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3x3::k:3840:3840:6145:2306:2306:4099:4099:772:6424:6145:6145:6145:6145:6662:6662:4099:772:6424:3335:3335:5384:6662:6662:6662:6424:6424:4106:3335:5384:5384:5384:5899:4620:4620:2829:4106:5646:2575:2575:2575:5899:5899:4620:2829:4106:5646:5646:3344:3344:5899:5899:3089:5906:5906:5646:3344:2067:2067:6420:6420:5909:5906:5906:3350:3350:3350:3095:3095:6420:5909:5906:3089:5385:5385:5385:773:773:6420:5909:5909:5909:

Prelims

a) R1C12 = {69/78}
b) R1C45 = {18/27/36/45}, no 9
c) R12C8 = {12}
d) R45C8 = {29/38/47/56}, no 1
e) Disjoint 12(2) cage at R6C7 = {39/48/57}, no 1,2,6
f) R7C34 = {17/26/35}, no 4,8,9
g) R8C45 = {39/48/57}, no 1,2,6
h) R9C45 = {12}
i) 10(3) cage at R5C2 = {127/136/145/235}, no 8,9
j) 21(3) cage at R9C1 = {489/579/678}, no 1,2,3

1a. Naked pair {12} in R12C8, locked for C8 and N3, clean-up: no 9 in R45C8
1b. 45 rule on N8 1 innie R7C4 = 5 -> R7C3 = 3, clean-up: no 4 in R1C5, no 7 in R8C45
1c. Naked pair {12} in R9C45, locked for R9 and N8
1d. 45 rule on N7 2 innies R7C12 = 8 = {17/26}, no 4,8,9
1e. 13(3) cage at R8C1 = {148/157/256} (cannot be {247} which clashes with R7C12), no 9
1f. 21(3) cage at R9C1 = {489/579} (cannot be {678} which clashes with R7C12), no 6, 9 locked for R9
1g. 45 rule on N69 2(1+1) outies R3C9 + R4C6 = 13 = {49/58/67}, no 1,2,3
1h. 45 rule on N3 1 innie R3C9 = 1 outie R1C6 + 1 -> R1C6 = {345678}
1i. 45 rule on C789 2 outies R14C6 = 12 = [39]/{48/57}, no 6, clean-up: no 7 in R3C9
1j. 45 rule on N2 2 innies R1C6 + R2C4 = 10 = [37/46/73/82], clean-up: no 6 in R3C9, no 7 in R4C6
1k. Hidden killer pair 1,2 in 13(3) cage at R8C1 and R8C7, 13(3) cage contains one of 1,2 -> R8C7 = {12}
1l. 23(5) cage at R7C7 = {13469/13478/13568/14567/23459/23468/23567} (cannot be {12}{578} which clashes with 21(3) cage at R9C1)
1la. 1,2 must in R8C7 -> no 1,2 in R7C7
1lb. R7C9 + R8C7 = {12} (hidden pair in N9)
1m. Hidden killer pair 1,2 in R45C7 and R8C7 for C7, R8C7 = {12} -> R45C7 must contain one of 1,2
1n. 18(3) cage at R4C6 must contain one of 1,2 = {189/279} -> R4C6 = {89}, R45C7 = {12789}, clean-up: no 7,8 in R1C6, no 8,9 in R3C9
1o. 18(3) cage at R4C6 = {189/279}, CPE no 9 in R4C9
1p. Max R3C9 = 5 -> min R45C9 = 11, no 1 in R4C9, no 1,2 in R5C9
1q. 16(3) cage at R1C6 = {349/358/367} (cannot be {457} = 4{57} which clashes with R1C6 + R3C9 = [45])
1r. 4 of {349} must be in R1C6 (cannot be 3{49} which clashes with R1C6 + R3C9 = [34]), no 4 in R12C7
1s. 16(3) cage = {349/358/367}, CPE no 3 in R1C9
1t. R1C6 + R3C9 = [34/45], CPE no 4 in R1C9 + R3C456
[Ignore the last two sub-steps, I’ve just spotted]
1u. 16(3) cage = {358/367} (cannot be {349} = 4{39} which clashes with 18(3) cage at R4C6 = 8{19}), no 9 -> R1C6 = 3, R2C4 = 7, R3C9 = 4, R4C6 = 9, clean-up: no 2,6 in R1C45
1v. Killer pair 7,8 in R12C7 and R45C7, locked for C7, clean-up: no 5 in R8C9
1w. 3 in N8 only in R8C45 = {39}, locked for R8, 9 locked for N8, clean-up: no 3,9 in R6C7
1x. R3C9 = 4 -> R45C9 = 12 = [39]/{57}, no 2,6,8, no 3 in R5C9
1y. 45 rule on N5 3 remaining innies R456C4 = 13 = {238/346} (cannot be {148} which clashes with R1C4), no 1, 3 locked for C4 and N5 -> R8C45 = [93]
1z. 45 rule on N1 1 innie R3C3 = 1 remaining outie R4C1, no 9 in R3C3, no 3,4 in R4C1

