Cells adjacent to green marks must total 8 or 9, blue must total 10, red must total 11 or 12, yellow total less than 8, grey total more than 12.
Also NC so horizontally/vertically adjacent cells cannot be {12}, {23}, … {78}, {89}, therefore at least one of the cells adjacent to each green or yellow mark must contain one of 1,2,3 as green cannot be {45}; similarly at least one of the cells adjacent to each red or grey mark must contain one of 7,8,9 as red cannot be {56}.
Prelims.
Delete 9 from cells either side of green marks.
Delete 7,8,9 from cells either side of yellow marks.
Delete 5 from cells either side of blue marks.
Delete 1 from cells either side of red marks.
Delete 1,2,3 from cells either side of grey marks.
Also delete 2 from R7C89 + R8C8 (two red marks)
Also delete 6 from R5C9 + R7C7 (two yellow marks)
Delete 4 from cells next to green marks (NC)
Delete 6 from cells next to red marks (NC)
Clean-ups and NCs only as stated.
1a. R5C8 = {56} -> R4C8 = {23} (green) -> R4C7 = {78} (blue)
1b. R5C8 = {56} -> R5C7 = {23} (green)
1c. R45C7 = [72] (green), R4C8 = 3, R5C8 = 6 (green)
1d. R45C9 = [91] (blue)
1e. R6C8 = 8 (hidden single in N6) -> R6C7 = 4 (red), R6C9 = 5
2a. R8C8 = 7, placed for D\, R9C8 = 2 (green), R8C9 = 3 (blue), R9C9 = 6 (green), placed for D\, R7C9 = 8 (red)
2b. Naked pair {59} in R89C7, locked for C7 and N9 -> R7C7 = 1, placed for D\, R7C8 = 4
2c. R3C8 = 5 (hidden single in C8)
Clean-ups: no 6,8 in R3C7, no 4 in R3C9, no 6,8 in R4C6, no 3 in R5C6, no 3 in R6C6, no 2 in R7C6
2d. R3C7 = 3, placed for D/
Clean-ups: no 7 in R12C6, no 2,4 in R3C6 (NC)
2e. R12C7 = {68}, R12C8 = {19} -> R12C78 = [6981/8169] (NC) -> no 9 in R12C6
3a. R1C56 = {28/46}/[73] (blue, cannot be [91] which clashes with R1C8), no 1,9, no 3 in R1C5
3b. R2C12 = {28}/[64/73] (blue, cannot be [19] which clashes with R1C8), no 1,9, no 3,4 in R2C1
3c. R6C23 = {19/37} (blue), no 2,6
3d. R9C45 = {19/37} (blue), no 4,8
3e. R78C6 = [64/91] (blue)
3f. R89C2 = {19}[28/64] (blue), no 4,8 in R8C2, no 3,7 in R9C2
4. 3 on D\ only in R1C1 + R2C2, locked for N1
Clean-ups: no 2,4 in R1C2, no 2 in R2C1 (NC), no 8 in R2C2 (blue)
R2C1 = {678} -> no 7 in R3C1 (NC)
5. 8 on D/ only in R5C6 + R9C1, CPE no 8 in R5C1, no 8 in R1C1 using D\
5a. R56C1 = {37}[46/91], no 2,9 in R6C1
5b. 2 in R6 only in R6C456, locked for N5
5c. 2 in R6 only in R6C456 -> no 3 in R6C5 (NC)
5d. R5C4 = 3 (hidden single in N5)
Clean-up: no 7 in R23C4, no 7 in R9C5 (blue)
5e. 3 in R6 only in R6C123 -> R56C1 = [73] or R6C23 = {37}, 7 locked for N4
5f. 2 in R4 only in R4C123 -> no 1 in R4C2 (NC)
6. Hidden killer pair 5,6 in R4C123 and R4C456 for R4, R4C456 cannot contain both of 5,6 (NC because 6 in R4C456 only in R4C5) -> R4C123 must contain at least one of 5,6
6a. R5C23 must contain one of 4,5 (cannot be {45} or {89}, NC)
6b. R56C1 = [73/91] (cannot be [46] which clashes with R4C123 + R5C23, killer ALS block)
6c. Naked quad {1379} in R5C1 + R6C123, 1 locked for R6 and N4
6d. R5C1 = {79}, no 8 in R4C1 + R5C2 (NC)
6e. R5C23 = [48/58] (cannot be {45}, NC) -> R5C3 = 8
Clean-ups: no 7,9 in R6C3 (NC), no 1,3 in R6C2 (blue)
6f. R4C4 = 8 (hidden single on D\)
6g. R9C1 = 8 (hidden single on D/), no 9 in R8C1 + R9C2 (NC)
6h. R89C1 = [64/91] (blue), no 1,2 in R8C2
6i. R2C12 = [64/73] (blue), no 2 in R2C2
Clean-ups: no 4 in R2C3 + R3C2, no 6 in R3C1, no 2 in R6C4 + R7C13 (NC)
7. R1C9 = 2 (hidden single on D/) -> R23C9 = [47], R2C2 = 3 -> R2C1 = 7 (blue), R56C1 = [91] (blue), R6C23 = [73], R7C1 = 3 (hidden single in C1)
Clean-ups: no 5 in R1C2, no 1 in R1C8, no 2 in R2C3 + R3C2, no 4,5 in R4C2, no 4 in R5C5, no 2,6 in R7C2, no 2,4 in R8C1 (NC)
7a. R5C5 = 5, placed for both diagonals, R5C26 = [47]
7b. R1C1 = 4, R3C1 = 2, R3C3 = 9, placed for D\, no 8 in R3C2 (NC)
7c. R89C2 = [91] (blue), 9 placed for D/, R2C8 = 1, placed for D/
7d. R6C4 = 6 -> R23C4 = [91] (blue, only remaining permutation)
The rest is naked singles, without using NC, diagonals or coloured marks.
