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3x3:d:k:7680:7680:2817:2817:2817:10498:10498:10498:10498:7680:7680:7683:4868:10498:10498:10498:3077:5894:7680:7683:7683:4868:4868:6407:5894:5894:5894:1288:2825:7683:7683:7683:6407:3077:5894:3077:1288:2825:5130:2315:2315:6407:2572:5901:5901:5130:5130:5130:2830:2830:6407:2572:4623:5901:6672:6672:4881:4881:7186:6407:4623:4623:5901:6672:6672:4881:4881:7186:2323:4623:6420:5901:6672:4881:7186:7186:7186:2323:6420:6420:6420:

Prelims

a) R45C1 = {14/23}
b) R45C2 = {29/38/47/56}, no 1
c) R5C45 = {18/27/36/45}, no 9
d) R56C7 = {19/28/37/46}, no 5
e) R6C45 = {29/38/47/56}, no 1
f) R89C6 = {18/27/36/45}, no 9
g) 11(3) cage at R1C3 = {128/137/146/236/245}, no 9
h) 19(3) cage at R2C4 = {289/379/469/478/568}, no 1
i) 41(7) cage at R1C6 = {2456789}

1a. 45 rule on N4 1 innie R4C3 = 9, clean-up: no 2 in R45C2
1b. 45 rule on N78 1 innie R7C6 = 8, clean-up: no 1 in R89C6
1c. 45 rule on C6789 1 outie R2C5 = 6, clean-up: no 3 in R5C4, no 5 in R6C4
1d. 45 rule on C6 2 innies R12C6 = 11 = {29/47}
1e. R89C6 = {36/45} (cannot be {27} which clashes with R12C6), no 2,7
1f. 41(7) cage at R1C6 = {2456789}, 5,8 locked for N3
1g. 19(3) cage at R2C4 = {289/478} (cannot be {379} which clashes with R12C6), no 3,5
1h. R1C45 + R3C6 = {135} (hidden triple in N2)
1i. 11(3) cage at R1C3 = {137} (only remaining combination) -> R1C3 = 7, R1C45 = {13}, locked for R1 and N2, R3C6 = 5, clean-up: no 4 in R2C6, no 4 in R89C6
1j. 41(7) cage at R1C6 = {2456789}, 7 locked for R2
1k. Naked pair {36} in R89C6, locked for C6 and N8
1l. 1 in C6 only in R456C6, locked for N5, clean-up: no 8 in R5C45
1m. 45 rule on N1 3 remaining innies R2C3 + R3C23 = 8 = {125/134}, 1 locked for N1
1n. 5 of {125} must be in R2C3 -> no 2 in R2C3
1o. R2C3 + R3C23 = 8, R4C3 = 9 -> R4C45 = 13 = {58}/[67]
1p. R6C45 = {29/38/47} (cannot be [65] which clashes with R4C45), no 5,6
1q. Hidden killer pair 5,6 in R4C45 and R5C45 for N5, R4C45 contains one of 5,6 -> R5C45 must contain one of 5,6 = {45}/[63], no 2,7
1r. 45 rule on N7 2 outies R78C4 = 1 innie R9C3
1s. Min R78C4 = 3 -> min R9C3 = 3
1t. R78C4 cannot total 4 -> no 4 in R9C3
1u. Max R9C3 = 8 -> no 9 in R78C4

2a. 6 in N3 only in R3C789, locked for R3
2b. 1,3,6 in N3 only in R2C89 + R3C789, CPE no 1,3,6 in R4C8
2c. 45 rule on N69 1 innie R4C8 = 1 innie R2C8 + 2 -> R2C8 = {23}, R4C8 = {45}
2d. 12(3) disjoint cage at R2C8 = {138/237} (cannot be {147/156} because only 2,3 in R2C8, cannot be {345} which clashes with R4C8, cannot be {246} which clashes with R24C8 = [24]), no 4,5,6
2e. {237} = 2{37} (cannot be 3{27} because R4C789 = <257> clashes with R4C45), no 2 in R4C79
2f. Killer pair 7,8 in R4C45 and R4C79, locked for R4, clean-up: no 3,4 in R5C2
[The 12(3) disjoint cage is one of the keys to this puzzle.]

