Cells adjacent to yellow lines must total less than 8, green total 8 or 9, blue must total 10, red must total 11 or 12, grey total more than 12.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally 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}.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.
Prelims.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green marks in even columns.
Delete 4,9 from cells either side of green mark in C5 (4 because of NC).
Delete 5 from cells either side of blue marks in R5.
Delete 1 from cells either side of red mark in R6
Delete 1,6 from cells either side of red marks in odd rows and columns (6 because of NC).
Delete 1,2,3 from cells either side of grey marks.
Clean-ups, AK, FNC and NC, separately or together, only when stated.
1a. R5C5 = 5, placed for R5 and C5
1b. R5C5 = 5 -> R5C6 = 7 (red), placed for R5, no 8 in R6C6
1c. R5C6 = 7 -> R5C7 = 4 (red), placed for R5 and C7
1d. R5C7 = 4 -> R5C8 = 6 (blue), placed for R5
1e. R5C5 = 5 -> R6C5 = 3 (green), placed for C5
1f. R6C5 = 3 -> R6C4 = 7 (blue)
1g. R6C5 = 3 -> R6C6 = 9 (red)
1h. 1 in C5 only in R78C5 -> no 2 in R78C5
1i. R9C5 = 2 (hidden single in C5), placed for R9, clean-up: no 1 in R8C5
1j. R9C5 = 2 -> R9C4 = 9 (red), placed for R9
1k. R7C5 = 1 (hidden single in C5), placed for R7
1l. R5C5 = 5 -> R5C4 = {12} (yellow)
1m. R5C4 = {12} -> R5C3 = {89} (blue)
1n. R5C1 = {89} -> R5C2 = {12} (blue)
1o. R5C9 = 3 (hidden single in R5), placed for C9, clean-up: no 2,4 in R4C9
1p. R5C9 = 3 -> R4C9 = 1 (yellow), placed for C9
1q. R23C5 = {47/48} (red), 4 locked for C5
1r. R1C5 = 6, placed for R1 and C5, clean-up: no 7 in R2C5
1s. R1C5 = 6 -> R1C6 = 1 (yellow), placed for R1
1t. R1C5 = 6 -> R2C5 = 8 (grey), placed for C5
1u. R3C5 = 4 (hidden single in C5), placed for R3
1v. R3C5 = 4 -> R4C5 = 9 (grey), placed for C5
1w. R4C5 = 9 -> R4C4 = 1(blue)
1x. R4C5 = 9 -> R4C6 = 1 (blue)
Clean-ups:
R1C5 = 6 -> no 5,7 in R1C4, no 5,6,7 in R2C46
R1C6 = 1 -> no 2 in R1C7 + R2C6, no 1,2 in R2C7
R2C5 = 8 -> no 8,9 in R1C4, no 9 in R2C46 no 7,8,9 in R3C46
R3C5 = 4 -> no 3,4 in R2C46, no 3,5 in R3C46
R4C4 = 1 -> no 1,2 in R3C3, no 2 in R35C4 + R4C3
R4C6 = 1 -> no 2 in R3C6 + R4C7, no 1,2 in R3C7
R4C9 = 1 -> no 1,2 in R3C8, no 2 in R3C9 + R4C8
R5C6 = 7 -> no 6,7,8 in R46C7
R5C7 = 4 -> no 3,5 in R46C7, no 3,4,5 in R46C8
R5C8 = 6 -> no 7 in R46C8, no 5,6,7 in R6C9
R5C9 = 3 -> no 2 in R6C8, no 2,4 in R6C9
R6C4 = 7 -> no 8 in R5C3, no 6,8 in R6C3 + R7C4, no 6,7,8 in R7C3
