SudokuSolver Forum

1:
N3 two 8(2) = {17/26/35}
N3 15(2) = {69/78}
--> {567} of N3 locked in these three cages
Innies N3: R1C7+R23C9 = 14 = {149/248}
--> R1 7(2) = [34/52/61]
N6 17(2) = {89} (R6,N6)
N56 19(3): R4C6 = [8/9] (or max sum = 5+6+7 = 18 < 19)
Outies N69: R23C9+R489C6 = 35
--> R89C6 <> {1234} (or max total = 4+9+4+8+9 = 34 < 35)

2:
Outies C789: R1489C6 = 28 = {5689} (C6)
--> N2 6(2) = {24} (C6,N2)
--> R1 7(2) = [52/61]
Step 1: R23C9 = {48/49} ([4] C9,N3)
--> C9 12(2) = {39/57}
Outies N36: R14C6+R7C9 = 22 = [589/697]
--> C9 12(2) = [39/57]

3:
Outies N9: R6C9+R89C6 = 18 = [3{69}/5{58}]
Outies N6: R237C9+R4C6 = 29
--> [9] locked in R237C9 (C9) (or max total = 4+8+7+9 = 28 < 29)
--> N9 11(2) = {38/56} must include [3/5]
--> N9 8(2) <> {35}, = {17/26}
N9 10(2) <> [5]
--> [5] of N9 locked in R89C9+R9C78
--> R6C9+R89C6 <> [5{58}], = [3{69}]

Midway mop-up:
C9 12(2) = [39], R89C6 = {69} (C6,N8)
--> R1 7(2) = [52], R4C6 = [8], N6 5(2) = [41]
--> N3 8(2) = [17], N9 8(2) = {17} (C7,N9)
--> R45C7 = {56} (C7,N6), N9 10(2) = {28} (C8,N9)
--> N3 8(3) = [35], N3 15(3) = [96], N6 17(2) = [89]
--> R4C89 = [72], R9C78 = [43]

4:
N12 19(4): R2C4 = [1] (or min sum = 3+4+6+7 = 20 > 19)
--> N25 15(3) = [{37}5/{38}4] ([3] R3,N2)
Innies N5: R46C4+R6C6 = 12
--> R6C6 = [1], R46C4 = 11 = [47/56]
--> N58 13(3) = [157]
--> R5C6 = [3], N9 8(2) = [17]

5:
N25 15(3): R3C45 must include [7/8]
--> R12C5 <> {78}, must include [6/9]
--> R456C5 <> {269}, must include [4/7]
Step 4: R46C4 <> [47], = [56]
--> R45C7 = [65]
N47 22(4): R78C1 <> {79} can't sum to 16
--> R6C12 <> {24}, must include [5/7]
N45 18(3): R56C3 = 12 <> [75], = [84]

6:
Innies R1: R1C15 = 12 = [39/48]
--> {46} of R1 locked in R1C123 (N1)
--> N14 16(4) <> {1249}, <> [9]
--> N14 16(4) must include [5] (R3C3 <> [5])
(Proof: {12378} dropping whichever candidate can't make 16(4))
[6] of R7 locked in R7C123 (N7)
[5] of C3 locked in R89C3 (N7)
--> N78 22(4) must include {25/58}, = {2578}

Final mop-up:
R89C3 = [57], R8C2 = [2/8]
--> R89C69 = [9665], R8C28 = {28} (R8)
--> N47 22(4) = [{57}64]
--> R14C1 = [31]
--> N14 16(4): R2C2+R3C12 = 15 = {258} (N1)

Naked singles from here.

346895217
729164358
851732964
193548672
268973541
574621893
632457189
485319726
917286435

I'll rate A228 at 1.5, based on my steps 25 and 29.

