Prelims
a) R4C34 = {19/28/37/46}, no 5
b) R4C67 = {19/28/37/46}, no 5
c) 22(3) cage at R1C5 = {589/679}
d) 10(3) cage at R5C4 = {127/136/145/235}, no 8,9
e) 9(3) cage at R9C4 = {126/135/234}, no 7,8,9
f) 28(4) cage at R8C6 = {4789/5689}, no 1,2,3
g) 17(5) cage at R1C2= {12347/12356}, no 8,9
h) 17(5) cage at R2C5= {12347/12356}, no 8,9
i) 32(5) cage at R4C2 = {26789/35789/45689}, no 1
j) 33(5) cage at R4C8 = {36789/45789}, no 1,2
k) 17(5) cage at R6C3 = {12347/12356}, no 8,9
l) 17(5) cage at R8C1= {12347/12356}, no 8,9
Steps resulting from Prelims
1a. 22(3) cage at R1C5 = {589/679}, 9 locked for R1
1b. 17(5) cage at R1C2= {12347/12356}, 1,2,3 locked for N1
1c. 32(5) cage at R4C2 = {26789/35789/45689}, 8,9 locked for N4, clean-up: no 1,2 in R4C4
1d. 33(5) cage at R4C8 = {36789/45789}, 7,8,9 locked for N6, clean-up: no 1,2,3 in R4C6
1e. 17(5) cage at R6C3 = {12347/12356}, 1,2,3 locked for R6
1f. 9 in N1 only in R3C13, locked for R3
1g. 1 in R5 only in 10(3) cage at R5C4, locked for N5
2a. R4C46 = {89} (hidden pair in N5), locked for R4
2b. R4C46 = {89} -> R4C37 = {12}, locked for R4
2c. 17(5) cage at R2C5 = {12347/12356}, 1,2 locked for N2
2d. R6C28 = {89} (hidden pair in R6)
2e. 45 rule on R6 2 remaining innies R6C19 = 11 = [56/65/74]
2f. 45 rule on R7 2 innies R7C19 = 15 = {69/78}
2g. R46C7 = {12} (hidden pair in N6), locked for C7
2h. 45 rule on N6 2 remaining innies R46C9 = 9 = [36/45/54]
3. 45 rule on N4 4 innies R46C13 = 13 = {1237/1246/1345}, 1 locked for C3
3a. 5,6,7 of {1237/1246/1345} must be in R6C1 -> no 5,6,7 in R4C1 + R6C3
4. 45 rule on R5 4 outies R46C28 = 30, R6C28 = {89} = 17 -> R4C28 = 13 = {67}, locked for R4
5. Hidden killer pair 8,9 in 30(7) cage at R7C2 and R8C6 for N8, 30(7) cage only contains one of 8,9 which must be in R7C456 -> R8C6 = {89}, no 8,9 in R7C2378
5a. Naked pair {89} in R48C6, locked for C6
5b. R17C5 = {89} (hidden pair in C5)
5c. Naked pair {89} in R7C5 + R8C6, locked for N8
[With hindsight it would have been better if I’d spotted step 5b first, then step 5 would have simplified to R7C5 + R8C6 = {89} (hidden pair for N8)]
6. Hidden killer pair 1,2 in R7C8 and R9C89 for N9, R9C89 cannot be {12} which would clash with 9(3) cage at R9C4 -> R7C8 = {12}, R9C89 must contain one of 1,2
6a. 9(3) cage at R9C4 = {135/234} (cannot be {126} which clashes with R9C89), 3 locked for R9 and N8
6b. Killer pair 1,2 in 9(3) cage and R9C89, locked for R9
6c. R7C7 = 3 (hidden single in N9)
7. 45 rule on N5 using R4C46 = {89} 1 remaining innie R4C5 = 2 outies R6C37 + 1
7a. Min R6C37 = {12} = 3 -> min R4C5 = 4
7b. R4C5 = {45} -> R6C37 = 3,4 = {12/13}, no 4
7c. 17(5) cage at R2C5= {12347/12356}, 3 locked for N2
7d. 4,5 of {12347/12356} must be in R4C5 -> no 4,5 in R2C5 + R3C456
7e. 10(3) cage at R5C4 contains 1 (step 1g) = {127/136} (cannot be {145} which clashes with R4C5), no 4,5
7f. Hidden killer pair 4,5 in 32(5) cage at R4C2 and 33(5) cage at R4C8 for R5, 33(5) cage contains both or neither of 4,5 -> 32(5) cage must contain both or neither of 4,5 = {26789/45689}, no 3, 6 locked for N4, clean-up: no 5 in R6C9 (step 2e), no 4 in R4C9 (step 2h)
8. R1C289 = {123} (hidden triple in R1)
8a. 45 rule on N3 4 innies R13C79 = 25, R1C9 = {123} -> R13C79 = {1789/2689/3589/3679}, no 4 -> R1C7 = 9, 1,2,3 of the combinations must be in R1C9 -> no 1,2,3 in R3C9 -> R3C79 = {5678}
8b. R1C7 = 9 -> R1C5 = 8, R1C6 = 5 (cage sum), R7C5 = 9, R8C6 = 8, R4C6 = 9 -> R4C7 = 1, R4C34 = [28], R6C3 = 1 (hidden single in N4)
8c. R46C13 (step 3) = {1237} (only remaining combination) -> R46C1 = [37], R4C28 = [67], R6C9 = 4 (step 2e), R4C59 = [45]
8d. 10(3) cage at R5C4 = {127} (hidden triple in R5), locked for N5
8e. R2C4 = 9 (hidden single in R2)
8f. R7C19 (step 2f) = [87] (only remaining permutation)
8g. 28(4) cage at R8C6 = {5689} (only remaining combination), 5,6,9 locked for R8 and N9
8h. 4 in N9 only in R9C78, locked for R9
8i. 9(3) cage at R9C4 = {135} (only remaining combination), locked for R9 and N8
8j. R7C8 = 1 (hidden single in N9)
8k. R9C123 = {679} (hidden triple in R9), locked for N7
9. 45 rule on N1 4 innies R13C13 = 28 = {4789/5689}
9a. 4,6 of {4789/5689} must be in R1C1 -> no 4,6 in R1C3 + R3C13 -> R1C3 = 7
9b. R13C13 = {4789} (only remaining combination) -> R1C1 = 4, R3C13 = [98]
9c. R1C7 + R3C9 = [96] -> R13C79 (step 8a) = {3679} (only remaining combination) ->R1C9 = 3, R3C7 = 7
9d. R2C56 = [74] (hidden pair in N2)
and the rest is naked singles.