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3x3:d:k:7168:7168:6145:6145:6145:5378:5378:5378:5378:7168:7168:7168:7168:6145:3587:3587:5378:4356:773:9990:8199:3080:3080:3587:5129:5129:4356:9990:9990:3082:8199:3080:5129:5129:2315:2315:773:9990:3082:3082:8199:7436:7436:7436:7436:2829:9990:9990:3086:3599:8199:7436:7436:8464:2829:9745:3086:3086:3599:3090:8199:2579:8464:9745:9745:9745:3860:3599:3090:2579:2579:8464:9745:9745:9745:3860:3599:3090:8464:8464:8464:

1. Disjoint 3(2)c1 = {12}
39(6)n14 = {456789}
-> Whichever of (12) is in r3c1 is in n4 in r45c3
Innies n7 = r7c13 = +7(2) (No 789)
-> Max r7c1 = 6 -> Min r6c1 = 5
-> 3 in n4 also in r45c3
-> 12(3)r4c3 = [{13}8] or [{23}7]
-> 15(2)n8 = {69}

2. 17(2)n3 = {89}
-> (89) in n9 in r7c7 or r9c78
Innies c6789 = [r6c6,r7c7] = +15(2) = {69} or {78}
9 in D/ either in n5 or in n7 in r89 which puts r7c7 = 9
Either way [r6c6,r7c7] cannot be [96]
-> Outies n9 = r6c69 = +13(2) from {67} or [85]

3. Given {12} already in c1 and 3 already in c3 ...
-> Innies n7 from [34], [52], [61]
Outies n8 = r7c45,r7c3 = +8(3)
r7c3 cannot be 2 since that puts r67c4 = {37} which leaves no solution in that case for r6c45 = +6(2)
-> Innies n7 from [34], [61]
-> r6c1 from {85)
-> (Outies n9) r6c69 = {67}
-> 10(3)n9 from {127} or {136}

4! 1 in r6 only in r6c4578
1 in c9 only in r145c9
Trying r7c3 = 1 puts r6c45 = +7(2) and (since r6c4 cannot be neither 1 nor 6) puts 1 in r6c78
But this leaves no place for 1 in c9
-> r7c13 = [34]
-> r6c1 = 8
-> r3c2 = 8
-> 8 in r89c3
-> 8 in D/ in n5
-> 12(3)r4c3 = [{23}7]
-> 3(2)c1 = [21]
Also -> r6c69 = [67]
-> r7c7 = 9 and 10(3)n9 = {127}

5. Continuing...
17(2)n4 = [89]
-> (Outies r12 = r3c69 = +14(2)) r3c6 = 5
Also since (34) in n1 in 28(6) and 8 not in 28(6) -> 28(6) = {134569}
-> (NS) r2c4 = 1
-> (Since 1 cannot be in 32(5)D\) r13c3 = [17]
-> 24(4)n12 = [18{69}]
-> 32(5)D\ = [72869]
Also (Remaining outies n8) r6c45 = [31]
-> r7c4 = 5
-> r4c5 = 5
-> r3c45 = [43]
Also (HS in n5) r5c6 = 4
-> (HS in n6) r4c7 = 4
Also (NS) -> r4c6 = 9
Also 8 in r9c78
-> r8c3 = 8
-> 12(3)n8 = [8{13}]
etc.

Prelims

a) R23C9 = {89}
c) R35C1 = {12}
d) R4C89 = {18/27/36/45}, no 9
e) R67C1 = {29/38/47/56}, no 1
f) R89C4 = {69/78}
g) 10(3) cage at R7C8 = {127/136/145/235}, no 8,9
h) 14(4) cage at R6C5 = {1238/1247/1256/1346/2345}, no 9
i) 32(5) cage at R3C3 = {26789/35789/45689}, no 1
j) 39(6) cage at R3C2 = {456789}

1a. R23C9 = {89}, locked for C9 and N3, clean-up: no 1 in R4C8
1b. R35C1 = {12}, locked for C1, clean-up: no 9 in R67C1
1c. 32(5) cage at R3C3 = {26789/35789/45689}, 8,9 locked for D\
1d. 45 rule on R12 2 outies R3C69 = 14 = [59/68]
1e. 45 rule on R12 3 innies R2C679 = 17 = {179/278/359/368} (cannot be {467} because R2C9 only contains 8,9, cannot be {269/458) = {26}9/{45}8 which clash with R2C9 + R3C69), no 4
1f. R2C9 = {89} -> no 8,9 in R2C6
1g. 45 rule on N7 2 innies R7C13 = 7 = {34}/[52/61], clean-up: no 3,4 in R6C1
1h. R45C3 + R5C1 = {123} (hidden triple in N4), 3 locked for C3, clean-up: no 4 in R7C1, no 7 in R6C1
1i. R45C3 = {13/23} -> R5C4 = {78}
1j. R89C4 = {69} (cannot be {78} which clashes with R5C4), locked for C4 and N8
1k. 45 rule on N9 1 innie R7C7 2 more than R6C9, no 2 in R7C7
1l. 45 rule on C6789 2 innies R6C6 + R7C7 = 15 = {69/78}, clean-up: no 1,2,3 in R6C9