R6C5 = 3 -> no 2,3,4 in R7C46
R6C6 = 9 -> no 8 in R7C6, no 8,9 in R7C7
R7C5 = 1 -> no 1,2 in R8C46
R8C5 = 7 -> no 7 in R7C4, no 6,7 in R7C6, no 6,8 in R8C46, no 6,7,8 in R9C6
R9C4 = 9 -> no 8,9 in R8C3, no 8 in R9C3
R9C5 = 2 -> no 3 in R8C46, no 1,3 in R9C6
R1C4 = {234} -> no 3 in R12C3
R6C9 = {89} -> no 8,9 in R7C89
R9C6 = {45} -> no 5 in R89C7
2a. R5C34 = [91], placed for R5, 9 also placed for C3
2b. R5C12 = [82], 8 placed for C1, clean-up: no 7,9 in R4C1
2c. R5C1 = 8 -> R4C1 = {56}
Clean-ups:
R5C1 = 8 -> no 7,8,9 in R46C2, no 7,9 in R6C1
R5C2 = 2 -> no 1,3 in R46C2 + R4C3, no 1,2,3 in R6C13
R5C3 = 9 -> no 8 in R4C3
R4C1 = {56} -> no 5,6 in R3C12
R6C1 = {456} -> no 5 in R7C12
3a. Naked pair {16} in R3C46, locked for R3
4a. Naked pair {59} in R7C46, locked for R7
4b. R7C2 = 8 (hidden single in R7)
Clean-ups:
R7C2 = 8 -> no 7 in R68C3 + R7C1, no 7,9 in R8C12
R7C3 = {234} -> no 3 in R8C23
5a. 2 in R3 only in R3C12 -> no 1,2,3 in R2C1, no 1,3 in R2C2, no 3 in R3C12
5b. 1 in C1 only in R89C1 -> no 2 in R8C12, no 1 in R9C2
5c. 9 in C1 only in R123C1 -> 8 in R2C2
5d. 7 in R7 only in R7C789 -> no 6,8 in R68C8, no 6 in R7C8
5e. 8 in C3 only in R123C3 -> no 7,9 in R2C2, no 7 in R2C3
5f. 2 in C7 only in R678C7 -> no 3 in R7C7, no 2,3 in R7C8
5g. 3 in R7 only in R7C13 -> no 2,4 in R6C2, no 4 in R8C2
Clean-ups:
R6C2 = {56} -> no 6 in R7C1
R6C3 = {45} -> no 4 in R7C3, no 5 in R7C4
R7C3 = {23} -> no 2 in R8C3
R7C1 = {234} -> no 3 in R8C1
6. R7C4 = 9, placed for R7 -> R7C6 = 5
Clean-up:
R7C6 = 5 -> no 6 in R78C7, no 4 in R8C6
7a. No 1,3 in R2C9 -> no 7,9 in R2C8 (blue)
7b. R8C34 = [19/55/64] (blue), R8C3 = {156}, R8C4 = {459}
[This was as far as I managed without using a forcing chain. HATMAN told me how he broke the deadlock.
It is solvable using a complex elimination of R3C4 which is 1/6.
If it is 6 R4C3 is 4 and R3C3 is 8, this means R3C2 is 2 so no value for R2C3.
Hence R3C4 is 1 and R3C6 is 6.]
[I searched for, and eventually found, a forcing chain which gives the same result in a slightly longer way.]
8. Consider placements for R4C3 = {4567} with alternatives for R3C3 = {78} when R4C3 = 4
R4C3 = 4 with R3C3 = 7 => no 6 in R3C4
or R4C4 with R3C3 = 8, no 7,8,9 in R3C2 => R3C2 = 2, no 1,2 in R2C3 => R2C3 = {56} => no 6 in R3C3
or R4C3 = {567} => no 6 in R3C4
-> R3C4 = 1, placed for R3, R3C6 = 6
Clean-ups:
R3C4 = 1 -> no 1,2 in R2C3, no 2 in R2C4
R3C6 = 6 -> no 5,6,7 in R2C7, no 5,7 in R3C7
[Cracked. Now it’s a lot easier.]