Prelims

a) R1C67 = {16/25/34}, no 7,8,9
b) R1C89 = {17/26/35}, no 4,8,9
c) R23C6 = {15/24}
d) R2C78 = {17/26/35}, no 4,8,9
e) R3C78 = {69/78}
f) R5C89 = {14/23}
g) R6C78 = {89}
h) R67C9 = {39/48/57}, no 1,2,6
i) R78C7 = {17/26/35}, no 4,8,9
j) R78C8 = {19/28/37/46}, no 5
k) R89C9 = {29/38/47/56}, no 1
l) 19(3) cage at R4C6 = {289/379/469/478/568}, no 1

1. Naked pair {89} in R6C78, locked for R6 and N6, clean-up: no 3,4 in R7C9
1a. Max R6C34 = 13 -> min R5C3 = 5
1b. 18(3) cage at R5C3 cannot be {189}, because 8,9 only in R5C3 -> no 1 in R6C34

2. 19(3) cage at R4C6 = {379/469/478/568} (cannot be {289} because 8,9 only in R4C6), no 2
2a. 8,9 only in R4C6 -> R4C6 = {89}

3. Killer triple 5,6,7 in R1C89, R2C78 and R3C78, locked for N3, clean-up: no 1,2 in R1C6
3a. 5 in N3 only in R1C89 or R2C78 -> one of these cages must be {35}, 3 locked for N3, clean-up: no 4 in R1C6

4. 45 rule on N36 3(2+1) outies R14C6 + R7C9 = 22
4a. Min R4C6 + R7C9 = 18 -> no 3 in R1C6, clean-up: no 4 in R1C7
4b. Max R14C6 = 15 -> min R7C9 = 7, clean-up: no 7 in R6C9
4c. 4 in N3 only in R23C9, locked for C9 and 21(4) cage at R2C9, no 4 in R4C89, clean-up: no 1 in R5C8, no 8 in R7C9, no 7 in R89C9

5. Killer triple 1,2,3 in R1C7, R1C89 and R2C78, locked for N3

6. 21(4) cage at R2C9 contains 4 = {1479/2469/2478/3468} (cannot be {3459} which clashes with R6C9), no 5

7. 45 rule on C789 4 outies R1489C6 = 28 = {5689} (cannot be {4789} because R1C6 only contains 5,6), locked for C6, clean-up: no 1 in R23C6
7a. 45 rule on N9 2 outies R89C6 = 1 innie R7C9 + 6
7b. R7C9 = {79} -> R89C6 = 13,15 = {58/69}
7c. 45 rule on N9 3 innies R7C9 + R9C78 = 16
7d. Min R7C9 = 7 -> max R9C78 = 9, no 9 in R9C78

8. Naked pair {24} in R23C6, locked for C6 and N2

9. R67C6 = {13/17} (cannot be {37} because 13(3) cage cannot contain both of 3,7), 1 locked for C6
9a. R67C6 = {13/17} = 4,8 -> R7C5 = 5,9 (cage sum)

10. Killer pair 5,9 in R7C5 and R89C6, locked for N8

11. Combined cage R1C6789 = 15 without 4,8,9 = {1257/1356}, 5 locked for R1, 1 locked for N3, clean-up: no 7 in R2C78
11a. R1C6789 = {1257/1356} -> R1C89 = {17/35} (cannot be {26}, locking-out cages), no 2,6 in R1C89

12. 45 rule on C9 2 innies R15C9 = 1 outie R4C8 + 1, IOU no 1 in R1C9, clean-up: no 7 in R1C8
12a. 1 in C9 only in R45C9, locked for N6
12b. Min R15C9 = 4 -> min R4C8 = 3
12c. Min R23C9 + R4C8 = 15 -> max R4C9 = 6

13. 19(3) cage at R4C6 (step 2) = {379/469/478/568}
13a. 21(4) cage at R2C9 (step 6) = {1479/2469/2478/3468}
13b. 1 in N6 only in 21(4) cage = {1479} = {49}[71] or R5C89 = [41] -> 19(3) cage = {379/469/568} (cannot be {479}, blocking cages)
13c. 19(3) cage = {379/469/568}, R6C9 = {35} -> 21(4) cage = {1479/2469/2478} (cannot be {3468}, ALS block), no 3 in R4C89
13d. 1,2 of 21(4) cage only in R4C9 -> R4C9 = {12}