2a. 45 rule on N8 1 innie R7C4 = 1 outie R6C5 + 4 -> R6C5 = {134}, R7C4 = {578}
2b. 45 rule on N78 3 outies R6C145 = 12 = {138/156/246/345} (cannot be {147/237} because R6C1 only contains 5,6,8), no 7
2c. R6C145 = {138/156/345} (cannot be {246} = [624] which clashes with R6C1 + R7C13 = [652], step 1g), no 2
2d. R6C145 = {138/345} (cannot be {156} = [651] which clashes with R6C5 + R7C4 = [15]), no 6, 3 locked for R6 and N5, clean-up: no 5 in R7C1, no 2 in R7C3 (step 1g)
2e. R6C1 = {58} -> no 5,8 in R6C4
2f. 45 rule on N4 using R45C3 + R5C1 = {123} = 6, 1 outie R3C2 = 1 innie R6C1 = {58}
2g. Killer pair 5,8 in R3C2 and R3C69, locked for R3
2h. 32(5) cage at R3C3 = {26789/45689}, 6 locked for D\
2i. 14(4) cage at R6C5 = {1238/1247/2345}, 2 locked for C5 and N8
2j. 2 in R6 only in R6C78, locked for N6 and 29(6) cage at R5C6, no 2 in R5C6, clean-up: no 7 in R4C89
2k. 2 in R5 only in R5C13, locked for N4
2l. 1 in R6 only in R6C4578, CPE no 1 in R5C6
2m. 45 rule on N6 2 innies R4C7 + R6C9 = 1 outie R5C6 + 7
2n. Min R5C6 = 4 -> min R4C7 + R6C9 = 11, max R6C9 = 7 -> min R4C7 = 4

3a. 45 rule on N9 using R6C6 + R7C7 = 15 = {69/78} (step 1l) 2 outies R6C69 = 13 = {67}/[94] (cannot be [85] which clashes with R6C1), no 5,8, clean-up: no 7 in R7C7
3b. 45 rule on R6789 using R6C145 = 12 = {138/345} (step 2d) and R6C69 = 13 4 innies R6C2378 = 20 containing 2 for R6 = {1289/2459/2567} (cannot be {2468} which clashes with R6C145)
3c. Consider placements for R6C6 = {679}
R6C6 = 6 => R3C6 = 5, R3C2 = 8 => R6C1 = 8 (hidden single in N4)
or R6C6 = 7 => R5C4 = 8, R45C3 = 4 = {13}, 1 locked for C3, R7C3 = 4 => R7C1 = 3 (step 1g), R6C1 = 8
or R6C6 = 9 => R6C2378 = {2459/2567} => R6C1 = 8 (hidden single in R6)
-> R6C1 = 8, R7C1 =3, R7C3 = 4, placed for D/, R6C45 = {13}, 1 locked for R6 and N5, R67C4 = 8 = [17/35]
3d. R6C1 = 8 -> R3C2 = 8 (step 2f), R23C9 = [89], R3C6 = 5 (hidden single in R3) -> R2C67 = 9 = {27/36}, no 1

4a. 32(5) cage at R3C3 (step 2h) = {26789} (only remaining combination, cannot be {45689} because R3C3 = 6 would clash with R6C6 + R7C7 (step 1l) = {69}), no 4,5, 2,7 locked for D\
4b. R7C4 = 5 (hidden single in C4) -> R6C4 = 3, placed for D/, R6C5 = 1
4c. R4C5 = 5 (hidden single in N5) -> R3C34 = 7 = [16/43], clean-up: no 4 in R4C89
4d. R5C6 = 4 (hidden single in N5)
4e. 1 in N8 only in R789C6 = {138} (only remaining combination), locked for C6, 3,8 locked for N8, clean-up: no 6 in R2C7 (step 3d)
4f. Naked triple {247} in R789C5, 4,7 locked for C5
4g. 6 in C5 only in R123C5, locked for N2, clean-up: no 3 in R2C7 (step 3d)
4h. R4C7 + R6C9 = R5C6 + 7 (step 2m), R5C6 = 4 -> R4C7 + R6C9 = 11 = {47} (only remaining combination), locked for N6, clean-up: no 7 in R6C6 (step 3a), no 8 in R7C7
4i. Naked pair {69} in R6C6 + R7C7, locked for D\
4j. Naked pair {78} in R5C45, locked for R5 and N5 -> R3C3 + R4C4 = [72], R5C5 = 8, placed for D/
4k. R5C4 = 7 -> R45C3 = 5 = [32], R35C1 = [21], R4C89 = [81] (hidden pair in R4)
4l. 45 rule on N1 1 outie R2C4 = 1 remaining innie R1C3 -> R1C3 = 1, R2C4 = 1, R3C4 = 4 -> R3C5 = 3 (cage sum)
4m. Naked pair {16} in R3C78, 6 locked for N3 and 20(4) cage at R3C7 -> R4C6 = 9, placed for D/, R4C7 = 4 (cage sum), R6C6 = 6, R6C9 = 7, R7C7 = 9
4n. R8C8 = 1 (hidden single on D\) -> R3C78 = [16], R7C8 + R8C7 = 9 = {27}, locked for N9 -> R7C9 = 6
4o. Naked pair {27} in R2C67, locked for R2 -> R2C8 = 5, R1C9 = 2, both placed for D/
4p. R2C12 = [43] (hidden pair in R2), R1C1 = 5, 3,5 placed for D\

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