Semi-Symmetric. Repeats allowed within killer cages, but not in rows, columns and nonets.
Prelims
a) 20(3) cage at R2C1 = {389/479/569/578}, no 1,2
b) 19(3) cage at R2C7 = {289/379/469/478/568}, no 1
c) 20(3) cage at R4C1 = {389/479/569/578}, no 1,2
d) 11(3) cage at R4C2 = {128/137/146/236/245}, no 9
e) 8(3) cage at R4C9 = {125/134}
f) 4(3) cage at R5C5 = {112}
g) 20(3) cage at R6C4 = {389/479/569/578} plus possible repeats which could include {29}9, no 1
h) 11(3) cage at R8C1 = {128/137/146/236/245}, no 9
i) R9C78 = {19/28/37/46}, no 5
1a. 8(3) cage at R4C9 = {125/134}, 1 locked for C9 and N6
1b. 4(3) cage at R5C5 = {112} -> R5C5 + R6C6 = {12}, locked for N5, R7C7 = 1, clean-up: no 9 in R9C78
1c. 20(3) cage at R6C4 cannot repeat in R6C45 -> no 2 in R7C6
1d. Min R5C6 + R6C7 = 5 -> no 9 in R7C8
1e. Min R5C6 + R7C8 = 5 -> no 9 in R6C7
2. 45 rule in R2 3 innies R2C123 = 6 = {123}, locked for N2, 2,3 locked for R2
3. 45 rule on N8 1 outie R7C3 = 1 innie R7C6 + 1
3a. Min R7C6 = 3 -> min R7C3 = 4
3b. Max R7C3 = 9 -> max R7C6 = 8
[Time to look at semi-symmetry.]
4. R5C5 = {12} is the non-paired number
4a. R2C456 = {123} corresponds with 16(3) cage at R8C4 -> 16(3) must contain one of 1,2 = {169/178/259/268}, no 3,4
4b. 3 and the other of 1,2 must be paired with two of 5,6,7,8,9
4c. 11(3) cage at R8C1 = {137/146/236/245} (cannot be {128} which clashes with 16(3) cage), no 8
4d. 18(3) cage at R8C7 = {369/378/459/468} (cannot be {279/567} which clash with 16(3) cage), no 2
4e. The non-paired number in R5C5 cannot be in R8C5 -> no 1,2 in R8C5
4f. The other of 1,2 is in R6C6 which corresponds with R4C4 -> no 3,4 in R4C4
4g. 12(3) cage at R9C4 = {138/147/237/246/345} (cannot be {129/156} which clash with 16(3) cage), no 9
4h. R7C7 = 1 corresponds with R3C3, R7C1 is either the non-paired number or is paired with one of 5,6,7,8,9 -> no 2,3,4 in R3C3
[Just spotted.]
5. 20(3) cage at R4C1 corresponds with 8(3) cage at R4C9, 8(3) cage must contain 1, no 1 in 20(3) cage -> 1 cannot be the non-paired number -> 2 must be the non-paired number
5a. R5C5 = 2 -> R6C6 = 1
5b. 8(3) cage at R4C9 = {134} (cannot be {125} because no 2 in 20(3) cage), 3,4 locked for C9 and N6
5c. R2C456 corresponds with 16(3) cage at R8C4, R2C46 contains 2 -> 16(3) cage must contain 2 = {259/268}, no 1,7, 2 locked for R8 and N8
5d. 11(3) cage at R8C1 (step 4c) = {137/146}, no 5, 1 locked for N7
5e. 12(3) cage at R9C4 (step 4g) = {138/147}, no 5,6
5f. R9C78 = {28/46} (cannot be {37} which clashes with 12(3) cage), no 3,7
5g. Killer pair 4,8 in 12(3) cage and R9C78, locked for R9
5h. 8 in N7 only in R7C123, locked for R7, clean-up: no 9 in R7C3 (step 3)
5i. 18(3) cage at R8C7 (step 4d) = {378/459} (cannot be {369} which clashes with 16(3) cage, cannot be {468} which clashes with R9C78), no 6
5j. Killer pair 4,8 in 18(3) cage and R9C78, locked for N9
5k. 1,3 paired with either 5,9 or 6,8 -> no 7 in R3C3 (step 4h) and R4C4 (step 4f)
5l. 18(3) cage at R4C8 = {279/567}, no 8, 7 locked for C8 and N6
5m. 45 rule in N6 3 innies R456C7 = 19 = {289/568}, 8 locked for C7, clean-up: no 2 in R9C8
5n. 45 rule on N9 3 innies R7C89 + R9C9 = 16 = {259/367}
5o. 3 of {367} must be in R7C8 -> no 6 in R7C8