14. Killer quad 1,2,3,5 in R456C9 and R89C9, locked for C9 -> R1C9 = 7, R1C8 = 1, R1C7 = 2, R1C6 = 5, R7C9 = 9, R6C9 = 3, R7C5 = 5, clean-up: no 6 in R2C78, no 8 in R3C78, no 2 in R5C89, no 6 in R7C7, no 3,6 in R8C7, no 2,8 in R89C9

15. R5C89 = [41], R4C9 = 2, R4C8 = 7 (step 13c), clean-up: no 3,6 in R78C8

16. Naked pair {56} in R45C7, locked for C7 -> R2C78 = [35], R3C78 = [96], R6C78 = [89]

17. R9C78 = [43] (hidden pair in N9)
17a. R9C78 = [43] = 7 -> R89C6 = 15 = {69}, locked for C6 and N8 -> R4C6 = 8

18. R7C5 = 5 -> R67C6 = 8 = {17}, R5C6 = 3 (hidden single in C6)
18a. Naked pair {17} in R7C67, locked for R7
18b. 6 in R7 only in R7C123, locked for N7

19. 19(4) cage at R1C2 = {1369/1468} (cannot be {1378} because 1,7 only in R2C4) -> R2C4 = 1, R1C234 = {369/468}, 6 locked for R1

20. 15(3) cage at R3C4 = {348/357} (cannot be {456} because 4,5 only in R4C4), no 6,9, 3 locked for R3 and N2

21. 45 rule on N5 3 remaining innies R4C4 + R6C46 = 12 = [471/561] -> R6C4 = {67}, R6C6 = 1, R7C6 = 7, R78C7 = [17]
21a. 5 in R6 only in R6C123, locked for N4

22. 18(3) cage at R5C3 = {279/468/567} (cannot be {459} because R6C4 only contains 6,7) -> R6C3 = {245}

23. Killer pair 8,9 in R1C234 and R1C5, locked for R1
23a. Killer pair 3,4 in R1C1 and R1C234, locked for N1

24. 25(5) cage at R4C5 = {23479/23569}
24a. 5 of {23569} must be in R5C4 with 6 in R46C5 (R5C45 cannot be {56} which clashes with R5C7), no 6 in R5C45

25. Min R6C12 = {25} = 7 (cannot be {24} = 6 because R78C1 cannot total 16)
25a. 45 rule on R6 3 innies R6C125 = 1 outie R5C3 + 6
25b. R6C125 cannot be 12 with R5C3 = 6 because R6C12 cannot be {24}
R6C125 cannot be 13 with R5C3 = 7 because R6C12 cannot be {24} and R6C125 = {256} clashes with 18(3) cage = [756]
-> min R6C125 = 14, min R5C3 = 8
25c. 18(3) cage at R5C3 (step 22) = {279/468} (cannot be {567} because R5C3 only contains 8,9), no 5
25d. 18(3) cage = [846/927]

26. 5 in R6 only in R6C12, locked for 22(4) cage at R6C1, no 5 in R8C1
26a. R6C125 (step 25a) = 14,15 = {257/456}
26b. 22(4) cage = {2569/2578/3568/4567} (cannot be {1579} because 1,9 only in R8C1), no 1
26c. 22(4) cage = {4567} must have 7 in R6C12 = {57}[64], no 4 in R6C12 + R7C1

27. 22(4) cage at R8C2 = {1489/2389/2479/2578/3478} (cannot be {1579} because R9C4 only contains 2,8)
27a. 7 of {2578} must be R9C3 -> no 5 in R9C3
27b. 1 of {1489} must be in R89C3 (R89C3 cannot be [49] which clashes with R56C3) -> no 1 in R8C2

28. 16(4) cage at R2C2 = {1249/1258/1267/1357/1456/2356} (cannot be {1348/2347} because 3,4 only in R4C1)
28a. 4 of {1249} must be in R4C1 -> no 9 in R4C1

