Cells adjacent to yellow lines must total less than 8, green 8 or 9, red 11 or 12, black more than 12.
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 yellow mark must contain one of 1,2,3 in even rows/columns or just one of 1,2 in odd rows/columns.
No repeats in Reverse Snakes and Old Lace.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.
Prelims
Delete 1 from cells either side of red marks.
Delete 1,2,3 from cells either side of black marks.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green marks.
Delete 4 from cells either side of green marks in R3 and C5 (NC)
Delete 6 from cells either side of red marks in C3 and C5 (NC)
Clean-ups, FNC and NC, only when stated.
1. R5C5 = 5, placed for R5, C5 and Old Lace
1a. R5C5 = 5 -> R4C5 = 3 (green), placed for C5
1b. R5C5 = 5 -> R6C5 = 7 (red), placed for C5
1c. R4C5 = 3 -> R3C5 = 1 (yellow + NC), placed for R3, C5, Old Lace and upper Reverse Snake
1d. R6C5 = 7 -> R7C5 = 9 (black + NC), placed for R7, C5, Old Lace and lower Reverse Snake
1e. R5C5 = 5 -> R5C6 = {12} (yellow)
1f. R5C5 = 5 -> R5C4 = {89} (black)
Clean-ups:
R3C5 = 1 -> no 2 in R2C5 + R3C4 (NC), no 2 in R24C46 (FNC)
R4C5 = 3 -> no 4 in R4C46 (NC), no 4 in R3C6, no 2 in R5C6 (FNC)
R5C5 = 5 -> no 6 in R4C46, no 4,6 in R6C46 (FNC)
R6C5 = 7 -> no 8 in R6C4 (NC), no 8 in R5C4, no 6 in R7C4,no 6,8 in R7C6 (FNC)
R7C5 = 9 -> no 8 in R8C5 (NC), no 8 in R8C46 (FNC)
R6C6 = {23} -> no 2,3 in R5C7 (FNC + Old Lace)
2a. R5C4 = 9, placed for R5
2b. R5C6 = 1, placed for R5
2c. R5C6 = 1 -> R6C6 = 3 (NC), placed for Old Lace
2d. Naked pair {78} in R4C46, locked for Old Lace
2e. R6C4 = 2, placed for Old Lace
2f. Naked pair {46} in R5C37, locked for R5
2g. R5C23 = [24] (yellow + NC), placed for R5, 4 placed for C3
2h. R5C7= 6, placed for C7
2i. R5C7 = 6 -> R4C6 = 8 (FNC) -> R4C4 = 7 (Old Lace)
2j. R5C2 = 2 -> R6C2 = 9 (red)
Clean-ups:
R4C4 = 7 -> no 6,8 in R3C4 + R4C3 (NC), no 6,8 in R3C3 (FNC)
R4C6 = 8 -> no 7,9 in R3C6 + R4C7 (NC), no 7,9 in R3C7 (FNC)
R5C2 = 2 -> no 3 in R4C2 + R5C1 (NC), no 3 in R4C1 + R6C3, no 1,3 in R4C3 + R6C1 (FNC)
R5C3 = 4 -> no 5 in R46C3 (NC), no 5 in R4C2 (FNC)
R5C6 = 1 -> no 2 in R46C7 (FNC)
R5C7 = 6 -> no 5 in R4C7, no 7 in R5C8, no 5,7 in R6C7 (NC), no 5,7 in R46C8 (FNC)
R6C2 = 9 -> no 8 in R6C3 + R7C2 (NC), no 8 in R5C1 (FNC)
R6C4 = 2 -> no 1,3 in R7C4 (NC), no 3 in R7C3 (FNC)