3a. 12(3) disjoint cage at R2C8 (step 2e) = {138/237} = 2{37}/3{18}
3b. Consider placement for 2 in 41(7) cage at R1C6
2 in R12C6 => R4C1 = 2 (hidden single in R4), R5C1 = 3, R5C45 = {45}, 5 locked for N5 => R4C45 = [67] => R4C79 = {18}
or 2 in R1C789 + R2C7, locked for N3 => R2C8 = 3, R4C79 = {18}
-> R4C79 = {18}, locked for R4 and N6, R2C8 = 3, placed for D/, R4C8 = 5 (step 2c), R4C45 = [67], 6 placed for D\, clean-up: no 4 in R5C1, no 5,6 in R5C2, no 2,9 in R56C7, no 4 in R6C4, no 4,8 in R6C5
3c. Naked pair {45} in R5C45, locked for R5, 4 locked for N5 -> R4C6 = 2, placed for D/, clean-up: no 6 in R6C7
3d. Naked pair {19} in R56C6, 9 locked for C6 and N5 -> R12C6 = [47], R6C45 = [83], 8 placed for D/, R1C45 = [31], clean-up: no 7 in R5C7
3e. Naked pair {29} in R23C4, locked for C4 and N2 -> R3C5 = 8
3f. Naked pair {34} in R4C12, locked for N4
3g. 41(7) cage at R1C6 = {2456789}, 2,9 locked for N3
3h. 2,9 in C5 only in R789C5 -> 28(5) cage at R7C5 (step 1v) = {24589/24679} (cannot be {23689} because 3,6 only in R9C3), no 1, 4 locked for N8
3i. 1 in C4 only in R78C4, locked for 19(5) cage at R7C3
3j. R78C4 = {15/17} -> R9C3 = {68} (step 1r)
3k. 19(5) cage = {12358/12367/12457/13456} (cannot be {12349} because R78C4 only contains 1,5,7), no 9
3l. 19(5) cage = {12367/12457/13456} (cannot be {12358} because R7C3 + R78C4 require two of 4,5,6,7), no 8
3m. 19(5) cage = {12367/12457} (cannot be {13456} = {346}{15} which clashes with R78C4 + R9C3 = {15}6), 2 locked for N7
3n. 6 of {12367} must be in R7C3 -> no 6 in R8C3 + R9C2
3o. Consider placement for 8 in C3
R5C3 = 8 => R5C2 = 7
or R9C3 = 8 => R78C4 = {17}, 7 locked for 19(5) cage at R7C3
-> no 7 in R9C2
3p. 1,7 in 19(5) cage only in R78C4 -> R78C4 = {17}, 7 locked for C4, R9C3 = 8
[Cracked. The rest is straightforward.]
3q. R5C2 = 8 (hidden single in N4) -> R4C2 = 3, R4C1 = 4 -> R5C1 = 1, R5C6 = 9 -> R6C6 = 1, placed for D\
3r. 7 in N4 only in R6C12, locked for R6, R6C7 = 4 -> R5C7 = 6, R5C3 = 2
3s. R5C89 = [73] = 10 -> R678C9 = 13 = {256} (only remaining combination, cannot be {148} because R6C9 only contains 2,9) -> R6C9 = 2, R78C9 = {56}, locked for C9 and N9, R1C9 = 9, placed for D/

4a. R2C3 + R3C23 (step 1m) = {134} (only remaining combination, cannot be {125} because R3C3 only contains 3,4) -> R3C3 = 3, placed for D\, naked pair {14} in R2C3 + R3C2
4b. 19(5) cage at R7C3 (step 3m) = {12457} (only remaining combination) -> R9C2 = 2, R78C3 = {45}, locked for C3 and N7
4c. R2C3 = 1 -> R2C9 = 4, R9C9 = 7, R3C9 = 1, R3C7 = 7, placed for D/
4d. R6C8 = 9, R7C7 = 2, placed for D\, R7C8 + R8C7 = 7 = [43], R8C8 = 8, placed for D\, R1C1 = 5, placed for D\

and the rest is naked singles, not using the diagonals.

.-------------------------------.-------------------------------.-------------------------------.
| 2589      25689     7         | 3         1         4         | 2589      289       59        |
| 24589     24589     145       | 29        6         7         | 2589      3         14        |
| 2349      1234      1234      | 29        8         5         | 1467      1467      1467      |
:-------------------------------+-------------------------------+-------------------------------:
| 34        34        9         | 6         7         2         | 18        5         18        |
| 12        78        1268      | 45        45        19        | 23679     2679      23679     |
| 12567     12567     1256      | 8         3         19        | 24679     24679     24679     |
:-------------------------------+-------------------------------+-------------------------------:
| 1345679   1345679   456       | 157       2459      8         | 1234579   124679    12345679  |
| 13456789  145679    2345      | 157       2459      36        | 123456789 124789    123456789 |
| 145679    23457     68        | 457       2459      36        | 123456789 1246789   12345789  |
'-------------------------------.-------------------------------.-------------------------------'