29. R6C125 (step 25a) = {257/456}
29a. Consider the permutations for R46C4 = [47/56] (step 21)
R46C4 = [47] => no 4 in R6C5
or R46C4 = [56] => R6C125 = {257}, no 4 in R6C5
-> no 4 in R6C5
29b. R6C125 = {257} (only remaining combination), locked for R6 -> R6C34 = [46], R5C3 = 8 (step 25d), R4C4 = 5, R45C7 = [65]

30. Naked pair {89} in R1C45, locked for R1 and N2
30a. Naked pair {37} in R3C45, locked for R3 and N2 -> R2C5 = 6
30b. R4C5 = 4 (hidden single in N5)
30c. R5C45 + R6C5 = {279}, 9 locked for R5

31. 22(4) cage at R6C1 (step 26b) = {2569/2578/4567} (cannot be {3568} because R6C12 must contain two of 2,5,7), no 3

32. 16(4) cage at R2C2 (step 28) = {1258/1357}, no 9, 5 locked for N1
32a. Killer pair 1,2 in 16(4) cage and R3C3, locked for N1

33. R8C3 = 5 (hidden single in C3), R89C9 = [65], R89C6 = [96]
33a. 1 in N7 only in R9C123, locked for R9
33b. Naked pair {28} in R9C45, locked for R9 and N8
33c. Naked pair {34} in R78C4, locked for C4 and N8 -> R3C45 = [73], R8C5 = 1

34. 22(4) cage at R8C2 (step 27) must contain 5 = {2578} (only remaining combination) -> R9C3 = 7, R2C3 = 9, R4C2 = 9 (hidden single in R4)

35. Naked pair {28} in R8C28, locked for R8 -> R8C1 = 4, R78C4 = [43], R1C1 = 3, R1C23 = [46], R1C4 = 8 (step 19), R3C13 = [13], R7C3 = 2, R8C2 = 8

36. 16(4) cage at R2C2 (step 32) = {1258} (only remaining combination) -> R2C2 = 2

and the rest is naked singles.

Thanks to Andrew for some corrections.
Prelims
i. 7(2)r1c6: no 7,8,9
ii. 8(2) cages in n3: no 4,8,9
iii. 6(2)n2: no 3,6..9
iv. 15(2)n3: no 1..5
v. 19(3)r4c6: no 1
vi. 5(2)n6: no 5..9
vii. 17(2)n6 = {89}
viii. 12(2)r6c9: no 1,2,6
ix. 8(2)n9: no 4,8,9
x. 10(2)n9: no 5
xi. 11(2)n9: no 1

1. "45" on n3: 3 innies r1c7 + r23c9 = 14
1a. Hidden killer pair 8,9 in n3 in 15(2) and h14(3)
1b. and h14(3) must have 4 for n3
1c. = {149/248}(no 3,5,6,7)
1d. no 1,2,4 in r1c6

2. "45" on c789: 4 outies r1489c6 = 28 (no 1,2,3)
2a. must have 5/6 for r1c6 = {5689} only: all locked for c6
2b. no 4 in r1c7 -> no 1,2 in r23c9 (step 1c)
2c. 6(2)n2 = {24} only: both locked for n2 & c6

3. 4 in n3 only in c9: locked for c9 and 21(4) cage: no 4 in r4c8
3a. no 1 in r5c8
3b. no 8 in 12(2)r6c9
3c. no 7 in 11(2)n9

4. 7(2)r1c6 = [61/52] = [6/2..]
4a. -> {26} blocked from 8(2)r1c8 (no 2,6)

5. 17(2)n6 = {89}: both locked for r6 and n6
5a. no 3 in r7c9

6. 19(3)r4c6 must have 8/9 -> r4c6 = (89)
6a. only combo with 2 is {289}: but 8 & 9 only in r4c6 -> no 2

7. 2 in n6 only in 5(2) = {23} or in r4c89 -> 3 in r4c89 must also have 2 or there would be no 2 for n6 (Locking out cages)
7a. -> 21(4)r2c9 (must have 4) = {1479/2469/2478}(no 3,5)

