SudokuSolver Forum

Prelims

a) 6(3) cage at R1C1 = {123}
b) 21(3) cage at R1C2 = {489/579/678}, no 1,2,3
c) 10(3) cage at R1C6 = {127/126/145/235}, no 8,9
d) 9(3) cage at R3C2 = {126/135/234}, no 7,8,9
e) 22(3) cage at R3C3 = {589/679}
e) 11(3) cage at R3C6 = {128/137/146/236/245}, no 9
f) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
g) 19(3) cage at R7C1 = {289/379/469/478/568}, no 1
h) 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
i) 8(3) cage at R8C2 = {125/134}
j) 23(3) cage at R9C6 = {689}
k) 27(4) cage at R1C9 = {3789/4689/5679}, no 1,2
l) 29(4) cage at R4C1 = {5789}

1a. Naked triple {123} in 6(3) cage at R1C1, locked for C1 and N1
1b. Naked triple {689} in 23(3) cage at R9C6, locked for R9
1c. Naked quad {5789} in 29(4) cage at R4C1, locked for N4
1d. 22(3) cage at R3C3 = {589/679}, 9 locked for R3
1e. 27(4) cage at R1C9 = {3789/4689/5679}, 9 locked for N3
1f. 45 rule on C1 1 outie R5C2 = 9
1g. 19(3) cage at R7C1 = {469} (hidden triple in C1) -> R9C1 = 4, R78C1 = {69}
1h. 8(3) cage at R8C2 = {125} (only remaining combination), locked for N7
1i. 8 in N7 only in R7C23, locked for R7
1j. 45 rule on R12 2 outies R3C19 = 10 = [28/37]
1k. Killer pair 7,8 in 22(3) cage at R3C3 = {589/679} and R3C9, locked for R3
1l. 45 rule on R89 2 outies R7C19 = 14 = [95] -> R8C1 = 6
1m. 9(3) cage at R3C2 = {126/135/234}
1n. R3C2 = {456} -> no 4,6 in R4C23
1o. 13(3) cage at R9C3 = {157} (only remaining combination) -> R9C3 = 7, R9C45 = {15}, locked for R9 and N8 -> R9C2 = 8, R9C9 = 3
1p. R79C9 = [53] = 8 -> R8C89 = 13 = {49}, locked for R8, 9 locked for N9
1q. R9C6 = 9 (hidden single in R9) -> R9C78 = {68}, locked for N9
1r. 1 in R7 only in R7C78 -> R7C78 = {17}, locked for N9, 7 locked for R7 -> R8C7 = 2
1s. R7C78 = {17} -> R6C8 = 5 (cage total)
1t. R7C456 = {246} (hidden triple in N8) -> 11(3) cage at R7C3 = {236} (only remaining combination) -> R7C3 = 3, R7C6 = 4 (hidden single in R7)
1u. R7C2 = 8 -> R6C3 = 10 = {46} (only remaining combination), locked for R6 and N4
1v. 7 in C2 only in 21(3) cage at R1C2 = {579/678} -> R12C2 = {57/67}, R2C3 = {89}
1w. Naked pair {12} in R45C3, locked for C3 and N4 -> R8C23 = [15]
1x. R4C2 = 3 -> R3C2 + R4C3 = 6 = [42/51]
[That looks to be where you went wrong, you have R3C2 = 6; it’s a 9(3) cage at R3C2, not a 9(2) cage]
1y. 9 in C7 only in R46C7, locked for N6
1z. 27(4) cage at R1C9 = {3789/4689}, 8 locked for N3

2a. 45 rule on C9 3 outies R258C8 = 20 = {389/479}, no 1,2,6
2b. 1,2 in C9 only in R456C9 -> 17(4) cage at R4C9 = {1268} (only remaining combination) -> R5C8 = 8, 1,2,6 locked for N6, 6 locked for C9
2c. R5C8 = 8 -> R28C8 = 12 = [39], R8C9 = 4, R9C78 = [86]
2d. Naked triple {789} in R123C9, 7 locked for N3
2e. 11(3) cage at R3C7 = {146/245} (only remaining combinations) -> R4C8 = 4, R3C78 = [52/61]
2f. Naked triple {379} in R456C7, 7 locked for C7, 3,7 locked for 30(5) cage at R4C7 -> R8C78 = [17]
2g. R456C7 = {379} = 19 -> R5C56 = 11 = {56}, locked for R5 and N5 -> R456C1 = [578], R456C7 = [739]
2h. R4C4 = 9 (hidden single in R4) -> R5C34 + R6C4 = 7 -> R5C4 = 4, R6C5 = {12}
2i. R6C56 = {37} (hidden pair in R6)
2j. 8 in R4 only in R4C56 -> 11(3) cage at R3C6 = {128} -> R3C6 = {12}
2k. R3C1 = 3 (hidden single in R3) -> R3C9 = 7 (step 1j)
2l. 22(3) cage at R3C3 = {589} (only remaining combination), 5 locked for R3
2m. R3C2 = 4, R4C2 = 3 -> R4C3 = 2 (cage sum)
2n. R3C7 = 6, R4C8 = 4 -> R3C8 = 1 (cage sum)
2o. R1C8 = 2 -> R1C67 = 8 = [35], R6C56 = [37]
2p. R1C5 = 4 (hidden single in R1), R1C3 = 6 (hidden single in N1) -> R1C4 = 8 (cage sum)
2q. 22(3) cage at R3C3 = [859]
2r. R6C23 = [64], R1C2 = 7 -> R2C2 = 5

and the rest is naked singles.

1 7 6 8 4 3 5 2 9
2 5 9 7 1 6 4 3 8
3 4 8 5 9 2 6 1 7
5 3 2 9 8 1 7 4 6
7 9 1 4 6 5 3 8 2
8 6 4 2 3 7 9 5 1
9 8 3 6 2 4 1 7 5
6 1 5 3 7 8 2 9 4
4 2 7 1 5 9 8 6 3