“I commented on the players forum that I could not find an NC puzzle that was fully Semi-symmetric (i.e. at least on number is paired with itself in at least one position pair) all I could find were asymmetric ones. Wecoc took this as a challenge and found a set of them, posting a nice vanilla puzzle.

From his puzzle I made a killer which I re-post here. I have solved it a couple of ways but find my solutions mucky, can anyone post a neat solution?”

Prelims, including effect of NC

a) R23C6 = {17/26/35}

b) R3C12 = {16/25} (cannot be {34})

c) R34C4 = {16/25} (cannot be {34})

d) R4C78 = {59/68}

e) R5C23 = {49/58} (cannot be {67})

f) R5C78 = {19/28/37/46}

g) R6C23 = {18/27/36} (cannot be {45})

h) R67C6 = {16/25} (cannot be {34})

i) R78C4 = {17/26/35}

j) R7C89 = {18/27/36} (cannot be {45})

NC only used as stated.

1a. R23C6 = {17/35} (cannot be {26} which clashes with R67C6)

1b. Killer pair 1,5 in R23C6 and R67C6, locked for C6

1c. R78C4 = {17/35} (cannot be {26} which clashes with R34C4)

1d. Killer pair 1,5 in R34C4 and R78C4, locked for C4

2a. R3C12 = {16/25} must have different combination from R34C4

2b. R3C12 = {16/25} corresponds with R7C89 = {18/27/36} -> {16} cannot correspond with {25} -> R34C4 must have the same combination as R67C6

[Possibly slightly simplified; see also wellbeback’s start.]

2c. R4C4 cannot be the same as R6C6 -> R34C4 and R67C6 must have the same vertical order

3a. R4C78 cannot be {68} because R5C78 = {19} (cannot be {37}, NC), R5C23 = {58}, R6C23 = {27/36}, R4C78 corresponds with R6C23, R5C23 corresponds with R5C78 but 8 cannot correspond both with one of 1,9 and one of 2,3,6,7

3b. R4C78 = {59}, locked for R4 and N6, clean-up: no 2 in R3C4, no 1 in R6C78

3c. R34C4 = {16}/[52] -> R67C6 = {16}[52] (steps 2b and 2c), no 2 in R6C6, no 5 in R7C6

4. R3C12 corresponds with R7C89, R4C78 corresponds with R6C23, R6C23 and R7C89 are both {18/27/36} neither containing 5, R4C78 = {59} corresponds with one of the combinations in R6C23

-> R3C12 = {16} (cannot be {25} because {25} and {59} cannot correspond with the same combination), locked for R3 and N1

4a. R3C45 = [52] -> R67C6 = [52] (step 2c), R78C4 = {17}, locked for C4 and N8, R23C6 = [17], clean-up: no 7 in R7C89

4b. R4C4 corresponds with R6C6 -> 2,5 paired

4c. R4C78 = {59} corresponds with R6C23 -> R6C23 = {27}, locked for R6 and N4

4d. 7 paired with 9

4e. R5C23 corresponds with R5C78, R5C23 contains one of 5,9 -> R5C78 must contain one of 2,7 but {58} cannot correspond with {28} since they are in the same row -> R5C23 = {49}, locked for R5 and N4, R5C78 = {37}, locked for R5 and N6

4f. R6C6 = 5 -> R5C46 = [68] (NC) -> R5C5 = 1, R5C19 = [52], R5C23 = [94] (NC), R5C78 = [37] (NC)

4g. 3,4 paired, 6,8 paired

4h. R4C5 = 7 (hidden single in N5)

4i. 1 can only correspond with itself

4j. R3C12 corresponds with R7C89, R3C12 = {16} -> R7C89 = {18} (cannot be {36} because 3 is paired with 4), locked for R7 and N9 -> R78C4 = [71]

[The rest will be very dependent on NC and corresponding cells.]

5a. R5C1 = 5 -> no 6 in R46C1 (NC)

5b. 6 in N4 only in R4C23, locked for R4

5c. R5C9 = 2 -> no 1 in R46C9 (NC)

5d. R46C1 correspond with R46C9, no 1 in R46C9 -> no 1 in R46C1

5e. Naked pair {38} in R46C1, locked for C1 and N4

5f. R46C1 corresponds with R46C9, 3 in R46C1 -> R46C9 must contain 4, locked for C9 and N6

5g. R5C8 = 7 -> R6C8 = 1 (NC), R7C89 = [81]

5h. R3C1 corresponds with R7C9 -> R3C12 = [16], R4C23 = [16]

5i. R1C7 = 1 (hidden single in N3)

5j. R9C3 = 1 (hidden single in N7)

5k. R4C5 corresponds with R6C5, R4C5 = 7 -> R6C5 = 9

5l. R6C6 = 5 -> R6C7 = 8 (NC), R46C9 = [46], R4C6 = 3, R46C1 = [83], R6C4 = 4, R4C78 = [59] (NC), R6C23 = [72] (NC)

5m. R3C4 = 5 -> no 4 in R3C5 (NC)

5n. R4C7 = 5 -> no 4 in R3C7 (NC)

5o. R3C8 = 4 (hidden single in R3)

5p. R6C3 = 2 -> no 3 in R7C3 (NC)

5q. R7C6 = 2 -> no 3 in R7C5 (NC)

5r. R7C2 = 3 (hidden single in R7)

5s. R7C8 = 8 -> no 9 in R7C7 (NC)

5t. 9 in R7 only in R7C13, locked for N7

5u. R3C3 corresponds with R7C7, R7C7 = {46} -> R3C3 = {38}

5v. 9 in R3 only in R3C79, locked for N3

6a. R12C4 = {38/39} (cannot be {89}, NC), 3 locked for C4 and N2

6b. R3C6 = 7 -> R3C5 = 2 (NC), R3C7 = 9

6c. R3C8 = 4 -> R3C9 = 8 (NC)

6d. R3C3 corresponds with R7C7, R3C3 = 3 -> R7C7 = 4

6e. R3C5 corresponds with R7C5, R3C5 = 2 -> R7C5 = 5, R7C13 = [69]

6f. R89C7 = {26/27} (cannot be {67}, NC), 2 locked for C7 and N9

6g. R89C8 = {35/36} (cannot be {56}, NC), 3 locked for C8 and N9

6h. R1C7 = 1 -> no 2 in R1C8 (NC)

6i. R2C8 = 2 (hidden single in N3)

6j. R7C2 = 3 -> no 2,4 in R8C2 (NC)

6k. R2C8 corresponds with R8C2, R2C8 = 2 -> R8C2 = 5

6l. R2C1 corresponds with R8C9, R8C9 = {79} -> R2C1 = {79}

6m. R2C1 = {79} -> R2C2 = 4 (NC)

6n. R2C2 corresponds with R8C8, R2C2 = 4 -> R8C8 = 3

6o. R7C5 = 5 -> R28C5 = [68] (NC), R2C7 = 7

6p. R2C2 = 4 -> R2C3 = 8 (NC)

6q. R8C8 = 3 -> R8C7 = 6 (NC)

and the rest is naked singles, without using corresponding pairs.