Cages are Renban groups, containing consecutive non-repeating numbers in any order.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally adjacent cells.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.
Prelims
The 6-cell cages containing 1 must be {123456} and the 7-cell cages containing 1 must be {1234567}
Cage at R3C2 = {123456}
Cage at R3C4 = {1234567}
Cage at R4C7 = {1234567}
Cage at R5C5 = {123456}
Clean-ups, AK, FNC and NC, separately or together, only when stated.
1a. R3C2 = 1, placed for R3 and cage at R3C2
1b. R4C7 = 1, placed for C7 and cage at R4C7
1c. R5C3 = 1, placed for R5, C3 and cage at R3C4
1d. R7C4 = 1, placed for R7 and cage at R5C5
1e. R6C4 = 9
Clean-ups:
R2C8 = 1 -> no 1,2 in R1C9, no 2 in R1C78 + R2C79 + R3C789
R3C2 = 1 -> no 1,2 in R24C1, no 2 in R2C23 + R3C13 + R4C23
R4C7 = 1 -> no 2 in R3C6 + R4C68 + R5C678
R5C3 = 1 -> no 1,2 in R6C2, no 2 in R4C4 + R5C24 + R6C3
R7C4 = 1 -> no 1,2 in R8C5, no 2 in R6C5 + R7C35 + R8C34
R8C2 = 1 -> no 1,2 in R9C1, no 2 in R7C12 + R8C1 + R9C23
2a. R1C1 = 1 (hidden single in C1), placed for R1
2b. R1C3 = 2 (hidden single in C3), placed for R1
2c. R3C4 = 2 (hidden single in cage at R3C4), placed for R3
2d. R6C1 = 2 (hidden single in cage at R3C2), placed for C1
Clean-ups:
R1C1 = 1 -> no 1 in R2C2
R1C3 = 2 -> no 1,2,3 in R2C4, no 3 in R1C24 + R2C23
R3C4 = 2 -> no 1,2,3 in R24C5, no 3 in R3C35 + R4C34
R6C1 = 2 -> no 3 in R5C12 + R6C2 + R7C12
R5C2 = {456} -> no 5 in R4C13 + R5C1 + R6C3
R7C1 = {456} -> no 5 in R67C2 + R8C1
3a. R9C5 = 1 (hidden single in C5), placed for R9
3b. R5C5 = 2 (hidden single in C5), placed for R5 and cage at R5C5
Clean-ups:
R5C5 = 2 -> no 1,3 in R4C6, no 1,2,3 in R6C6, no 3 in R5C46 + R6C5
R9C5 = 1 -> no 2 in R89C6
R6C5 = {456} -> no 5 in R5C46 + R7C56
4. 3 in cage at R3C4 only in R678C3, locked for C3
Clean-up:
3 in R678C3 -> no 4 in R7C23
5. Cage at R1C9 doesn’t contain 2 -> no 1 in R2C9 + R4C8
6. 3 in cage at R3C2 only in R4C2 + R8C1 -> no 3 in R3C1 (AK)
7. Hidden killer pair 8,9 in R7C2 and R7C89 for R7, R7C89 cannot be {89} (NC) -> R7C2 = {89}, R7C89 contain one of 8,9
Clean-up:
R7C89 contain one of 8,9 -> no 8,9 in R68C9
[4-cell cages cannot have their lowest or highest numbers at the ends.]
