = {789}
7b. 6 locked in R8C56, locked for N8, clean-up: no 9 in R7C7
7c. Killer pair 8,9 in R8C4 + R9C45 and R7C6, locked for N8
8. 45 rule on C1234 3 outies R279C5 = 1 innie R4C4 + 1
8a. Min R279C5 = 8 -> min R4C4 = 7
8b. Max R4C4 = 9 -> max R279C5 = 10 -> max R27C5 = 5, R2C5 = {1234}
8c. Min R27C5 = 3 -> max R9C5 = 7
9. 3 in C4 locked in R12C4, locked for N2
9a. 6 in C4 locked in R23C4, locked for N2
10. R279C5 = R4C4 + 1 (step 8)
10a. R279C5 = {125/127/145}, 1 locked in R27C5 for C5
10b. R279C5 = 8 or 10 -> no 8 in R4C4
11. 45 rule on C1 4 innie R3489C1 = 12 = 12{36/45}, no 7,8,9
12. R567C1 = {389/479/578} (cannot be {569} which clashes with R12C1), no 6
12a. 4,5 of {479/578} must be in R6C1 -> no 7 in R6C1
13. 45 rule on R789 2 innies R7C19 = 1 outie R6C4 + 9
13a. Max R6C4 = 4 -> max R7C19 = 13, max R7C9 = 5
14. 45 rule on R89 3 outies R7C238 = 14 = {257/347/356} (cannot be {167} which clashes with R7C7), no 1
15. Hidden killer quad 5,7,8,9 in R8C19, R8C34 and R8C7 -> R8C19 must contain 5/7
15a. 5 in R8 locked in R8C149
15b. 45 rule on R9 4 outies R8C1349 = 23 = {1589/2579/3578}, no 4
16. Hidden killer pair 8,9 in R8C7 and R9C78 for N9, R9C78 must contain 8/9 (cannot contain both) -> R8C7 = {89}, clean-up: no 4 in R8C56 (step 7)
16a. R9C678 = {159/168/249/258/348} (cannot be {267/357/456} which don’t contain 8,9), no 7
16b. 1 of {159/168} must be in R9C6 -> no 1 in R9C78
17. Naked pair {89} in R8C37, locked for R8
17a. Naked pair {57} in R8C4 + R9C5, locked for N8
18. 4 in R8 locked in R8C28 = {14}, locked for R8, clean-up: no 4,5 in R7C8, no 7 in R9C9
19. R7C238 (step 14) = {347/356} (cannot be {257} because R7C8 only contains 3,6) = 3{47/56}, no 2, 3 locked for R7
20. 45 rule on N5 4 innies R4C4 + R5C46 + R6C4 = 13 = {1246/1345} (cannot be {1237} because 3,7 only in R4C4) = 14{26/35}, no 7, 4 locked for N5
20a. 3,6 only in R4C4 -> R4C4 = {36}
21. 12(3) cage at R3C5 = {138/156/237/246/345} (cannot be {129/147} because R4C4 only contains 3,6), no 9
21a. 1 of {138} must be in R3C6 -> no 8 in R3C6
22. 25(4) cage at R1C5 = {1789/3589/4579}, no 2
23. 45 rule on N4 2 outies R37C1 = 1 innie R5C3 + 7
23a. Min R37C1 = 9 -> min R5C3 = 2, clean-up: no 5 in R5C4
23b. Max R5C3 = 5 -> max R37C1 = 12, max R3C1 = 4
24. Naked triple {124} in R567C4, locked for C4 -> R1C4 = 3
24a. Naked triple {12} in R1C23, locked for N1
25. Min R2C45 = 6 -> max R2C3 = 7
26. 3 in N1 locked in R2C3 + R3C1
26a. 45 rule on N1 3 remaining innies R2C3 + R3C13 = 16 = {349/358/367}
26b. 8 of {358} must be in R3C3 -> no 5 in R3C3, clean-up: no 9 in R3C4
26c. 7 of {367} must be in R2C3 -> no 6 in R2C3
27. 45 rule on N6 2 outies R37C9 = 1 innie R5C7 + 9
27a. Min R37C9 = 10 -> no 3,4,5 in R3C9 (R37C9 cannot be [55]), clean-up: no 7,8,9 in R2C7
28. 25(4) cage at R1C5 (step 22) = {3589/4579} (cannot be {1789} because only 3,4,5 in R2C7), no 1, 9 locked for N2, CPE no 5 in R2C4
29. R2C345 = {148/157/238/247/256/346}
29a. 7 of {157/247} must be in R2C4 -> no 7 in R2C3, clean-up: no 6 in R3C3 (step 26a), no 8 in R3C4
30. Killer pair 8,9 in R38C3, locked for C3
31. Hidden killer pair 1,2 in R2C5 and R3C56 for N2, R3C56 must contain 1/2 (cannot contain both) -> R2C5 = {12}
