Numbers are 0 to 9.

The numbers in the grey cells repeat horizontally and vertically and are present in every nonet.

No repeats in any other rows or columns.

Each of the other numbers is missing from one and only one nonet.

Five pairs of unknown numbers are semi-symmetric, with the corresponding cell containing the same number or its partner.

The two numbers in the grey cells repeat horizontally and vertically; they are in all nonets

Note that in the steps below locked, placements and killer pairs in R6, R7 and C6 don’t apply for R67C6, as appropriate. However placements and locked for N3 and N6 DO apply for R67C6, as appropriate.

Prelims

a) 13(2) cage at R2C7 = {49/58/67}

b) 11(2) cage at R3C6 = {29/38/47/56}, no 0,1

c) 13(2) cage at R4C4 = {49/58/67}

d) 7(2) cage at R4C6 = {07/16/25/34}, no 8,9

e) 3(2) cage at R4C9 = {03/12}

f) 4(2) cage at R5C2 = {04/13}

g) 8(2) cage at R5C6 = {08/17/26/35}, no 4,9

h) 17(2) cage at R5C10 = {89}

i) 1(2) cage at R6C4 = {01}

j) 16(2) cage at R8C5 = {79}

k) 6(2) cage at R8C9 = {06/15/24}, no 3,7,8,9

l) 8(2) cage at R9C5 = {08/17/26/35}, no 4,9

m) 5(2) cage at R9C7 = {05/14/23}

n) 4(3) cage at R5C5 = {013}

o) 6(3) cage at R6C5 = {015/024/123}

p) 24(3) cage at R7C1 = {789}

q) 15(6) cage at R1C1 = {012345}

r) 9(2) cage at R2C6 = {09/18/27/36/45}, no initial eliminations

1a. R5C56 = {13} (cannot be {01/13} which clash with R5C23), locked for R5 and N3 -> R6C6 = 0, clean-up: no 4,6,7 in R4C67, no 0,2 in R4C9

1b. 8(2) cage at R5C6 = [17/35]

1c. Naked pair {25} in R4C67, locked for R4, 5 locked for N3 -> R5C7 = 7 -> R5C56 = [31], clean-up: no 6 in R2C6, no 8 in R3C5, no 4 in R3C6, no 6 in R3C8, no 6,8 in R4C45, no 7 in R9C5, no 5 in R9C6

1d. Naked pair {04} in R5C23, locked for R5 and N2 -> R45C9 = [12], R67C4 = [10], R4C3 = 3, 0 has been placed in R6C6, cannot also be in R7C6 because they must be different -> R7C4 = 0 placed for R7, clean-up: no 4,5 in R8C10

1e. R6C6 = 0 -> R6C57 = 6 = [24], R6C1 = 5, clean-up: no 7 in R2C6, no 7 in R3C6, no 9 in R3C8, no 6 in R9C6, no 1 in R9C8

1f. Naked pair {49} in R4C45, locked for R4

1g. Naked pair {89} in R56C10, locked for C10 and N4

1h. Naked pair {79} in R8C56, locked for R8 and N6 -> R8C2 = 8, clean-up: no 1 in R9C5

1i. Naked pair {79} in R7C1 + R9C3, locked for N5

1j. 15(6) cage at R1C1 = {012345} -> R2C5 = 1, 2 in R1C6 + R3C4, locked for N1, clean-up: no 8 in R2C6, no 7 in R3C5, no 9 in R3C67

1k. 9(2) cage at R2C6 = {09/45} (cannot be [36] which clashes with R3C67), no 3,6

1l. 13(2) cage at R2C7 = [67] (cannot be {58} which clashes with R3C67, cannot be [94] which clashes with 9(2) cage), clean-up: no 5 in R3C67

[Time to look at semi-symmetry and I remembered that, in addition to pairs, the numbers missing from corresponding nonets must be paired.]

