Prelims
a) R12C7 = {29/38/47/56}, no 1
b) R4C45 = {18/28/36/45}, no 9
c) R5C34 = {14/23}
d) R89C9 = {59/68}
e) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
f) 19(3) cage at R4C8 = {289/379/469/478/568}, no 1
g) 20(3) cage at R5C5 = {389/479/569/578}, no 1,2
h) 9(3) cage at R7C1 = {126/135/234}, no 7,8,9
i) 22(3) cage at R8C3 = {589/679}
j) 38(8) cage at R2C8 = {12345689}, no 7
1a. 45 rule on C1234567 3 outies R2C8 + R3C89 = 15, 45 rule on N3 4 innies R2C8 + R3C789 = 16 -> R3C7 = 1
1b. 45 rule on C7 2 remaining innies R45C7 = 11 = {29/38/56}, no 4
1c. 45 rule on C123456 2 innies R45C6 = 11 = {29/38/56}, no 4
1d. 38(8) cage at R2C8 = {12345689}, 4 locked for N3, clean-up: no 7 in R12C7
1e. 45 rule on N12 two outies R4C13 = 12 = {48/57}/[93], no 1,2,6, no 9 in R4C3
1f. 45 rule on N2 two outies R34C3 = 9 = [27/45/54/63], clean-up: no 4 in R4C1
1g. 45 rule on N124 two outies R56C4 = 5 = {14/23}
1h. Whatever is in R5C3 must be in R6C4 and in N6 in R4C789, no 1 in R4C789 -> no 1 in R5C3, no 1 in R6C4, clean-up: no 4 in R5C4
1i. 45 rule on R12345 2 innies R5C59 = 10 = {37/46}/[82/91], no 5, no 8,9 in R5C9
1j. 1 in N5 only in R4C45 = {18} or in R56C4 = [14] -> no 4 in R4C45 (locking-out cages), clean-up: no 5 in R4C45
[I ought also to have looked at 1 in N5 only in R4C45 = {18} or R5C34 -> R4C13 = [57/75/93] (cannot be {48}), no 4,8. Then I could have looked at combinations for the 15(3) cages in N2 including R123C4 = 15.]
1k. 22(3) cage at R8C3 = {589/679}, CPE no 9 in R8C2
1l. 45 rule on N7 1 outie R8C4 = 1 innie R7C3 + 2, no 1,2,8,9 in R7C3
2a. R4C13 = 12 (step 1f) = [57/75/84/93], R5C59 = 10 (step 1i)
2b. R5C34 = 5, R56C4 = 5 (step 1g) -> R5C3 + R6C123 = 20(4) cage at R6C1
2c. 20(4) cage = R5C3 + R6C123 = {1289/1379/1469/1478/2369/2468/2567} (cannot be {2378/2459/3458/3467} which clash with R4C13, cannot be {1568} because R6C4 only contains 2,3,4)
2d. Consider combinations for R56C4 = [14]/{23}
R56C4 = [14] => R4C2 = 1 (hidden single in R4) => 20(4) cage = R5C3 + R6C123 = {2369/2468/2567}
or R56C4 = {23}, 1 then only in R4C45 = {18}, locked for R4 => 20(4) cage = R5C3 + R6C123 = {1289/2369/2468/2567} (cannot be {1379} which clashes with R4C13 = [57/75/93] cannot be {1469/1478} because R6C4 then only contains 2,3)
-> 20(4) cage = R5C3 + R6C123 = {1289/2369/2468/2567}, 2 locked for R6 and N4
[Alternatively the eliminations of {1469/1478} can be made in a similar way to step 1h, cannot contain both of 1,4.]
