Prelims
a) R34C5 = {59/68}
b) R5C12 = {69/78}
c) R6C12 = {14/23}
d) 11(3) cage at R1C2 = {128/137/146/236/245}, no 9
e) 11(3) cage at R1C4 = {128/137/146/236/245}, no 9
f) 21(3) cage at R1C9 = {489/579/678}, no 1,2,3
g) 19(3) cage at R2C1 = {289/379/469/478/568}, no 1
h) 10(3) cage at R4C1 = {127/136/145/235}, no 8,9
i) 11(3) cage at R6C7 = {128/137/146/236/245}, no 9
j) 21(3) cage at R7C1 = {489/579/678}, no 1,2,3
k) 11(3) cage at R7C5 = {128/137/146/236/245}, no 9
l) 19(3) cage at R7C6 = {289/379/469/478/568}, no 1
m) 8(3) cage at R8C2 = {125/134}
1a. 45 rule on N4 1 outie R5C4 = 2 -> R56C3 = 15 = {69/78}
1b. 5 in N4 only in 10(3) cage at R4C1 = {145/235}, 5 locked for R4, clean-up: no 9 in R3C5
1c. Combined cage R6C12 + 11(3) cage = 16(5) = {12346}, locked for R6, 6 locked for N6, clean-up: no 9 in R5C3
1d. 6 in N4 only in R5C123, locked for R5
1e. 5 in N6 only in R5C789, locked for R5
1f. 8(3) cage at R8C2 = {125/134}, 1 locked for N7
1g. 45 rule on N78 2 innies R7C34 = 9 = [27]/{36/45}/[81], no 9, no 7 in R7C3, no 8 in R7C4
2a. 5 in N6 only in 23(4) cage at R4C8 = {1589/3578} (cannot be {2579} = 2{579} which clashes with R5C12), no 2,4, 8 locked for N6
2b. 4 in R5 only in R5C56, locked for N5
2c. 45 rule on N6 2 innies R4C79 = 11 = {29/47}, no 1,3
2d. Hidden killer quad 6,7,8,9 in R5C123 and 23(4) cage, R5C123 contains 6 and two of 7,8,9, 23(4) cage contains 8 and one of 7,9 -> R4C8 = {789}, 7,8,9 locked for R5
2e. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 14
2f. Min R5C5 + R6C6 = 6 -> max R4C4 = 8
[Outies from D/ = 13 also gives this result.]
2g. R5C5 + R6C6 cannot total 7 -> no 7 in R4C4
2h. R4C4 + R5C5 cannot total 6 -> no 8 in R6C6
2i. 45 rule on N2 3 innies R1C56 + R3C5 = 18 = {189/369/378/459/468/567} (cannot be {279} because R3C5 only contains 5,6,8), no 2 in R1C56
2j. 45 rule on N236 3(2+1/1+2) innies R3C57 + R4C7 = 17
2k. R3C5 + R4C7 cannot total 11,16 -> no 1,6 in R3C7
2l. R3C5 + R4C7 cannot total 14 (which clashes with R34C5, CCC) -> no 3 in R3C7
3a. R34C5 = [59/68/86], R3C57 + R4C7 = 17 (step 2j), R4C4 + R5C5 + R6C6 = 14 (step 2e), R4C79 = {29/47} (step 2c)
3b. R3C57 + R4C7 = [584]/6{29}/6{47}/8{27}/[854]
3c. Consider combinations for R4C4 + R5C5 + R6C6 = 14 = {149/158/167/347/356}
R4C4 + R5C5 + R6C6 = {149}, locked for N5
or R4C4 + R5C5 + R6C6 = {158/167/356} => R5C6 = 4 (hidden single in N5), no 4 in R4C7 => no 5 in R3C5
or R4C4 + R5C5 + R6C6 = {347} = [347] => 10(3) cage at R4C1 = {145}, locked for R4 => R4C79 = {29}, locked for R4
-> R34C5 = {68}, locked for C5
3d. R3C57 + R4C7 = 6{29}/6{47}/8{27}/[854], no 8 in R3C7
3e. R5C5 = {134}, 11(3) cage at R7C5 = {137/245} -> combined half cage R5789C5 = 1{245}/3{245}/4{137}, 4 locked for C5
3f. R1C56 + R3C5 = 18 (step 2i), R3C5 is even, R1C5 odd -> R1C6 must be odd, no 4,6,8 in R1C6
