Prelims
a) R23C1 = {89}
b) R2C23 = {16/25/34}, no 7,8,9
c) R2C56 = {79}
d) R3C23 = {12}
e) R45C3 = {59/68}
f) R56C7 = {19/28/37/46}, no 5
g) R7C78 = {39/48/57}, no 1,2,6
h) R78C9 = {18/27/36/45}, no 9
i) R8C45 = {29/38/47/56}, no 1
j) R8C78 = {59/68}
k) 11(3) cage at R2C9 = {128/137/146/236/245}, no 9
l) 20(3) cage at R5C9 = {389/479/569/578}, no 1,2
m) 10(3) cage at R7C1 = {127/136/145/235}, no 8,9
n) 10(3) cage at R9C7 = {127/136/145/235}, no 8,9
o) 16(5) cage at R1C4 = {12346}
p) 45(9) cages = {123456789}
1a. Naked pair {79} in R2C56, locked for R2 and N2 -> R23C1 = [89]
1b. Naked pair {12} in R3C23, locked for R3 and N1, clean-up: no 5,6 in R2C23
1c. Naked pair {34} in R2C23, locked for R2 and N1
1d. Naked triple {567} in 18(3) cage at R1C1, locked for R1
1e. R8C45 = {29/38/47} (cannot be {56} which clashes with R8C78), no 5,6
1f. 45 rule on N36 1 innie R1C7 = 4, clean-up: no 6 in R56C7, no 8 in R7C8
1g. Naked triple {123} in R1C456, locked for R1 and N2 -> R2C4 = 6
1h. Naked pair {89} in R1C89, locked for 45(9) cage at R1C8, 8 locked for N3
1i. R3C456 = {458} (hidden triple in N2), 5 locked for R3
1j. 11(3) cage at R2C9 = {137/236} -> R2C9 = {12}, R3C89 = {36/37}, 3 locked for N3
1k. 5 in N2 only in R2C78, locked for 45(9) cage at R1C8
1l. 45(9) cage at R1C8 = {123456789}, 3,4 locked for N6, clean-up: no 7 in R56C7
1m. 45 rule on N47 1 innie R9C3 = 9, clean-up: no 5 in R45C3
1n. Naked pair {68} in R45C3, locked for C3 and N4
1o. 45(9) cage at R5C2 = {123456789}, 9 locked for N4
1p. 45 rule on N8 3 remaining innies R7C456 = 21 = {489/579/678}, no 1,2,3
2a. Combined cage R78C78 = {39}{68}/{57}{68}/[84]{59}, 8 locked for N9, clean-up: no 1 in R78C9
2b. 1 in N9 only in 10(3) cage at R9C7 = {127/136/145}, 1 locked for R9
2c. R8C6 = 1 (hidden single in N8)
2d. R8C6 = 1, R9C3 = 9 -> R9C456 = 12 = {246/345} (cannot be {237} which clashes with R8C45), no 7,8, 4 locked for R9 and N8, clean-up: no 7 in R8C45
2e. R9C2 = 8 (hidden single in R9)
2f. 45 rule on R9 1 remaining innie R9C1 = 6, clean-up: no 2 in R9C456
2g. Naked triple {345} in R9C456, 3,5 locked for N8, clean-up: no 8 in R8C45
2h. 10(3) cage at R9C7 = {127} (hidden triple in N9), 2,7 locked for N9, clean-up: no 5 in R7C78
2i. Naked pair {29} in R8C45, locked for R8, 9 locked for N8, clean-up: no 5 in R8C78
2j. Naked pair {68} in R8C78, locked for N9, clean-up: no 4 in R7C8, no 3 in R78C9
2k. Naked pair {39} in R7C78, 3 locked for R7
2l. Naked pair {45} in R78C9, locked for C9
2m. Naked triple {678} in R7C456, 7 locked for R7, 6 locked for 24(4) cage at R5C6, no 6 in R56C6
2n. R6C8 = 5 (hidden single in N6)
2o. R1C2 = 6 (hidden single in R1)
2p. R2C7 = 5 (hidden single in R2)
2q. Naked pair {12} in R2C89, CPE no 1,2 in R4C9
2r. R29C9 = {12} (hidden pair in C9)
3a. 24(4) cage at R5C6 contains 6 in R7C56 = {3678}, 3 locked for C6 and N5 -> R1C6 = 2
3b. 40(7) cage at R3C6 = {1456789} (only remaining combination), no 2, 1 locked for N5
3c. 19(4) cage at R3C4 = {2458} (only remaining combination), 2 locked for C4 -> R8C45 = [92]
3d. 7 in C4 only in R67C4, locked for 40(7) cage
4a. Consider placement for 6 in 45(9) cage at R1C8
R3C7 = 6 => R8C7 = 8 => R56C7 = {19}
or 6 in R4C456 + R5C5, locked for N6 => R56C9 = 15 = {78}, locked for N6 => R56C7 = {19}
-> R56C7 = {19}, locked for C7 and N6, R7C78 = [39], R1C89 = [89], R8C78 = [86], clean-up: no 6 in R56C9
[Cracked]
4b. Naked pair {78} in R56C9, 7 locked for C9 and N6
4c. 45(9) cage at R1C8 = {123456789} -> R2C8 = 1, R3C7 = 7, R2C9 = 2, R3C89 = [36], R49C7 = [62], R45C3 = [86], R4C9 = 3
4d. R6C5 = 6 (hidden single in N5) -> R7C6 = 6 (hidden single in N6)
4e. Naked pair {78} in R7C45, CPE no 8 in R5C5
4f. 40(7) cage at R3C6 = {1456789}, CPE no 8 in R3C4
4g. 7 in R4 only in R4C12, locked for N4
4h. 12(3) cage at R4C1 = {147/237}, no 5
4i. 3 of {237} must be in R5C1 -> no 2 in R5C1
4j. R56C2 = [59] (hidden pair in N4) -> R56C7 = [91]
4k. 1 in N4 only in 12(3) cage = {147}, 4 locked for N4
4l. Naked pair {14} in R5C15, locked for R5
4m. Naked pair {23} in R6C13, locked for 45(9) cage at R5C2, 3 locked for R6
4n. Naked pair {47} in R8C23, locked for N7, 4 locked for R8
and the rest is naked singles.
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