R6C6 = 3 -> no 4 in R6C7, no 2,4 in R7C6 (NC), no 2,4 in R7C7 (FNC)
3. R5C1 = 7, placed for R5 and C1
Clean-ups:
R5C1 = 7 -> no 6,8 in R4C1, no 6 in R6C1 (NC), no 6,8 in R4C2 (FNC)
Naked pair {38} in R5C89 -> no 2,4,9 in R4C8, no 2,4,7,9 in R4C9, no 2,4 in R6C8, no 2,4,7 in R6C9 (NC+FNC)
4. R3C67 = [58/68/85] (black), no 4, 8 locked for R3
4a. R3C89 = {49} (hidden pair in R3)
Clean-up:
Naked pair {49} in R3C89 -> no 3,5,8 in R2C89 + R4C9, no 3,8 in R4C8 (NC+FNC)
4b. R4C89 = [66] (red), 6 placed for C9
Clean-up:
R4C8 = 6 -> no 5 in R3C7 (FNC)
4c. R3C7 = 8, placed for R3 and C7
Clean-up:
R3C7 = 8 -> no 7,9 in R2C7, no 9 in R3C8 (NC), no 7,9 in R2C68 (FNC)
4d. R3C89 = [49], 9 placed for C9 and upper Reverse Snake
Clean-up:
R3C8 = 4 -> no 3,5 in R2C79, no 3,5 in R2C8, no 3 in R4C7 (FNC)
R3C9 = 9 -> no 8 in R2C8 (FNC)
5a. R67C3 = [75/92] (red), no 2 in R6C3
5b. R7C34 = [24/25/52] (yellow), 2 locked for R7
Clean-ups:
2 in R7 only in R7C34 -> no 1,3 in R8C34 (NC+FNC)
8 in R7 only in R7C89 -> no 7 in R8C89 (NC+FNC)
9 in C7 only in R68C7 -> no 8 in R7C8 (FNC)
6. R7C9 = 8 (hidden single in R7), placed for C9 and lower Reverse Snake
6a. R5C89 = [83], 3 placed for C9
6b. R6C89 = [35/81] (green), no 1,6 in R6C8
Clean-ups:
R5C8 = 8 -> no 9 in R6C7 (FNC)
R7C9 = 8 -> no 7 in R7C8 (NC)
6c. R8C7 = 9 (hidden single in C7)
Clean-up:
R8C7 = 9 -> no 8 in R9C68 (FNC)
7. R4C12 = {29}/[47/57] (red), no 4 in R4C2
7a. Consider combinations for R4C12
R4C12 = {29}/[47] => no 3 in R3C12 (NC or FNC) => 3 in R3 only in R3C34 = {35} (green), 5 locked for R3
or R4C12 = [57] => no 6 in R3C12 (NC+FNC) => R3C6 = 6 (hidden single in R3)
-> R3C6 = 6, placed for R3
Clean-up:
R3C6 = 6 -> no 5 in R2C6 (NC)
7b. R3C12 = [27]/{35} (green), no 2 in R3C2
7c. R3C34 = [27]/{35} (green), no 7 in R3C3
7d. R3C1234 = [27]{35}/[3527] (cannot be [5327], NC), no 5 in R3C1, no 3 in R3C2
Clean-ups:
R3C1 = {23} -> no 2,3 in R2C1, no 2 in R4C1 (NC), no 2,3 in R2C2 (FNC + upper Reverse Snake)
R3C2 = {57} -> no 6 in R2C1 (FNC), no 6 in R2C2 (NC)
R3C34 = [27]/{35} -> no 2 in R24C3 (C3 + NC+FNC)
2 in R3 only in R3C13 -> no 2 in R1C3 (C3 + upper Reverse Snake)
7 in R3 only in R3C24 -> no 6,8 in R2C3 (FNC)
7e. Naked pair {79} in R46C3, locked for C3
7f. R4C12 = [47/57/92], no 9 in R4C2
8. R67C1 = [24/25/41/51] (yellow + NC), no 3,6 in R7C1
[Getting harder, it took me a while to spot this.]