3g. Variable hidden killer pair 2,4 in 11(3) cage at R1C4 and disjoint 16(3) cage at R2C6, 16(3) cage cannot contain both of 2,4 -> 11(3) cage must contain at least one of 2,4 = {128/146/236/245}, no 7
3h. 2 of {236/245} must be in R2C5 -> no 3,5 in R2C5
3i. Killer pair 1,2 in R2C5 and 11(3) cage at R7C5, locked for C5
3j. Killer pair 3,4 in R5C5 and 11(3) cage at R7C5, locked for C5
3k. Min R13C5 = 11 -> max R1C6 = 7
3l. R4C4 + R5C5 + R6C6 = {149/347/356} (cannot be {158/167} because R5C5 only contains 3,4), no 8
3m. 26(5) cage at R4C7 = {14579/24569} (cannot be {13679} because 1,3,6 only in R5C6 + R7C4, cannot be {23579} = [23]{579} when 1 then in R4C46 and R4C7 = 2 clash with 10(3) cage at R4C1), no 3, clean=up: no 6 in R7C3 (step 1g)
3n. R4C4 + R5C5 + R6C6 = {347/356} = [347/635] (cannot be {149} which clashes with R5C6), no 1,9, 3 locked for N5 and D\
3o. 26(5) cage at R4C7 = {14579} (cannot be {24569} = [24956] which clashes with R4C4 + R5C5 + R6C6 = [635], CCC), no 2,6, clean-up: no 9 in R4C9 (step 2c), no 3 in R7C4 (step 1g)
[This 45 was seen earlier but is only helpful after eliminating 1 from R4C4]
4a. 45 rule on R4 4 remaining innies R4C4568 = 24 = {1689/3678}
4b. 1 of {1689} only in R4C6 -> no 9 in R4C6
4c. 9 in R4 only in R4C78, locked for N6
4d. 9 in R5 only in R5C12 = {69}, locked for N4
4e. Naked pair {78} in R56C3, locked for C3, clean-up: no 1 in R7C4 (step 1g)
4f. 26(5) cage at R4C7 (step 3o) = {14579} -> R5C6 = 1, R5C5 = 4 (hidden single in N5), placed for both diagonals, R4C4 = 3, R6C6 = 7 (step 3n), placed for D\, R56C3 = [78], clean-up: no 2 in 10(3) cage at R4C1, no 2 in R7C3 (step 1g)
4g. R5C789 = {358} = 16 -> R4C8 = 7 (cage sum)
4h. Naked triple {145} in 10(3) cage at R4C1, 1,4 locked for N4, 4 locked for R4
4i. Naked pair {23} in R6C12, locked for R6
4j. 11(3) cage at R7C5 = {137}, only remaining combination), locked for N8, 1,7 locked for C5
5a. R4C7 = 9 -> R6C5 = 5, R7C4 = 4, R6C4 = 9, R7C3 = 5, both placed for D/
5b. 45 rule on N8 2 remaining innies R89C4 = 11 = {56}, locked for C4, N8 and 22(4) cage at R8C4)
5c.8(3) cage at R8C2 = {134} (only remaining combination) -> R8C3 = 4, R8C2 + R9C1 = {13}, 3 locked for N7
5d. 21(3) cage at R7C1 = {678} (only remaining combination), 7,8 locked for N7
5e. Naked pair {29} in R9C23, locked for R9
5f. R9C6 = 8 -> R4C6 = 6, placed for D/
5g. R1C9 + R2C8 = [78] -> R2C7= 6 (cage sum)
5h. R34C5 = [68], R1C5 = 9 -> R1C6 = 3 (step 2i)
5i. R1C56 = [93] = 12 -> R1C78 = 9 = {45}, locked for R1 and N3
5j. 11(3) cage at R1C4 = [812]
5k. R2C3 = 3 -> R1C23 = 8 = {26}, locked for N1
5l. R1C1 = 1 -> R2C2 + R3C3 = [59], all placed for D\
5m. 16(3) cage at R7C7 = [826]
5n. 15(3) cage at R7C8 = {159} (only remaining combination) -> R8C9 = 5, R7C89 = {19}, locked for R7, 1 locked for N9
and the rest is naked singles without using the diagonals.