Paste candidates into A432 in SudokuSolver

End step 3n above (though with some previous clean-ups missing)

Then
4. from step 3m, 19(5) cage = {12367/12457}
4a. must have 7 which are only in r78c4 or r9c2
4b. r9c4 sees all those -> no 7 in r9c4 (Common Peer Elimination)

5. naked pair {45} in r59c4: 5 locked for c4
[Andrew noticed you can go straight to step 6 from step 4 through 'hidden pair {17} in r78c4' etc.]

6. naked pair {17} in r78c4: 7 locked for 19(5)
6a. {17} = 8 -> r9c3 = 8

On from there

1. Outies c6789 = r2c5 = 6
Innies c6 = r12c6 = +11(2)
41(7)n23 = {2456789}
-> r12c6 = {29} or {47}
-> 19(3)n2 = {289} or {478}
-> Remaining innies n2 = r1c45 + r3c6 = +9(3) = {135}
Since 11(3)r1 cannot contain both (15) nor both (35) -> r3c6 = 5 and 11(2)r1 = [7{13}]

2. Innies n4 = r4c3 = 9
Innies n78 = r7c6 = 8
-> r456c6 = +12(3)
1 in c6 only in n5 in r456c6
-> r456c6 = {129} or {147}
-> 9(2)c6 = {36}

3. Innies n69 = r4c789 = +14(3)
-> r4c8 = r2c8 + 2
-> r2c8 is Max 7
But...
7 in 41(7) in r2c67
6 in r2c5
5 in 41(7) in n3
-> r2c8 is Max 4
Also 6 in n3 in r3 -> r4c8 not 6 -> r2c8 not 4
Also 3 in n3 in 23(5) or r2c8 -> r4c8 not 3 -> r2c8 not 1
-> r2c8 from (23) and r4c8 from (45)

4! r4c45 = +13(2) = {58} or [67]
-> 11(2)n6 not {56}
-> 6 in n5 only in r45c4. I.e., Either r4c56 = [67] or 9(2)n5 = [63]
2 in r4 in one of r4c1679
-> Either 5(2)n4 = [23] which puts 9(2)n5 not [63]
Or 2 in r4c679 which puts r2c8 = 3 which again puts 9(2)n5 not [63]
-> 3 in n5 only in 11(2)n5 = {38}
-> r4c45 = [67]
-> 9(2)n5 = {45}
-> r456c6 = {129}
-> r12c6 = [47]

5. Remaining Innies r4 = r4c126 = +9(3) (No 8)
-> 8 in r4 in r4c79
-> Disjoint 12(3)n36 = [3{18}]
-> r4c8 = 5
Also r456c6 = [2{19}]
-> r4c12 = {34}
Also 11(2)n5 = [83] (3 already on D/)
-> r1c45 = [31]
Also 19(3)n2 = [{29}8]

6. IOD n8 -> r9c3 = r7c4 + r8c4
-> Since (23) already in c4 -> r9c3 is Min 5
-> Whatever is in r9c3 is in n8 in r78c6. I.e., be from (368)
-> Either r9c3 = 6 and r78c4 = {15}
or r9c3 = 8 and and r78c4 = {17}

7. r78c3 cannot be {34} since that leaves no solution for remaining innies n7 r9c23 = +12(2)
-> At least one of (34) in c12 in n7
-> At least one of (34) in c3 in r23c3
-> Remaining innies n1 = +8(3) = {134}
-> 30(5)n1 = {25689}

8. 7 in n8 only in r789c4
Trying r9c3 = 6 and r78c4 = {15} puts r9c4 = 7 which leaves no solution for 19(5)n78
(Cannot have {238} in n7 since all of (238) already on D/)
-> r9c3 = 8 and r78c4 = {17}
-> (HS 8 in r5) 11(2)n4 = [38]
-> 5(2)n4 = [41]
-> 7 in n4 in r6c12
-> 10(2)n6 = [64] (Only remaining solution)
-> 20(4)n4 = [2{567}]
Also r56c6 = [91]
Also 3 in n1 in c3
-> 3 in n7 in c1
-> Remaining Innies n7 = [{45}2]
-> Innies n1 = [143]
Also 1 in n9 in r9
-> 25(4)n9 = [8{179}]
etc.