2e. Consider placement for 1 in N5
1 in N5 only in R4C45 = {18}, 8 locked for R4
or in R56C4 = [14] => 20(4) cage = {268}4, 8 locked for N4)
-> R4C13 = [57/75/93], no 4,8, clean-up: no 5 in R3C3 (step 1f)
2f. Consider combinations for R45C7 (step 1b) = {29/38/56}
R45C7 = {29} blocks R5C3459 (step 1i) = {23}[91] => 1 in N6 only in R6C89, locked for R6
or R45C7 = {38}, locked for N6 and 3 in R6 in 20(4) cage = {2369}
or R45C7 = {38}, locked for N6 and 3 in R6 in 20(3) cage at R5C5, locked for N5 => R56C4 = [14] => 20(4) cage = {2468}
or R45C7 = {56} => R45C6 = {29/38} => R56C4 = [14] (cannot be {23} which then clashes with R56C4) => 20(4) cage = {2468}
-> 20(4) cage = R5C3 + R6C123 = {2369/2468/2567}, no 1, 6 locked for R6 and N4
2g. 1 in R6 only in R6C89, locked for N6, clean-up: no 9 in R5C5 (step 1i)
2h. Consider placement for 4 in N5
4 in 20(3) cage = {479}, 9 locked for R6
or R6C4 = 4 => 20(4) cage = {268}4
-> 20(4) cage = R5C3 + R6C123 = {2468/2567}, no 3,9, clean-up: no 2 in R5C4, no 3 in R5C3
2i. Consider permutations for R56C4 = [14/32]
R56C4 = [14] => 20(4) cage = {268}4
or R56C4 = [32] => R45C7 = {56}, 6 locked for N5, R5C3 = 2, R5C59 = [46] => 20(3) cage = 4{79}, 7 locked for R6
-> 20(4) cage = R5C3 + R6C123 = {2468}, 4,8 locked for R6 and N4
2j. 20(3) cage at R5C5 = {389/479/569/578}
2k. 4,6,8 only in R5C5 -> R5C5 = {468}, clean-up: no 3,7 in R5C9
2l. Killer pair 2,4 in R5C3 and R5C59, locked for R5, clean-up: no 9 in R4C6, no 9 in R4C7
2m. 4 in R4 only in R4C89, locked for N6, clean-up: no 6 in R5C5
2n. 19(3) cage at R4C8 = {469/478}, no 2,3,5
2o. 6 in N5 only in R4C45 = {36} or R45C6 (step 1c) = {56} -> no 3 in R45C6 (locking-out cages), clean-up: no 8 in R45C6
2p. 38(8) cage at R2C8 = {12345689}, CPE no 8 in R12C7, clean-up: no 3 in R12C7
2q. 6 in N5 only in R4C45 + R45C6, CPE no 6 in R4C7, clean-up: no 5 in R5C7
2r. 4 in C7 only in R789C7, locked for N9
2s. Consider combinations for 19(3) cage = {469/478}
19(3) cage = {469}, 6,9 locked for N6, R5C9 = 2 => R5C5 = 8, R45C7 = [83], R5C4 = 1, R4C23 = [13] (hidden pair in N4) => R4C1 = 9
or 19(3) cage = {478} => 9 in R4 only in R4C12
-> 9 in R4C12, locked for R4 and N4
[The last hard step, maybe the hardest step]
2t. 13(3) cage at R4C2 = {157} (cannot be {139} = 9{13} which clashes with R5C4), locked for N4 -> R4C13 = [93], R3C3 = 6, clean-up: no 6 in R4C45, no 8 in R5C7, no 5,8 in R8C4 (step 1l)
2u. 6 in N5 only in R45C6 = {56}, locked for C6 and 38(7) cage at R2C8, 5 locked for N5
2v. 9 in N5 only in R6C56, locked for R6
2w. Killer pair 2,8 in R4C45 and R4C7, locked for R4
2x. 19(3) cage = {469/478} -> R5C8 = {89}
[Fairly straightforward from here]
3a. 15(3) cage at R1C6 = {249/348}, no 1,7, 4 locked for C6 and N2
3b. 1 in C6 only in R789C6, locked for N8
3c. 12(3) cage at R8C5 = {237/246/345}, no 8,9
3d. 24(5) cage at R1C4 = {13569/23568}, no 7, 5 locked for C4 and N2
3e. Killer pair 8,9 in 24(5) cage and 15(3) cage at R1C6, locked for N2
3f. 7 in N2 only in 15(3) cage at R1C5 = {267} (only remaining combination), locked for C5, 2 locked for N2, clean-up: no 8 in 24(5) cage, no 9 in 15(3) cage at R1C6, no 2,7 in R4C45
3g. Naked triple {159} in R123C4, 1,9 locked for C4 -> R4C45 = [81], R5C3456789 = [2346986], R4C67 = [62], R6C456 = [297], clean-up: no 7 in R7C3 (step 1l)
3h. Naked pair {56} in R12C7, locked for C7 and N3 -> R6C7 = 3
3i. Naked triple {478} in R789C7, 7,8 locked for N9
3j. Naked pair {59} in R89C9, locked for C9 and N9 -> R6C89 = [51]
3h. Naked pair {35} in R89C5, locked for N8, R9C4 = 4 (cage sum)
3i. R7C5 = 8, R789C6 = {129} = 12 -> R7C34 = 11 = [56] (cannot be [47] which clashes with R7C7)
3j. R8C4 = 7 -> R8C3 + R9C2 = 15 = [96], R89C9 = [59], R89C5 = [35]
3k. 9(3) cage at R7C1 = {234} (only remaining combination), locked for C1 and N7
3l. R4C1 = 9 -> R23C1 = 12 = {57}, locked for N1, 7 locked for C1 -> R5C12 = [17], R78C2 = [18], R6C2 = 4
3m. R1C1 = 8 -> R1C23 = 6 = [24]
3n. R1C48 = [19] (hidden pair in R1) -> R12C9 = 9 = [72]
and the rest is naked singles.