2a. R67C9 = {12} (hidden pair in C9)
2b. 23(5) cage at R6C8 = {12389/12479/12569} (cannot be {12578} which clashes with R45C8), 9 locked for C8
2c. 45 rule on C8 using R678C8 = 20, 2 remaining innies R39C8 = 11 = {38/56}/[74], no 7 in R9C8
2d. 3 in N9 only in 23(5) cage at R7C7 = {13469/23468/23567} (cannot be {12389} because 1,2 only in R8C7, cannot be {13478} which clashes with R8C9, cannot be {13568} = [61]{358} or {23459} = [92]{345} which clash with 21(3) cage at R7C1), 6 locked for N9
2e. R678C8 = 3{89}/{479}/[695]
2f. 23(5) cage at R7C7 = {23468/23567} (cannot be {13469} which clashes with R78C8, ALS block in the case of {479}), no 9 -> R8C7 = 2, R67C9 = [21], clean-up: no 7 in R7C12 (step 1d)
2g. Naked pair {26} in R7C12, 6 locked for R7 and N7
2h. R7C7 = 4, R6C7 = 5 -> R8C9 = 7 (cage sum), R45C9 = [39], clean-up: no 6,8 in R45C8
2i. Naked pair {47} in R45C8, locked for C8, 7 locked for N6
2j. Naked pair {18} in R45C7, 8 locked for C7 and N6
2k. R6C8 = 6 -> R78C8 = [95]
2l. R12C7 = [76] -> R9C789 = [386], R3C78 = [93], clean-up: no 8 in R1C12
2m. Naked triple {148} in 13(3) cage at R8C1, 4,8 locked for R8
2n. Naked pair {78} in R7C56, locked for N8 -> R89C6 = [64]
2o. Killer pair 5,8 in R1C45 and R1C9, locked for R1
2p. Naked pair {69} in R1C12, locked for N1, clean-up: no 6 in R4C1 (step 1z)
2q. 24(5) cage at R1C3 contains 3,4 for N1 and 7 = {23478}, 2,8 locked for N1, clean-up: no 2,8 in R4C1 (step 1z), 8 locked for R2 -> R12C9 = [85], clean-up: no 1 in R1C45
2r. R1C45 = [45] -> R1C3 = 2, R12C8 = [12], R2C56 = [91]
2s. Naked pair {78} in R67C6, locked for C6 -> R35C6 = [25]
2t. R456C4 (step 1y) = {238} (only remaining combination), 2,8 locked for C4 and N5 -> R6C6 = 7
2u. 13(3) cage at R6C3 = {238/346} (cannot be {139/148} because 1,4,9 only in R6C3), no 1,9 -> R6C4 = 3, R45C4 = [82], R45C7 = [18], clean-up: no 1 in R3C3 (step 1z)
2v. R5C4 = 2 -> R5C23 = 8 = {17}, locked for R5 and N4 -> R5C8 = 4, R45C5 = [46], R45C1 = [53], R3C3 = 5 (step 1z)
2w. R4C23 = [26], R7C2 = 6 -> R6C3 = 4 (cage sum)

and the rest is naked singles.

1. Innies n8 -> 8(2)r7c3 = [35]
-> (Remaining Innies n7) r7c12 = +8(2) = {17} or {26}
3(2)n8 = {12}
-> One each of (12) in r7 and r8 in n7

2. 3(2)n3 = {12}
Innies r9 = r9c6789 = +21(4)
Min r9c6 = 3 -> Max r9c789 = +18(3) -> Min r78c7 = +5(2) (Cannot have both (12))
-> HP r7c9,r8c7 = {12}

3. Whichever of (12) is in r7c9 is in n6 in r45c7
-> 18(3)n56 = {189} or {279} with r4c6 from (789)
-> Outies c789 = r14c6 = +12(2) from [57], [48], or [39]
Innies n2 = r1c6,r2c4 = +10(2) -> No 5
-> r14c6 = [48] or [39]

4. IOD n3 -> r3c9 = r1c6 + 1
-> r3c9 from {45}
Trying r14c6 = [48] puts r3c9 = 5 and r45c7 = {19} which leaves no solution for 16(3)r1c6
-> r14c6 = [39]
-> r3c9 = 4
Also r2c4 = 7

5! 3 in n8 in r8c45 -> 12(2)n8 = {39}
-> Disjoint cage 12(2) not {39}
-> r6c7 from {4578}
Outies n9 = r6c789 = +13(3)
-> No 9 in r6c789
-> (HS 9 in n6) r45c9 = [39]
-> (HP in n3) r3c78 = {39}

6. Whichever of (12) is in r8c7 must go in n6 in r6c9
-> r678c8 = +20(3)
-> Remaining Innies c8 = r39c8 = +11(2) = [38]
-> r3c7 = 9

7. r1245c7 = [76{18}] or [{58}{27}] - i.e., (78) locked in c7 in r1245c7
-> (Only remaining solution) Disjoint +12(2) = [57]
-> r12c7 = [76] and r12c9 = {58}
-> r45c7 = {18}, 11(2)n6 = {47}
-> 23(5)n69 = [62915]
-> 23(5)n9 = [42386]
-> r7c12 = {26}
-> 25(4)n8 = [{78}64]
Also 13(3)n7 = {148} and 21(3)n7 = {579}
Also 15(2)n1 = {69}
Also (IOD n1) r3c123 = +13(3) and has a 7 and no 4 so must be {157}
-> r3c456 = {268}
-> r2c56 = [91]
-> 9(2)n2 = [45]
-> 3(2)n3 = [12] and r12c9 = [85]
-> 24(5)n12 = [2{348}7]
Also 12(2)n8 = [93]
Also Innies n5 = r456c4 = +13(3)
-> Remaining Innies c4 = r39c4 = +7(2) = [61]
-> r456c4 = {238}
etc.