5p. 2 in N9 only in R7C89 + R9C79 -> 2 in N1 only in R1C13 + R3C12
5q. 2 in N7 only in R7C12 + R9C123 -> 2 in N3 only in R1C789 + R3C89
5r. Max R7C6 = 7 -> min R6C45 = 13, no 3 in R6C45
6. R7C89 + R9C9 (step 5n) = {259/367}
6a. 45 rule on N8 3 innies R7C456 = 17 = {359/467}
6b. Consider combinations for R7C456
R7C456 = {359}, 3,5 locked for R7 => R7C8 = 2
or R7C456 = {467}, 6,7 locked for R7
-> R7C89 + R9C9 = {259}, locked for N9, clean-up: no 8 in R9C8
6c. Naked pair {46} in R9C78, locked for R9, 4 locked for N9, clean-up: no 7 in 12(3) cage at R9C4 (step 5e)
6d. Naked triple {378} in 18(3) cage at R8C7, locked for R8
6e. Naked triple {146} in 11(3) cage at R8C1, 4,6 locked for N7, 6 locked for R8, clean-up: no 3,5 in R7C6 (step 3)
6f. Naked triple {138} in 12(3) cage at R9C4, 3 locked for R9 and N8
6g. R7C456 = {467} (only remaining combination), 7 locked for R7, clean-up: no 6 in R7C6 (step 3)
6h. 1,3 paired with 5,9
6i. 20(3) cage at R4C1 corresponds with 8(3) cage at R4C9, 8(3) = {134} -> 20(3) cage = {389/569} (cannot be {479/578} because 7,8 not paired with 1,3), no 4,7, 9 locked for C1 and N4
6j. 4 paired with one of 6,8
6k. 11(3) cage at R4C2 = {128/137/245} (cannot be {146} because {146} which clashes with R8C2, cannot be {236} which clashes with 20(3) cage), no 6
6l. 11(3) cage corresponds with 18(3) cage at R4C8, 18(3) cage doesn’t contain 1,3 and only contains one of 5,9 -> 11(3) cage at R4C2 = {128/245}, no 3,7, 2 locked for C2 and N4
6m. 11(3) cage contains 2 -> 18(3) cage (step 5l) must contain 2 = {279}, 2,9 locked for C8 and N6
6m. R7C8 = 5, R7C3 = 8 -> R7C6 = 7 (step 3)
6n. Naked pair {29} in R79C9, locked for C9
6o. R7C8 = 5 -> R5C6 + R6C7 = 8 = [35]
6p. Naked pair {68} in R45C7, 6 locked for C7 -> R9C78 = [46]
6q. R2C6 = 2 -> R8C4 = 2 (hidden single in N8)
6r. R1C7 = 2 (hidden single in C7)
6s. R1C7 corresponds with R9C7 -> R9C7 = 2, R79C9 = [29], R7C1 = 3
6t. 20(3) cage = {569} (only remaining combination), 5,6 locked for C1 and N4 -> R9C12 = [75]
6u. 11(3) cage = {128} (only remaining combination), 1,8 locked for C2, 1 locked for N4
6v. Naked triple {347} in R456C3, locked for C3
6w. R7C2 = 9 -> R5C4 + R6C3 = 9 = [54/63]
6x. R5C6 = 3 corresponds with R5C4 -> R5C4 = 5, R6C3 = 4, R45C3 = [37], R6C9 = 3, R5C18 = [69], R46C1 = [59], R45C7 = [68], R5C2 = 1, R45C9 = [14]
6y. 3 paired with 5 -> 1 paired with 9
6z. R5C1 corresponds with R5C9 -> 4 paired with 6 -> 7 must be paired with 8
7a. R7C6 = 7 -> R6C45 = 13 = {67}, 7 locked for R6 and N5 -> R46C8 = [72], R46C2 = [28]
7b. R4C4 corresponds with R6C6, R6C6 = 1 -> R4C4 = 9
7c. R2C7 corresponds with R8C3, no 4 in R2C7, no 8 in R8C3 -> R2C6 = 9, R8C3 = 1, R8C12 = [46], R2C18 = [84], R13C1 = [12], R2C2 = 7
7d. R1C2 corresponds with R9C8, R9C8 = 6 -> R1C2 = 4, R3C2 = 3, R3C7 = 7, 18(3) cage at R8C7 = [387], R13C8 = [31]
7e. R1C3 corresponds with R9C7, R9C7 = 4 -> R1C3 = 6, R23C3 = [59]
7f. R9C6 = 8, R4C56 = [84]
7g. R4C6 corresponds with R6C4, R4C6 = 4 -> R6C4 = 6, R137C4 = [784], R23C9 = [65]
7h. R3C456 = [846], R4C5 = 8 -> R2C5 = 3 (cage sum)
7i. R2C5 corresponds with R8C5, R2C5 = 3 -> R8C5 = 5
and the rest is naked singles, without using corresponding pairs.