8a. Cage at R1C4 = {4567/5678/6789}
8b. {4567} can only have 4 in the middle cells -> no 4 in R1C4 + R4C3
8c. {6789} can only have 9 in the middle cells -> no 9 in R1C4 + R4C3
Clean-up:
R4C3 = {678} -> no 7 in R3C3 + R5C4
R5C4 = {46} -> no 5 in R4C45 + R6C5
9a. Naked pair {46} in R5C4 + R6C5 (because of AK), CPE no 4,6 in R5C6
9b. 5 in cage at R5C5 only in R89C4 -> no 4 in R89C4, no 4,6 in R8C35, no 4,5,6 in R9C3
9c. 4 in cage at R5C5 only in R67C5 -> no 3 in R7C5
9d. Naked pair {46} in R67C5, locked for C5, 6 locked for cage at R5C5
9e. R7C5 = {46} -> no 5 in R8C4
9f. R89C4 = [35], 5 locked for R9, no 4 in R7C5, no 5 in R8C3
9g. R7C3 = 5 (hidden single in cage at R3C4), placed for R7 and C3, no 4,6 in R6C3
9h. R7C5 = 6, placed for R7, R6C5 = 4, R7C1 = 4, placed for R7, C1 and cage at R3C2, no 4 in R5C4, no 3,7 in R7C6, no 3 in R8C1
9i. R8C1 = 6, placed for C1 and cage at R3C2 -> R5C2 = 5, placed for R5, R4C2 = 3, R5C4 = 6, placed for R5 and cage at R3C4, no 7 in R4C4 + R6C3
9j. R4C4 = 4, R68C3 = [37], 7 placed for C3, no 8 in R7C2 + R9C3
9k. R7C2 = 9, placed for R7
9l. R9C3 = 9, placed for R9 and C3
9m. R7C6 = 2, placed for R7 and cage at R4C7, no 3 in R7C7
9n. R7C7 = 7, placed for R7, C7 and cage at R4C7, no 8 in R7C8
9o. R7C89 = [38], 8 placed for C9 and cage at R6C9
Clean-ups:
R4C4 = 4 -> no 4 in R3C3, no 5 in R3C5
R5C4 = 6 -> no 6 in R4C3, no 7 in R4C5
R7C2 = 9 -> no 8 in R6C2
R7C3 = 5 -> no 4,6 in R6C2
R7C5 = 6 -> no 5,6,7 in R6C6, no 5,7 in R8C5, no 5,6 in R8C6
R7C6 = 2 -> no 3 in R6C7 + R8C56, no 2,3 in R8C7
R7C7 = 7 -> no 8 in R6C6, no 6 in R6C7, no 6,7,8 in R6C8, no 6,8 in R8C7, no 6,7 in R8C8
R7C8 = 3 -> no 4 in R68C7, no 2,4 in R68C8, no 2,3,4 in R68C9
R7C9 = 8 -> no 9 in R68C8, no 7 in R68C9
R8C1 = 6 -> no 7 in R9C1
R8C3 = 7 -> no 6,7,8 in R9C2
R4C5 = {89} -> no 8,9 in R3C56 + R5C6
R6C2 = {79} -> no 8 in R5C1
[A few clean-ups have been deliberately, or accidentally, omitted in this and later steps.]
10a. R6C7 = 5, placed for C7, R8C6 = 4, R5C7 = 3, placed for R5 and C7, R9C6 = 6, placed for R9
10b. R5C6 = 7, placed for R5 and cage at R1C7, no 8 in R4C5
10c. R5C1 = 9, placed for R5, C1 and cage at R1C2
10d. R5C89 = [84], placed for cage at R1C9, 4 placed for C9
10e. R4C5 = 9, placed for C5
Clean-ups:
R5C1 = 9 -> no 8 in R4C1, no 9 in R6C2
R5C6 = 7 -> no 6,8 in R4C6
R5C8 = 8 -> no 7,9 in R4C89
R5C9 = 4 -> no 3,5 in R4C89 + R6C8, no 5 in R6C9
R6C7 = 5 -> no 4 in R6C6
R9C2 = {34} -> no 3 in R9C1
11a. R234C3 = [468], 6 placed for R3, 6,8 placed for cage at R1C4, no 5,7 in R2C4
11b. Cage at R1C4 can only be {6789} -> R12C4 = [79], 7 placed for R1
11c. R1238C5 = [3578], 3 placed for R1, 7 placed for R3, no 4,5 in R3C6
11d. R3C6 = 3, placed for R3, no 4 in R2C7
11e. R35C6 = [37] -> cage at R1C7 = {34567} -> R4C6 = 5, R12C7 = [46], 4 placed for R1 and C7
11f. R9C1 = 8, placed for R9 and C1
11g. R3C1 = 5, placed for R3, C1 and cage at R1C2
11h. R3C9 = 9, placed for R3 and C9
11i. R3C78 = [84]
11j. R9C7 = 2, placed for R9
Clean-ups:
R1C5 = 3 -> no 2,3,4 in R2C6
R2C7 = 6 -> no 5,6 in R1C68, no 5,7 in R2C6
R3C3 = 6 -> no 6,7 in R2C2
R3C5 = 7 -> no 6,8 in R2C6
R3C7 = 8 -> no 9 in R2C6
R3C8 = 4 -> no 3,5 in R2C9
R9C7 = 2 -> no 1,3 in R8C8, no 3 in R9C8
12a. R4C8 = 6, R12C9 = [57], placed for C9, no 8 in R1C8
12b. R1C268 = [689], no 7 in R2C1
12c. R24C1 = [37], no 4 in R2C2
12d. R9C289 = [473], no 6 in R8C9
12e. R468C9 = [261]