Cells adjacent to green marks must total less than 10, blue must total 10, red must total more than 10. However in N5 green means total 8 or 9, red means 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 R1C89, R5C6 and R8C89 (two red marks)
Also delete 8 from R2C79, R3C3, R7C78 and R8C1378 (two green marks)
Also delete 7,8 from R2C8 (three green marks)
R1C2 = {789} (only way to satisfy four red marks)
R5C5 = {789} (only way to satisfy two red and two grey marks)
R8C2 = {123} (only way to satisfy four green marks)
Clean-ups and NCs only as stated.
1. 9 in N5 only in R4C6 + R5C5, R45C6 and R5C56 must both total 11 or 12 (red) -> R5C6 = 3, R4C6 + R5C5 = {89}, locked for N5 and D/
1a. R56C5 must total 11 or 12 (red) = [84/92]
1b. R56C6 must total 8 or 9 (green) = [35/36]
1c. R45C4 = [17] (hidden pair in N5), 1 placed for D\, no 8 in R5C5, no 6 in R6C4 (NC)
1d. R5C5 = 9, placed for D\, R6C5 = 2 (red), R4C6 = 8
1e. R6C5 = 2 -> R6C6 = 5 (yellow), placed for D\, R6C4 = 4, placed for D/, R4C5 = 6
NCs: no 2 in R3C4 + R4C3, no 5,7 in R3C5, no 7,9 in R3C6 + R4C7, no 6,8 in R5C3, no 2,4 in R5C7, no 3 in R6C3, no 6 in R6C7, no 3,5 in R7C4, no 1,3 in R7C5 and no 4,6 in R7C6
2. R2C2 = {78} -> no 7,8 in R13C2 + R2C13 (NC)
2a. No 9 in R2C2 -> no 2 in R13C2 + R2C13 (red)
Clean-ups: no 2,3,8 in R1C1, no 9 in R1C2 (blue), no 7 in R3C3 (green)
2b. R2C3 + R3C23 = {23456} must contain at least one of 4,6 (cannot be [352/532], NC) -> R1C12 = [73] (cannot be {46} which clashes with R2C3 + R3C23), R2C2 = 8, 7,8 placed for D\, no 6,9 in R2C1 (NC)
2c. Naked triple {456} in R2C13 + R3C2, locked for N1 -> R3C3 = 2, placed for D\
3. Naked triple {346} in R7C7 + R8C8 + R9C9, locked for N9
3a. R8C8 + R9C9 = {346} -> no 5 in R8C9 (red)
3b. R8C9 = {789} -> no 8 in R7C9 (NC)
3c. No 2,9 in R9C8, no 6 in R9C9 (blue)
3d. R9C8 = {78} -> no 7,8 in R9C7 (NC)
3e. 6 in N9 only in R7C7 + R8C8 -> no 5,7 in R7C8 + R8C7 (NC)
3f. Naked pair {12} in R7C8 + R8C7, locked for N9, no 1 in R6C8 (NC)
3g. Naked pair {12} in R8C27, locked for R8
Clean-up: no 8,9 in R8C4, no 8 in R8C5 (blue)
3h. R8C9 = 8 (hidden single in R8), R9C89 = [73] (blue), no 9 in R7C9 (NC)
3j. R7C9 = 5, R9C7 = 9, no 6 in R6C9 (NC)
4. R7C1 + R9C3 = [98] (hidden pair in N7) -> R1C3 + R3C1 = [91], no 8 in R6C1 (NC)
4a. R8C6 = 9 (hidden single in N8)
4b. R8C45 = [37] (blue, cannot be [64] which clashes with R8C8), no 2 in R79C4, no 8 in R7C5, no 4 in R8C3 (NC)
4c. R7C5 = 4, R7C7 + R8C8 = [64], R7C4 = 8
4d. R7C23 = [73] (blue), 3 placed for D/
4e. Naked pair {56} in R8C13, locked for N7 -> R9C1 = 2, placed for D/, R89C2 = [14], R8C7 = 2, R7C68 = [21]
5. R1C9 + R2C8 + R3C7 = [657], R13C8 = [83], no 6 in R3C6, no 2 in R4C8 (NC)
5a. R456C9 = [926], no 1 in R5C79 (NC)
The rest is naked singles, without using NC, diagonals or coloured marks.
