3x3::k:7168:7168:6401:3074:3331:1284:1284:4613:4613:2054:7168:6401:3074:3331:2055:2055:5896:4613:2054:7168:6401:6401:3849:3331:5896:5896:5896:2054:7168:11530:11530:3849:11531:11531:5896:11531:11530:4108:2061:2061:11530:11531:2062:2062:11531:11530:4108:4108:4108:11530:11531:4111:4111:11531:4624:11530:11530:11530:2577:2577:11531:11531:5650:4624:4624:3859:2068:2068:3349:5650:5650:5650:2582:2582:3859:3859:3349:3349:4119:4119:4119:

1! 16(2)n6 = {79}
Innies n9 = r7c78 = +7(2) (No (789))
-> The values from r7c78 can only go in n6 in r4c8 and one of r5c78
-> r5c7 = r7c8 and r4c8 = r7c7

Also whatever is in r7c7 and r4c8 is in r12c9
-> whatever is in r7c8 and r5c7 is in r3c9 (Cannot go in r12c9 since 18(3) cannot contain +7(2))

2! HP (79) in 45(9)r4c6 -> r45c6 = {79}
-> Whatever is in r5c8 (from (2356)) is in 45(9) in r6c6

3! Innies n8 = r79c4 = +14(2)
Outies c1234 = r568c5 = +13(3)

15(2)c5 = [96] or [78]
Whichever of (79) is in r3c5 is in c4 in r789c4
-> Either 15(2)c5 = [96] and r79c4 = {59}
Or 15(2)c5 = [78] and 8(2)n8 = [71]

But the latter gives no solution for remaining outies c1234 = r56c5 = +12(2)
-> 15(2)c5 = [96]
-> r79c4 = {59}
-> 12(2)n2 = {48}
Also r6c6 only from (235)

4. 8(2)n8 from {26} or {17}
8 in n5 only in r56c5
-> Outies c1234 = r568c5 = +13(3) = [{48}1] or[{38}2]
-> r8c4 from (67)

5! Remaining outies c789 = r126c6 = +10(3)
Remaining innies n2 = r12c6 + r3c4 = +11(3)
-> Whatever goes in r6c6 (from 235) is in n2 in r12c5
-> and it also goes in n8 in r789c4
-> Since r789c4 = <5(6|7)9> and r6c6 only from (235) -> r6c6 = 5

6. Easy continuation...
-> 8(2)n6 = [35] (Since r5c8 = r6c6)
-> r7c78 = [43] (Since r5c7 = r7c8)
-> r4c8 = 4 and r3c9 = 3

Also (remaining outies c789) r12c6 = +5(2)
-> (remaining innie n2) r3c4 = 6
-> (HP (57) in n2) 13(3)n2 = [{57}1]
-> 5(2)r1 = [32]
-> 8(2)r2 = [26]
-> 23(5)n3 = [1{78}34]
-> 18(3)n3 = {459}

Also r789c6 = {468}
-> 10(2)n8 = [28]
-> 13(3)n8 = <436>
-> 8(2)n8 = [71]
-> r56c5 = {48}

Also outies r89 = r7c19 = +12(2) = {57}
-> r79c4 = [95]
etc.

Prelims

a) R12C4 = {39/48/57}, no 1,2,6
b) R1C67 = {15/24}
c) R2C67 = {17/26/35}, no 4,8,9
d) R34C5 = {69/78}
e) R5C34 = {17/26/35}, no 4,8,9
f) R5C78 = {17/26/35}, no 4,8,9
g) R6C78 = {79}
h) R7C56 = {19/28/37/46}, no 5
i) R8C45 = {17/26/35}, no 4,8,9
j) R9C12 = {19/28/37/46}, no 5
k) 8(3) cage at R2C1 = {125/134}

1a. Naked pair {79} in R6C78, locked for R6 and N6, clean-up: no 1 in R5C78
1b. 8(3) cage at R2C1 = {125/134}, 1 locked for C1, clean-up: no 9 in R9C2
1c. 45 rule in N9 2 innies R7C78 = 7 = {16/25/34}, no 7,8,9
1d. 7,9, in 45(9) cage at R4C6 only in R45C6 = {79}, locked for C6 and N5, clean-up: no 1 in R2C7, no 6,8 in R3C5, no 1 in R5C3, no 1,3 in R7C5
1e. 45 rule on N8 2 innies R79C4 = 14 = {59/68}
1f. 45 rule on N3 3(2+1) outies R12C6 + R4C8 = 9
1g. Min R12C6 = 3 -> max R4C8 = 6
1h. 8 in N6 only in R4C7 + R456C9, locked for 45(9) cage at R4C6, no 8 in R6C6
1i. Combined cage R1279C4 = {39}{68}/{48}{59}/{57}{68}, 8 locked for C4
1j. 8 in N5 only in R456C5, locked for C5, clean-up: no 2 in R7C6
1k. 8 in R456C5, CPE no 8 in R4C3
1l. 45 rule on R89 2 outies R7C19 = 12 = {39/48/57}, no 1,2,6
1m. 45 rule on R9 2 outies R8C36 = 9 = {18/27/36/45}/[72], no 2,9 in R8C3