8. "45" on c9: 2 outies r14c8 - 7 = 1 innie r5c9
8a. -> no 7 in r1c8 since it would force r4c8 = r5c9 (IOU)
8b. no 1 in r1c9

9. "45" on c9: 3 outies r145c8 = 12
9a. {156} blocked by r5c8 = (234)
9b. {246} blocked by r1c8 = (135)
9c. {345} blocked by r4c8 = (1267)
9d. = {147/237}(no 5,6)
9e. must have 7 -> r4c8 = 7
9f. r15c8 = [14/32]
9g. no 2 in r5c9
9h. no 3 in r1c9
9i. no 8 in r3c7
9j. no 1 in r2c7
9k. no 3 in 10(2)n9
9l. no 5 in r7c9

10. r1c9 = (57) -> {57} blocked from 12(2)r6c9
10a. -> r67c1 = [39]
10b. -> r5c89 = [41]
10c. r45c7 = {56}: both locked for c7 & n6: sums to 11 -> r4c6 = 8
10d. 10(2)n9 = {28} only: both locked for c8 & n9
10e. 11(2)n9 = {56}: both locked for n9 and c9
10f. r1c89 = [17]
10g. r1c67 = [52]
10h. r2c78 = [35]
10i. r3c78 = [96]
10j. r9c7 = 4 (hidden single n9)
10k. r9c8 = 3
10l. r4c9 = 2

11. "45" on c6789: 1 outie r7c5 - 2 = 1 innie r5c6
11a. -> r7c5 = 5, r5c6 = 3

12. 19(4)r1c2 = {1369/1378/1468}[Andrew noticed that the {1378} is not valid because 1,7 only in r2c4: which then locks 6 for r1. My walk-through uses that lock in step 21]
12a. must have 1 -> r2c4 = 1

13. 15(3)r3c4 must have two of (378) for r3c45
13a. = {348/357}(no 6,9)
13b. must have 3 -> 3 locked for r3 & n2

14. "45" on n5: 3 remaining innies r46c4 + r6c6 = 12 = [471/561]
14a. r6c6 = 1, r7c6 = 7
14b. r78c7 = [17]
14c. r6c4 = (67)

15. r78c1 cannot sum to 16 (no 7) -> from cage sum 22(4)r6c1, r6c12 cannot sum to 6 (ie can't be {24} (no eliminations yet)
15a. ->18(3)r5c3, {567} blocked
15b. 18(3)r5c3 must have 6/7 for r6c4 = {279/468} (no 5)
15c. can't have both 6&7 -> no 6,7 in r56c3
15d. must have 8,9 -> r5c3 = (89)

16. "45" on n5: 1 remaining innie r4c4 + 7 = 2 outies r56c3
16a. = [4][92]/[5][84]
16b. must have 4 -> no 4 in common peers in r4c123 & r6c5

17. 5 in r6 only in 22(4)r6c1: 5 locked for n4 and no 5 in r8c1
17a. 22(4): {1579} blocked by 1 & 9 only in r8c1
17b. = {2569/2578/3568/4567}(no 1)
17c. {57} in {4567} must be in r6c23 -> no 4 in r6c12

18. r6c3 = 4 (hidden single r6)
18a. r5c3 + r6c4 = 14 = [86]
18b. r4c4 = 5 (h11(2)r46c4)
18c. r4c5 = 4 (hsingle r4)
18d. r45c7 = [65]
18e. r3c45 = 10 = {37} only: 7 locked for r3 & n2

19. 4 in r1 only in n1: locked for n1

20. 16(4)r2c2 = {1258/1357/2356}(no 9) ({1267} blocked by 6&7 only in r2c2
20a. must have 5 -> locked for n1