32. 45 rule on C123 6 innies R1C2 + R12358C3 = 29, R1C23 = 3, R38C3 = 17 -> R25C3 = 9 = {45}, locked for C3, clean-up: no 4 in R5C4
33. R3C1 = 3 (hidden single in N1)
34. R567C1 (step 12) = {479/578} -> R5C1 = 7, clean-up: no 6 in R12C1
34a. 4,5 only in R6C1 -> R6C1 = {45}
35. Killer pair 4,5 in R12C1 and R6C1, locked for C1 -> R8C1 = 2, clean-up: no 9 in R8C7 (step 7), no 6 in R9C9
36. R8C7 = 8 (naked single), R8C3 = 9, R9C4 = 8, R7C6 = 9, R7C7 = 6, R78C8 = [34], R7C1 = 8, R6C1 = 5, R5C34 = [42], R4C6 = 6, R5C6 = 1 (both step 20), R5C7 = 5, R6C4 = 4, R7C12 = [12], R7C9 = 5, R7C23 = [47], R8C2 = 1, R8C56 = [63], R9C6 = 4, R89C9 = [71], R8C4 = 5, R9C5 = 7, R3C34 = [86], R2C345 = [571], R1C23 = [21], R23C2 = [67], R4C123 = [182], R9C123 = [653], R4C4 = 9, R3C9 = 9, R2C8 = 2, R9C78 = [29], R2C6 = 8, R1C6 = 5, R3C56 = [42], R1C5 = 9, R12C1 = [49], R3C78 = [15], R1C7 = 7, R6C36 = [67], R4C8 = 7
37. R5C2 = 9 (hidden single in R5)
and the rest is naked singles and cage sums
I'll rate it as a moderate to harder 1.0.
Here is my A79 walkthrough.
Prelims
a) R12C1 = {49/58/67}, no 1,2,3
b) R23C2 = {49/58/67}, no 1,2,3
c) R3C34 = {59/68}
d) R5C34 = {15/24}
e) R5C67 = {15/24}
f) R7C67 = {69/78}
g) R78C8 = {16/25/34}, no 7,8,9
h) R89C9 = {17/26/35}, no 4,8,9
i) R1C234 = {123}, locked for R1
j) 8(3) cage in N3 = 1{25/34}, 1 locked for N3
k) 19(3) cage in N6 = {289/379/469/478/568}, no 1
l) R567C1 = {389/479/569/578}, no 1,2
m) 7(3) cage at R6C4 = {124}, CPE no 1 in R89C4
n) 14(4) cage at R3C1 = {1238/1247/1256/1346/2345}, no 9
o) 29(4) cage at R8C3 = {5789}, CPE no 5,7,8,9 in R8C56
p) 32(5) cage in N5 = {26789/35789/45689}, no 1, 8,9 locked for N5
1. Naked quad {1245} in R5C3467, locked for R5
2. 45 rule on R12 2 innies R2C28 = 8 = [53/62/71], clean-up: no 4,5,9 in R3C2
3. 45 rule on R89 2 innies R8C28 = 5 = {14/23}, clean-up: no 1,2 in R7C8
4. 45 rule on N7 2 innies R7C1 + R8C3 = 17 = {89}, locked for N7
4a. 5,7 of 29(5) cage locked in R8C4 + R9C45, locked for N8, clean-up: no 8 in R7C7
5. Killer pair 8,9 in R7C1 and R7C67, locked for R7
6. 45 rule on N3 2 innies R2C7 + R3C9 = 12 = {39/48/57}, no 2,6
7. R8C567 = {269/368/467} (cannot be {179/278/359/458} because 5,7,8,9 only in R8C7), no 1, 6 locked for R8C567, clean-up: no 2 in R9C9
7a. 7,8,9 only in R8C567 -> R8C7 = {789}
7b. 6 locked in R8C56, locked for N8, clean-up: no 9 in R7C7
7c. Killer pair 8,9 in R8C4 + R9C45 and R7C6, locked for N8
8. 45 rule on C1234 3 outies R279C5 = 1 innie R4C4 + 1
8a. Min R279C5 = 8 -> min R4C4 = 7
8b. Max R4C4 = 9 -> max R279C5 = 10 -> max R27C5 = 5, R2C5 = {1234}
8c. Min R27C5 = 3 -> max R9C5 = 7
9. 3 in C4 locked in R12C4, locked for N2
9a. 6 in C4 locked in R23C4, locked for N2
10. R279C5 = R4C4 + 1 (step 8)
10a. R279C5 = {125/127/145}, 1 locked in R27C5 for C5
10b. R279C5 = 8 or 10 -> no 8 in R4C4
11. 45 rule on C1 4 innie R3489C1 = 12 = 12{36/45}, no 7,8,9
12. R567C1 = {389/479/578} (cannot be {569} which clashes with R12C1), no 6
12a. 4,5 of {479/578} must be in R6C1 -> no 7 in R6C1
13. 45 rule on R789 2 innies R7C19 = 1 outie R6C4 + 9
13a. Max R6C4 = 4 -> max R7C19 = 13, max R7C9 = 5
14. 45 rule on R89 3 outies R7C238 = 14 = {257/347/356} (cannot be {167} which clashes with R7C7), no 1
