Prelims
a) R1C12 = {16/25/34}, no 7,8,9
b) R12C5 = {14/23}
c) R1C89 = {49/58/67}, no 1,2,3
d) R2C12 = {59/68}
e) R2C89 = {39/48/57}, no 1,2,6
f) R34C1 = {13}
g) R34C9 = {39/48/57}, no 1,2,6
h) R4C23 = {29/38/47/56}, no 1
i) R4C78 = {16/25/34}, no 7,8,9
j) R67C1 = {79}
k) R6C23 = {18/27/36/45}, no 9
l) R6C78 = {29/38/47/56}, no 1
m) R67C9 = {18/27/36/45}, no 9
n) R8C12 = {39/48/57}, no 1,2,6
o) R89C5 = {18/27/36/45}, no 9
p) R8C89 = {49/58/67}, no 1,2,3
q) R9C12 = {59/68}
r) R9C89 = {16/25/34}, no 7,8,9
s) 11(3) cage at R2C7 = {128/137/146/236/245}, no 9
t) 23(3) cage at R4C5 = {689}
u) 10(3) cage at R7C2 = {127/136/145/235}, no 8,9
v) 10(3) cage at R7C4 = {127/136/145/235}, no 8,9
w) 10(3) cage at R8C4 = {127/136/145/235}, no 8,9
x) 19(3) cage at R8C6 = {289/379/469/478/568}, no 1
1. Naked pair {13} in R34C1, locked for C1 and NR1C1, clean-up: no 4,6 in R1C12, no 8 in R4C23, no 9 in R8C2
1a. Naked pair {25} in R1C12, locked for R1 and NR1C1, clean-up: no 8 in R1C89, no 9 in R2C12, no 3 in R2C5, no 6,9 in R4C23
1b. Naked pair {68} in R2C12, locked for R1 and NR1C1, clean-up: no 4 in R2C89
1c. Naked pair {47} in R4C23, locked for R4 and NR1C1 -> R5C3 = 9, clean-up: no 5,8 in R3C9, no 3 in R4C78
1d. R5C3 = 9 -> R5C12 = 5 = [23/41]
2. Naked pair {79} in R67C1, locked for C1 and NR5C1, clean-up: no 2 in R6C23, no 3,5 in R8C2, no 5 in R9C2
3. Naked triple {689} in 23(3) cage at R4C5, locked for C5, clean-up: no 1,3 in R89C5
3a. Killer pair 2,4 in R12C5 and R89C5, locked for C5
4. 2 in NR1C3 only in R2C7 + R3C8, locked for 11(3) cage at R2C7, no 2 in R3C7
4a. 11(3) cage = {128/236/245}, no 7
5. 45 rule on R12 2 innies R2C37 = 9 = [45/54/72], no 1,3, no 2 in R2C3
6. 45 rule on R89 2 innies R8C37 = 6 = {15/24}
6a. Killer pair 4,5 in R8C12 and R8C37, locked for R8, clean-up: no 8,9 in R8C89, no 4,5 in R9C5
6b. Naked pair {67} in R8C89, locked for R8 and NR5C7 -> R8C5 = 2, placed for NR6C5, R9C5 = 7, placed for NR7C2, clean-up: no 3 in R1C5, no 4,5 in R6C78, no 2,3 in R67C9, no 5 in R8C1, no 1 in R9C89
6c. Naked pair {48} in R8C12, locked for R8
6d. Naked pair {15} in R8C37, locked for R8 -> R8C4 = 3, R8C6 = 9, both placed for NR6C5
6e. R8C6 = 9 -> R9C67 = 10 = {28/46}, no 3,5
[I’ve deliberately avoided using several CPEs, based on naked pairs, because they aren’t necessary in this puzzle.]
7. Naked pair {14}, locked for C5 -> R7C5 = 5, placed for NR6C5, R3C5 = 3, placed for NR2C3, R34C1 = [13], R8C7 = 1, placed for NR6C5, R8C3 = 5, placed for NR7C2, clean-up: no 4 in R2C7 (step 5), no 9 in R34C9, no 6 in R4C8, no 4 in R6C2, no 4 in R6C9
7a. Naked pair {47} in R24C3, locked for C3, clean-up: no 5 in R6C2
7b. R8C7 = 1 -> R7C78 = 13 = {67}, locked for R7 and NR6C5 -> R7C4 = 4, R7C6 = 1 (cage sum), placed for NR3C4, R67C1 = [79], R7C9 = 8, placed for NR5C7, R6C9 = 1, R6C5 = 8, R5C5 = 6, placed for NR3C4, R4C5 = 9, placed for NR2C3, R4C9 = 5, R3C9 = 7, both placed for NR1C9, R8C89 = [76], R7C78 = [76], clean-up: no 5 in R2C8, no 2 in R9C8
7c. Naked pair {28} in R4C46, locked for R4 and NR3C4 -> R4C78 = [61]
7c. Naked pair {36} in R6C23, locked for R6 and NR5C1
7d. Naked pair {29} in R6C78, locked for R6 and NR5C7 -> R6C46 = [54], R5C4 = 7, R4C4 = 2 (cage sum), R4C6 = 8, R5C6 = 3 (cage sum), R5C2 = 1, R5C1 = 4 (cage sum)
7e. R3C4 = 9, R3C6 = 6 (cage sum), R9C6 = 2, R9C7 = 8 (cage sum)
8. R5C9 = 2, R5C7 = 5, R3C7 = 4, placed for NR3C7 -> R1C9 = 9
and the rest is naked singles, without using the nonets.