21. 19(4)r1c2 = {1369/1468}
21a. must have 6 -> 6 locked for n1 & r1

22. naked pair {69} in r89c6: locked for n8

23. 6 in r7 only in n7: locked for n7

24. 5 in c3 only in 22(4)r8c2: 5 locked for n7
24a. 22(4) must have 2/8 for r9c4 = {2578} only
24b. r9c3 = 7
24c. r8c3 = 5
24d. naked pair {28} in r8c2+r9c4 -> no 2,8 in r9c12, r8c45

25. naked pair {28} in r8c28: both locked for r8
25a. r89c9 = [65]
25b. r89c6 = [96]

26. 22(4)r6c1 must have 3/4 for r8c1 = {3568/4567}(no 2)[Actually, can't be {3568} because 6,8 only in r7c1. Thanks Andrew!]
26a. must have 6 -> r7c1 = 6

Rest is straight forward

1:
C9 12(2) = {39/48/57}
R9 15(2) = {69/78}
Outies N89: R6C69+R9C3 = 11 = [137/146/236]
--> R6C6 = [1/2], C9 12(2) = [39/48], R9 15(2) = [69/78]
Innie-outies N8: R8C6+R9C46 = R6C6+22 = 23/24 = {689/789}

2:
N7 10(2) = {19/28/37/46}
--> N7 10(2), R9 15(2) & R9C6 together must include {6789} (R9)
C7 8(2), C9 8(2) = {17/26/35}
--> N9 13(2) must include [8/9] of N9, = {49/58}
--> C7 8(2) & C9 8(2) each must include [6/7] of N9
--> C7 8(2) = {17/26}, C9 8(2) = [62/71]

3:
N8 6(2) = {15/24}
Outies R9: R8C569 = 16 = [187/196/286]
--> N8 6(2) = [15/24], R8C6+R9C4 = {89} (N8)
--> R9C36 = {67} (R9)
--> R89C6 + R9 15(2) = 6+7+8+9 = 30
--> R89C6 = 30-15 = 15
N89 22(4): R9C78 = 22-15 = 7
[3] of N9 locked in R9C78 = {34} (R9,N8)

Mop-up:
N8 6(2) = [15], N9 13(2) = {58} (C8,N9)
--> C9 12(2) = [39], N8 7(2) = {34} (C4,N8)
--> N6 5(2) = {14} (R5,N6), N58 10(3) = [1{27}] (R7,N8)
--> R89C6 = 15 = [96] (step 3)
--> R9 15(2) = [78]
--> N7 10(2) = {19} (R9,N7)
--> C9 8(2) = [62]
--> C7 8(2) = [17], N7 7(2) = {25} (R8,N7) (R8C4: not {34})
--> N9 13(2) = [58], N7 11(2) = {38} (R7,N7)
--> R78C1 = [64], N8 7(2) = [43]
--> C1 6(2) = {15} (C1)
--> N7 10(2) = [91]
--> N4 14(2) = [86]
--> C1 10(2) = {37} (C1,N1)
--> N47 19(4) = [2764], C2 10(2) = {28} (C2,N1)
--> N45 15(3) = [546], N7 11(2) = [38], N7 7(2) = [52]
--> C1 6(2) = [51], N4 12(2) = [93], N6 14(2) = [59]
--> N56 13(3) = [562]
--> N36 24(4) = [5478]
--> N3 15(2) = [96]
--> C3 10(2) = [91]

All naked singles from here.

I'll rate my walkthrough for A228A at 1.5 because of my breakthrough steps 23 and 24.
I hope Simon won't mind if I also give a rating for his walkthrough, which I'll rate at 1.25.