9. R3C34 = {35} (green) (cannot be [27] because R37C3 = [25] clashes with R2C3, NC), locked for R3
9a. R3C1 = 2, placed for C1 and upper Reverse Snake, R3C2 = 7
9b. R6C1 = {45} -> R7C1 = 1 (yellow), placed for R7, C1 and lower Reverse Snake
9c. R2C3 = 1 (hidden single in C3)
Clean-ups:
R2C3 = 1 -> no 2 in R1C24 (FNC)
R3C2 = 7 -> no 8 in R2C1 (FNC), no 8 in R2C2 (NC)
R7C1 = 1 -> no 2 in R8C2 (FNC)
R2C8 = {46} -> no 5 in R1C79 (FNC), no 5 in R1C8 (NC)
R3C3 = {35} -> no 4 in R2C24 (FNC)
R3C4 = {35} -> no 4 in R2C5 (FNC)
R2C5 = {68} -> no 7 in R1C46 (FNC), no 7 in R2C4 (NC)
10. Consider positions for 4 in R7
4 in one of R7C24 => no 5 in R78C3 (NC+FNC)
or R7C8 = 4 => R7C2 = 6 (hidden single in R7), no 5 in R78C3 (NC+FNC)
-> R7C3 = 2, placed for R7 and C3
and no 5 in R8C3
10a. R7C3 = 2 -> R6C3 = 9 (red), placed for C3 -> R4C3 = 7
Clean-ups:
R7C3 = 2 -> no 3 in R7C2 (NC), no 3 in R8C2 (FNC)
R8C3 = {68} -> no 7 in R7C2 (FNC), no 7 in R8C24 (NC)
10b. 7 in lower Reverse Snake only in R8C6 + R9C7 -> no 6 in R8C6 (FNC), no 6 in R9C6 (NC)
10c. 5 in C7 only in R79C7 -> no 4 in R8C6, no 4,6 in R8C8 (FNC)
10d. R6C89 = [35/81] (green) -> no 4 in R7C8 (NC+FNC)
10e. Consider placement for 5 in C7
R7C7 = 5 => no 5,6 in R7C8 (NC) => R7C8 = 3 => no 2 in R8C8 (NC), R8C8 = {35} => no 4 in R9C7 (FNC)
or R9C7 = 5
-> no 4 in R9C7
10f. 4 in lower Reverse Snake only in R8C24 -> no 3,5 in R9C3 (FNC)
10g. R9C3 = 6, placed for R9, C3 and lower Reverse Snake -> R8C3 = 8, placed for C3
Clean-ups:
R9C3 = 6 -> no 5 in R8C24 (FNC), no 5,7 in R9C24 (NC)
10h. R8C24 = [42], 2 placed for lower Reverse Snake
10i. R2C7 = 2 (hidden single in C7)
Clean-ups:
R2C7 = 2 -> no 1,3 in R1C68 (FNC), no 3 in R1C7 + R2C6 (NC)
R8C2 = 4 -> no 5 in R7C2, no 3,5 in R8C1, no 3 in R9C2 (NC), no 3,5 in R9C1 (FNC)
R8C3 = 8 -> no 9 in R9C24 (FNC)
R8C4 = 2 -> no 1,3 in R9C4 (NC)
R8C8 = {35} -> no 4 in R8C9 + R9C8 (NC), no 4 in R9C9 (FNC)
11a. R1C1 = 3 (hidden single in C1), placed for R1
11b. R1C3 = 5, placed for R1, C3 and upper Reverse Snake
11c. R3C34 = [35]
11d. R2C2 = 7, R1C7 = 4, placed for R1 and C7, R2C468 = [386], all upper Reverse Snake
11e. R46C7 = [13], 3 placed for C7
11f. R89C1 = [68] (hidden pair in C1), 8 placed for R9
11g. Naked pair {24} in R9C45, locked for R9 -> R9C2 = 1, placed for R9
11h. Naked pair {57} in R9C79, locked for R9
Clean-ups:
R1C1 = 3 -> no 4 in R2C1 (NC)
R1C3 = 5 -> no 6 in R1C24 (NC)
R2C2 = 7 -> no 8 in R1C2 (NC)
R2C4 = 3 -> no 2 in R1C5 (FNC)
R2C8 = 6 -> no 7 in R1C8 + R2C9 (NC), no 7 in R1C9 (FNC)
R3C3 = 3 -> no 2 in R4C2 (FNC)
R3C4 = 5 -> no 6 in R2C5 (FNC)
R9C5 = {24} -> no 3 in R9C6 (NC)
11i. R12C5 = [68], 6 placed for R1
11j. R4C2 = 7 -> R4C1 = {45} (red)
Clean-up:
R2C5 = 8 -> no 9 in R1C46 (FNC)
11k. R9C6 = 9, placed for R9 -> R9C8 = 3
11l. R1C28 = [79] (hidden pair in R1)
Clean-up:
R9C8 = 3 -> no 2 in R8C9 (FNC)
11m. Naked pair {15} in R68C9, locked for C9 -> R9C9 = 7, placed for R9
11n. R9C7 = 5, placed for C7 and lower Reverse Snake -> R7C7 = 7, placed for R7, R8C68 = [73]
Clean-ups:
R7C7 = 7 -> no 6 in R7C8 (NC), no 8 in R6C8 (FNC)
R8C6 = 7 -> no 6 in R8C5 (NC)
R8C5 = {24} -> no 3 in R7C6 (FNC)
R7C6 = 5 -> no 4 in R8C5 (FNC)
11o. R7C2468 = [6453]
Clean-up:
R7C2 = 6 -> no 5 in R6C1 (FNC)
11p. R6C8 = 3 -> R6C9 = 5 (green)
and the rest is singles in R1, R9, C1, C5 and C9