2a. R5C6 = 1 corresponds with R8C6 = {79}, R5C7 = 7 corresponds with R8C5 = {79}, no 1 in R8C6 -> 1 is paired with 9 (cannot be R5C6 = 1 paired with R8C6 = 7 because then R5C7 = 7 cannot be paired with R8C5 = 9) -> R8C56 = [79], clean-up: no 0 in R3C5

2b. R2C5 = 1 corresponds with R11C7 -> R11C7 = {19}

2c. R4C9 = 1 corresponds with R9C3, no 1 in R9C3 -> R9C3 = 9, R7C1 = 7

2d. R6C4 = 1 corresponds with R7C8 -> R7C8 = {19}

2e. R8C2 = 8 corresponds with R5C10, R5C10 cannot be 9 because 9 paired with 1 -> R5C10 = 8, R6C10 = 9

2f. R6C10 = 9 corresponds with R7C2, no 9 in R7C2 -> R7C2 = 1, R7C8 = 9

2g. R2C7 = 6 corresponds with R11C5, R3C7 = {38} corresponds with R10C5, R3C8 = 7 corresponds with R10C4 -> no 9 in R10C4 and R10,11C5

2h. Combined cage R1C6 + R3C3 and 9(2) cage at R2C6 = [02]{45}/{24}[09] -> 0 in R12C6, also R6C6 = 0 is the repeated 0 -> 0 locked for C6, clean-up: no 8 in R9C5

2i. 8 in C5 only in R10,11C5, locked for N8

2j. R4C45 = {49} corresponds with R9C78, no 9 in R9C78 -> R9C78 = [14], R4C45 = [49], R3C4 = 2, R11C7 = 9, clean-up: no 0 in R2C6

2k. Naked pair {45} in 9(2) cage at R2C6, locked for N1 -> R1C6 = 0, R5C23 = [40]

2l. No 9 in N1 -> no 1 in N8

2m. 7 in C6 only in R10,11,12C6, locked for N8

2n. R5C4 = 9 (hidden single in N2, which must contain both of 1,9)

2o. R5C4 = 9 corresponds with R8C8, no 9 in R8C8 -> R8C8 = 1, clean-up: no 5 in R8C9

2p. R6C3 = 8 (hidden single in R6)

[All the 1s and 9s have now been placed]

3a. R1C6 = 0 corresponds with R11C6 and R6C6 = 0 corresponds with R7C6, neither of R7C6 and R11C6 contain 0 -> R7C6 and R11C6 must contain the same number, the second repeated number in C6 = {2356} -> 0 must be paired with one of 2,3,5,6

3b. R7C1 = 7 corresponds with R6C11, 7 doesn’t correspond with 0 -> no 0 in R6C11

3c. R5C3 = 0 corresponds with R8C9, 4 doesn’t correspond with 0 -> no 4 in R8C9, clean-up: no 2 in R8C10

3d. R5C2 = 4 corresponds with R8C10, 4 doesn’t correspond with 0 -> R8C10= 6, R8C9 = 0

3e. 4 paired with 6

3f. R6C8 = 0 (hidden single in R6 apart from repeated 0 in R6C6, alternatively naked triple {367} in R6C2911, locked for R6)

3g. R10C7 = 0 (hidden single in C7)

3h. R9C5 = 0 (hidden single in C5) -> R9C6 = 8, R3C67 = [38]

3i. 3 placed for C6, 4 paired with 6, R1C6 corresponds with R12C6 -> 0 paired with one of 2,5, no 3,6 in R7C6, no 6 in R11C6

3j. Naked pair {25} in R412C6 (plus one of them in repeated R7C6), locked for C6 -> R2C6 = 4, R3C5 = 5

3k. R4C6 = 4 corresponds with R11C6, no 4 in R11C6 -> R11C6 = 6, R10C6 = 7

3l. R3C6 = 3 corresponds with R10C6 = 7 -> 3 paired with 7

3m. R2C7 = 6 corresponds with R11C5, no 6 in R11C5 -> R11C5 = 4, R10C5 = 8, R7C5 = 6

3n. R3C8 = 7 corresponds with R10C4, no 7 in R10C4 -> R10C4 = 3, R8C4 = 5

3o. R9C4 = 6 corresponds with R4C8, no 4 in R4C8 -> R4C8 = 6, R5C8 = 5, R10C8 = 2

3p. R1C6 = 0 corresponds with R12C6 = 5 -> 0 paired with 5

3q. Repeated R6C6 = 0 corresponds with R7C6 -> R7C6 = 5

3r. The remaining pair are 2 with 8

3s. R5C9 = 2 corresponds with R8C3, no 8 in R8C3 -> R8C3 = 2, R7C3 = 4

3t. R6C5 = 2 corresponds with R7C7, no 8 in R7C7 -> R7C7 = 2

3u. R7C3 = 4 corresponds with R6C9, no 4 in R6C9 -> R6C9 = 6, R6C211= [73]

3v. R6C3 = 8 corresponds with R7C10, no 2 in R7C10 -> R7C10 = 8

3w. Naked singles R4C67 = [25], R7C11,12 = [35], R8C7 = 3, R9C410 = [67]