9a. R1C7 = 5 (hidden single in C7), placed for R1
9b. R9C7 = 6 (hidden single in C7), placed for R9, no 7 in R8C7, no 5 in R9C6
9c. R7C7 = 7 (hidden single in C7), placed for R7
9d. R7C8 = 4, placed for R7
9e. R7C9 = 6 (hidden single in R7), placed for C9
9f. R9C6 = 4, placed for R9
Clean-ups:
R1C7 = 5 -> no 4 in R1C8, no 4,5,6 in R2C8
R7C7 = 7 -> no 7 in R8C68, no 8 in R8C7
R7C8 = 4 -> no 3 in R8C7, no 3,5 in R8C8, no 4,5 in R8C9
R7C9 = 6 -> no 7 in R8C9
R9C7 = 6 -> no 5 in R8C6, no 5,7 in R9C8
9a. R23C7 = {38} (hidden pair in C7) -> no 3,7,8,9 in R3C8
9b. R3C8 = 5, placed for R3
Clean-up:
R3C8 = 5 -> no 4,5 in R2C9, no 6 in R4C8
10a. R1C9 = 4 (hidden single in C9), placed for R1
10b. R9C9 = 5 (hidden single in C9), placed for R9
10c. Naked pair {23} in R7C13 -> no 1 in R8C2
Clean-ups:
R1C9 = 4 -> no 3 in R12C8 -> no 7 in R2C9 (blue)
R9C9 = 5 -> no 4 in R8C8
R1C4 = {23} -> no 2 in R1C3
R1C3 = {78} -> no 7,8 in R1C2, no 8 in R2C3
11a. R7C3 = 2 (hidden single in C3), placed for R7, no 1 in R8C3
11b. R7C1 = 3, placed for C1
11c. R9C3 = 1 (hidden single in C3), placed for R9
11d. R9C1 = 7, placed for R9 and C1, no 8 in R9C2
11e. R9C28 = [38], no 8,9 in R8C9
11f. R8C9 = 2, placed for C9
11g. R3C9 = 7 (hidden single in C9), placed for R3, no 8 in R2C9
11h. R2C9 = 9, placed for C9
11i. R2C9 = 9 -> R2C8 = 1 (blue)
Clean-ups:
R2C8 = 1 -> no 2 in R1C8
R2C9 = 9 -> no 8,9 in R1C8
R3C9 = 7 -> no 8 in R4C8
R6C9 = 8 -> no 9 in R6C8
R6C8 = 1 -> no 2 in R6C7
R7C1 = 3 -> no 4 in R68C1
R8C9 = 2 -> no 1 in R8C8
R9C1 = 7 -> no 6 in R8C1, no 6,8 in R8C2
R8C2 = 5 -> no 6 in R8C3
R9C8 = 8 -> no 9 in R8C78
R8C8 = 2 -> no 1 in R8C7
12a. R1C8 = 7, placed for R1
12b. R1C3 = 8, placed for C3, no 9 in R1C2
12c. R3C3 = 3, placed for R3
12d. R3C7 = 8, placed for R3 and C7, no 9 in R4C7
12e. R1C1 = 9 (hidden single in R1), placed for C1
12f. R3C1 = 2, placed for R3
12g. R8C1 = 1 (hidden single in C1)
12h. R6C7 = 9 (hidden single in C7)
Clean-ups:
R1C3 = 8 -> no 8 in R2C4
R2C4 = 1 -> no 2 in R1C4
R3C1 = 2 -> no 2 in R24C2
R3C3 = 3 -> no 4 in R24C23
R3C7 = 8 -> no 8 in R2C6, no 9 in R4C8
13a. R1C4 = 3, placed for R1
13b. R8C3 = 5, placed for C3
13c. R8C3 = 5 -> R8C4 = 5 (blue)
13d. R2C3 = 6, placed for C3
Clean-ups:
R2C3 = 6 -> no 5 in R2C2
R4C3 = 7 -> no 6 in R4C2
R6C3 = 4 -> no 5 in R6C2
R6C2 = 6 -> no 5 in R6C1
14. R246C1 = [456]