Prelims
a) R23C7 = {69/78}
b) R78C3 = {18/27/36/45}, no 9
c) R7C67 = {16/25/34}, no 7,8,9
d) R78C8 = {29/38/47/56}, no 1
e) R89C6 = {29/38/47/56}, no 1
f) 11(3) cage at R4C2 = {128/137/146/236/245}, no 9
g) 10(3) cage at R5C1 = {127/136/145/235}, no 8,9
h) 27(4) cage at R1C1 = {3789/4689/5679}, no 1,2
i) 11(4) cage at R8C4 = {1235}
j) 32(5) cage at R6C2 = {26789/35789/45689}, no 1
Steps resulting from Prelims
1a. 27(4) cage at R1C1 = {3789/4689/5679}, 9 locked for N1
1b. 11(4) cage at R8C4 = {1235}, CPE no 1,2,3,5 in R9C56, clean-up: no 6,8,9 in R8C6
2a. 45 rule on C56789 2 outies R67C4 = 16 = {79}, locked for C4 and 34(7) cage at R3C6
2b. 45 rule on C6789 2 innies R34C6 = 7 = {16/25/34}, no 8
2c. 45 rule on C5 3 innies R456C5 = 11 = {128/146/245} (cannot be {236} which clashes with R34C6 in 34(7) cage), no 3
2d. 17(3) cage at R7C5 = {278/359/368/467} (cannot be {179} which clashes with R7C4, cannot be {269/458} which clashes with R456C5), no 1
2e. 45 rule on N9 2(1+1) outies R6C9 + R7C6 = 11 = [56/65/74/83/92] -> R6C9 = {56789}, R7C6 = {23456}, clean-up: no 6 in R7C7
2f. R6C9 + R7C6 = 11 -> R67C9 cannot total 11 (CCC) -> no 3 in R8C9
2g. 45 rule on N9 3 innies R7C7 + R78C9 = 10 = {127/136/145/235}, no 8,9 in R78C9
2h. 1 in N8 only in R89C4, locked for C4 and 11(4) cage at R8C4
3. 45 rule on N23456789 1 innie R4C1 = 1 outie R3C3 + 5 -> R4C1 = {6789}, R3C3 = {1234}
3a. 19(4) cage at R1C4 = {1468/2368/2458}, 8 locked for C4 and N2
4. Consider placement for 8 in C5
8 in R456C5 (step2c) = {128}, locked for 34(7) cage at R3C6 => R34C6 (step 2b) = {34}, locked for C6
or 8 in 17(3) cage at R7C5, locked for N8
-> R89C6 = [29/47/56/74] (cannot be [38]), no 3,8
4a. 8 in N8 only in 17(3) cage at R7C5, locked for C5
4b. 17(3) cage (step 2d) = {278/368}, no 4,5,9
4c. R456C5 (step 2c) = {146/245}, 4 locked for C5, N5 and 34(7) cage at R3C6, clean-up: no 3 in R34C6 (step 2b)
4d. Deleted, replaced by step 4g
4e. R89C6 = [29/47/74] (cannot be [56] which clashes with R34C6), no 5,6
4f. Killer pair 7,9 in R7C4 and R89C6, locked for N8
4g. 7,9 in C5 only in 17(3) cage at R1C5 = {179}, locked for N2, 1 locked for C5
4h. R456C5 (step 2c) = {245} (only remaining combination), locked for C5, N5 and 34(7) cage at R3C6 -˃ R34C6 = [61], clean-up: no 9 in R2C7, no 5 in R6C9 (step 2e), no 1 in R7C7
4i. Naked triple {368} in 17(3) cage at R7C5, 3 locked for N8, clean-up: no 8 in R6C9 (step 2e), no 4 in R7C7
4j. Naked pair {36} in R45C4, 3 locked for C4 and N5
4k. 19(4) cage at R1C4 (step 3a) = {2458} (only remaining combination), no 1,3, 5 locked for C4 and N2, clean-up: no 6,8 in R4C1 (step 3)
4l. Naked pair {12} in R89C4, locked for C4, N8 and 11(4) cage at R8C4, clean-up: no 9 in R6C9 (step 2e), no 5 in R7C7, no 9 in R9C6
4m. Naked triple {458} in R123C4, 4 locked for N2 and 19(4) cage at R1C4 -˃ R3C3 = 2, R4C1 = 7 (step 3), clean-up: no 7 in R78C3
4n. 11(3) cage at R4C2 = {236} (only remaining combination, cannot be {245} which clashes with R4C5) -˃ R4C2 = 2, R4C34 = {36}, locked for R4
4o. Naked pair {47} in R89C6, locked for C6 and N8 -˃ R67C4 = [79], R6C9 = 6, R7C6 = 5 -˃ R7C7 = 2, clean-up: no 4 in R8C3, no 6,9 in R8C8
4p. R9C23 = {35}, locked for R9 and N7, clean-up: no 4,6 in R7C3, no 6 in R8C3
4q. Naked pair {18} in R78C3, locked for C3 and N7
4r. 7 in N7 only in R78C2, locked for C2
4s. 7 in C3 only in 27(4) cage at R1C1 = {3789/5679}, no 4
4t. 4 in C3 only in R56C3, locked for N4
4u. 10(3) cage at R5C1 = {136/145}, 1 locked for C1 and N4
4v. 22(4) cage at R5C2 contains 4 in R56C3 = {3469} (only remaining combination), no 5,8
4w. R6C2 = 8 (hidden single in N4)
4x. R56C1 = {15} (hidden pair in N4), 5 locked for C1, R7C1 = 4 (cage sum), clean-up: no 7 in R8C8
4y. R6C6 = 9 -˃ R6C78 = 5 = [14/32/41], R5C6 = 8
4z. 9 in R4 only in R4C789, locked for N6
5. R12C6 = {23} = 5 -˃ R1C78 = 15 = {69/78}
5a. Naked quad {6789} in R1C78 + R23C7, locked for N3
5b. 45 rule on N3 using R1C78 + R23C7 = 30, 1 outie R4C8 = 1 innie R3C9 + 5 –˃ R4C8 = {89}, R3C9 = {34}
5c. R6C9 = 6 -> R78C9 = 8 = [17/35/71], no 4 in R8C9
5d. 15(3) cage at R3C9 = [483] (only possible combination, cannot be [357] which clashes with R78C9, cannot be [384/492] which clash with R3C9 + R4C8 = [38/49], CCC), R4C8 = 9, clean-up: no 6 in R1C7, no 2 in R6C8 (step 4y), no 5 in R8C9
5e. R5C234 = [946], R6C3 = 3, R4C34 = [63], R9C23 = [35]
5f. Naked pair {14} in R6C78, locked for R6 and N6 -˃ R4C7 + R5C78 = [572], clean-up: no 8 in R1C8 + R23C7
5g. R23C7 = [69], R1C78 = [87], R12C3 = [97] = 16 -˃ R1C12 = 11 = [65], clean-up: no 4 in R8C8
5h. R8C8 = 5 (hidden single in N9) -> R7C8 = 6
and the rest is naked singles.