15. Hidden killer quad 5,7,8,9 in R8C19, R8C34 and R8C7 -> R8C19 must contain 5/7
15a. 5 in R8 locked in R8C149
15b. 45 rule on R9 4 outies R8C1349 = 23 = {1589/2579/3578}, no 4
16. Hidden killer pair 8,9 in R8C7 and R9C78 for N9, R9C78 must contain 8/9 (cannot contain both) -> R8C7 = {89}, clean-up: no 4 in R8C56 (step 7)
16a. R9C678 = {159/168/249/258/348} (cannot be {267/357/456} which don’t contain 8,9), no 7
16b. 1 of {159/168} must be in R9C6 -> no 1 in R9C78
17. Naked pair {89} in R8C37, locked for R8
17a. Naked pair {57} in R8C4 + R9C5, locked for N8
18. 4 in R8 locked in R8C28 = {14}, locked for R8, clean-up: no 4,5 in R7C8, no 7 in R9C9
19. R7C238 (step 14) = {347/356} (cannot be {257} because R7C8 only contains 3,6) = 3{47/56}, no 2, 3 locked for R7
20. 45 rule on N5 4 innies R4C4 + R5C46 + R6C4 = 13 = {1246/1345} (cannot be {1237} because 3,7 only in R4C4) = 14{26/35}, no 7, 4 locked for N5
20a. 3,6 only in R4C4 -> R4C4 = {36}
21. 12(3) cage at R3C5 = {138/156/237/246/345} (cannot be {129/147} because R4C4 only contains 3,6), no 9
21a. 1 of {138} must be in R3C6 -> no 8 in R3C6
22. 25(4) cage at R1C5 = {1789/3589/4579}, no 2
23. 45 rule on N4 2 outies R37C1 = 1 innie R5C3 + 7
23a. Min R37C1 = 9 -> min R5C3 = 2, clean-up: no 5 in R5C4
23b. Max R5C3 = 5 -> max R37C1 = 12, max R3C1 = 4
24. Naked triple {124} in R567C4, locked for C4 -> R1C4 = 3
24a. Naked triple {12} in R1C23, locked for N1
25. Min R2C45 = 6 -> max R2C3 = 7
26. 3 in N1 locked in R2C3 + R3C1
26a. 45 rule on N1 3 remaining innies R2C3 + R3C13 = 16 = {349/358/367}
26b. 8 of {358} must be in R3C3 -> no 5 in R3C3, clean-up: no 9 in R3C4
26c. 7 of {367} must be in R2C3 -> no 6 in R2C3
27. 45 rule on N6 2 outies R37C9 = 1 innie R5C7 + 9
27a. Min R37C9 = 10 -> no 3,4,5 in R3C9 (R37C9 cannot be [55]), clean-up: no 7,8,9 in R2C7
28. 25(4) cage at R1C5 (step 22) = {3589/4579} (cannot be {1789} because only 3,4,5 in R2C7), no 1, 9 locked for N2, CPE no 5 in R2C4
29. R2C345 = {148/157/238/247/256/346}
29a. 7 of {157/247} must be in R2C4 -> no 7 in R2C3, clean-up: no 6 in R3C3 (step 26a), no 8 in R3C4
30. Killer pair 8,9 in R38C3, locked for C3
31. Hidden killer pair 1,2 in R2C5 and R3C56 for N2, R3C56 must contain 1/2 (cannot contain both) -> R2C5 = {12}
32. 45 rule on C123 6 innies R1C2 + R12358C3 = 29, R1C23 = 3, R38C3 = 17 -> R25C3 = 9 = {45}, locked for C3, clean-up: no 4 in R5C4
33. R3C1 = 3 (hidden single in N1)
34. R567C1 (step 12) = {479/578} -> R5C1 = 7, clean-up: no 6 in R12C1
34a. 4,5 only in R6C1 -> R6C1 = {45}
35. Killer pair 4,5 in R12C1 and R6C1, locked for C1 -> R8C1 = 2, clean-up: no 9 in R8C7 (step 7), no 6 in R9C9
36. R8C7 = 8 (naked single), R8C3 = 9, R9C4 = 8, R7C6 = 9, R7C7 = 6, R78C8 = [34], R7C1 = 8, R6C1 = 5, R5C34 = [42], R4C6 = 6, R5C6 = 1 (both step 20), R5C7 = 5, R6C4 = 4, R7C12 = [12], R7C9 = 5, R7C23 = [47], R8C2 = 1, R8C56 = [63], R9C6 = 4, R89C9 = [71], R8C4 = 5, R9C5 = 7, R3C34 = [86], R2C345 = [571], R1C23 = [21], R23C2 = [67], R4C123 = [182], R9C123 = [653], R4C4 = 9, R3C9 = 9, R2C8 = 2, R9C78 = [29], R2C6 = 8, R1C6 = 5, R3C56 = [42], R1C5 = 9, R12C1 = [49], R3C78 = [15], R1C7 = 7, R6C36 = [67], R4C8 = 7
37. R5C2 = 9 (hidden single in R5)
and the rest is naked singles and cage sums