2a. 8 in C6 only in R3789C6, 8 in N8 only in R79C4 and R789C6
2b. 45 rule on C6789 4 innies R3789C6 = 19 = {1468/2368/2458}
2c. 8 in R3789C6 only in R789C6 (cannot be 8{146/236} which clashes with R79C4 (step 1e) = {68}, cannot be 8{245} = [84]{25} because R7C56 = [64] clashes with R79C4 = {68}) -> no 8 in R3C6
2d. 8 in N2 only in R12C4 = {48}, locked for C4 and N2, clean-up: no 1 in R1C7, no 6 in R79C4
2e. Naked pair {59} in R79C4, locked for C4 and N8, clean-up: no 3 in R5C3, no 1 in R7C6, no 3 in R8C45
2f. 13(3) cage at R1C5 = {157/256} (cannot be {139}, because R1C67 = [23] clashes with R2C6 = 5 (then hidden single in N2), R2C7 = 3), no 3,9, 5 locked for N2, clean-up: no 3 in R2C7
[Cracked, the rest is fairly straightforward.]
2g. R3C5 = 9 (hidden single in N2) -> R4C5 = 6, clean-up: no 2 in R5C3, no 4 in R7C6, no 2 in R8C4
2h. Naked triple {123} in R456C4, locked for C4 and N5, clean-up: no 7 in R8C5
2i. Killer pair 6,7 in 13(3) cage and R3C4, locked for N2, clean-up: no 2 in R2C7
2j. 3 in N2 only in R12C6, locked for C6, clean-up: no 7 in R7C5
2k. 13(3) cage at R8C6 = {238/346} (cannot be {148} which clashes with R7C56, cannot be {247} which clashes with R7C5), no 1,7 -> R9C5 = 3, clean-up: no 7 in R9C12
2l. R8C45 = [71] (hidden pair in N8)
2m. R3C4 = 6 -> 13(3) cage at R1C5 = {157} -> R3C6 = 1, R12C5 = {57}, 5 locked for C5, clean-up: no 4 in R1C7, no 7 in R2C7
2n. Naked pair {48} in R56C5, locked for 45(9) cage at R4C3, 4 locked for C5 and N5 -> R6C6 = 5, R7C5 = 2, R7C6 = 8, clean-up: no 4 in R7C19 (step 1l)

3a. 2 in 45(9) cage at R4C6 only in R4C7 + R456C9, locked for N6, clean-up: no 6 in R5C78
3b. Naked pair {35} in R5C78, locked for R5 and N6
3c. 4 in R7 only in R7C78 (step 1c) = {34}, locked for N9, 3 locked for R7, 4 locked for 45(9) cage at R4C6, clean-up: no 9 in R7C19 (step 1l)
3d. R4C8 = 4 (hidden single in N6 or from 45 rule on N3) -> R7C78 = [43], R5C78 = [35], R1C67 = [32], R2C6 = 2 -> R2C7 = 6
3e. Naked pair {57} in R7C19, locked for R7 -> R79C4 = [95]
3f. Naked pair {16} in R7C78, locked for N7 and 45(9) cage at R4C3, clean-up: no 4,9 in R9C1, no 4 in R9C2
3g. Naked pair {28} in R9C12, locked for R9 and N7
3h. R9C4 = 5 -> R89C3 = 10 = [37], R5C3 = 6 -> R5C4 = 2, R7C19 = [57], R8C12 = {49}, locked for R8 -> R89C6 = [64]
3i. R4C4 = 3 -> R6C1 = 2, R4C1 = 1
3j. Naked pair {34} in R23C1, locked for N1, 4 locked for C1 -> R8C12 = [94]
3k. R6C3 = 4 (hidden single in N4)
3l. R348C7 = [785], R3C8 = 8, R4C8 = 4 -> R2C8 + R3C9 = 4 = [13]

and the rest is naked singles.