Prelims

a) R12C1 = {19/28/37/46}, no 5
b) R12C5 = {69/78}
c) R1C67 = {19/28/37/46}, no 5
d) R1C89 = {17/26/35}, no 4,8,9
e) R23C2 = {19/28/37/46}, no 5
f) R23C3 = {19/28/37/46}, no 5
g) R23C6 = {39/48/57}, no 1,2,6
h) R2C78 = {14/23}
i) R34C1 = {15/24}
j) R3C78 = {69/78}
k) R4C23 = {39/48/57}, no 1,2,6
l) R5C12 = {59/68}
m) R5C89 = {14/23}
n) R6C78 = {59/68}
o) R67C9 = {39/48/57}, no 1,2,6
p) R7C23 = {29/38/47/56}, no 1
q) R78C4 = {16/25/34}, no 7,8,9
r) R78C7 = {17/26/35}, no 4,8,9
s) R78C8 = {49/58/67}, no 1,2,3
t) R8C23 = {16/25/34}, no 7,8,9
u) R89C5 = {15/24}
v) R89C9 = {17/26/35}, no 4,8,9
w) R9C12 = {19/28/37/46}, no 5
x) R9C34 = {69/78}
y) 10(3) cage at R6C6 = {127/136/145/235}, no 8,9

1. R78C4 = {16/34} (cannot be {25} which clashes with R89C5), no 2,5
1a. Killer pair 1,4 in R78C4 and R89C5, locked for N8
1b. 10(3) cage at R6C6 = {127/136/235} (cannot be {145} because 1,4 only in R6C6), no 4
1c. 1 of {127/136} only in R6C6 -> no 6,7 in R6C6

2. 31(5) cage at R4C5 must contain 9, locked for N5

3. 45 rule on N1 3(2+1) outies R12C4 + R4C1 = 7
3a. Min R12C4 = 3 -> max R4C1 = 4, clean-up: no 1 in R3C1
3b. Max R12C4 = 6, no 6,7,8,9 in R12C4

4. 45 rule on N12 3(1+2) outies R1C7 + R4C14 = 11
4a. Min R4C14 = 3 -> max R1C7 = 8, clean-up: no 1 in R1C6
4b. 1 in C6 only in R456C6, locked for N5
[There was a CPE from the 1s in N2 but I didn’t need it.]

5. 45 rule on N2 5 innies R12C4 + R1C6 + R3C45 = 18 = {12348/12357/12456}, no 9, clean-up: no 1 in R1C7

6. 45 rule on N89 3(2+1) outies R6C69 + R9C3 = 11
6a. Min R9C3 = 6 -> max R6C69 = 5 -> max R6C6 = 2, max R6C9 = 4, clean-up: R7C9 = {89}
6b. Min R6C69 = 4 -> max R9C3 = 7, clean-up: no 6,7 in R9C4
6c. Killer pair 3,4 in R5C89 and R6C9, locked for N6

7. 10(3) cage at R6C6 (step 1b) = {127/235} (cannot be {136} which clashes with R89C4), no 6
7a. Killer triple 1,2,3 in 10(3) cage, R78C4 and R89C5, locked for N8
[While checking my walkthrough I realised that there’s also
Killer pair 2,5 in 10(3) cage at R6C6 and R89C5, locked for N8
which then gives Killer quad 6,7,8,9 in R9C12, R9C34 and R9C6, locked for R9.
Since this doesn’t seem to have much effect on my later solving path I haven’t reworked to include these steps. Clearly I didn’t look closely enough when I typed the last sentence; Simon made excellent use of it, getting more out of 45 rule on R9 than I did in my step 17.]

8. 45 rule on N9 3 innies R7C9 + R9C78 = 16
8a. Min R7C9 = 8 -> max R9C78 = 8, no 8,9 in R9C78

9. Hidden killer pair 8,9 in R78C8 and R7C9 for N9, R7C9 = {89} -> R78C8 must contain one of 8,9 -> R78C8 = {49/58}, no 6,7
[Alternatively R78C8 cannot be {67} because at least one of the 8(2) cages in N9 must contain one of 6,7.]

10. 45 rule on N7 3(2+1) outies R6C12 + R9C4 = 17
10a. Min R9C4 = 8 -> max R6C12 = 9, no 9 in R6C12

11. 45 rule on C1234 1 innie R5C4 = 1 outie R3C5 + 6 -> R5C4 = {789}, R3C5 = {123}

12. 45 rule on C6789 1 innie R5C6 = 1 innie R7C5 + 1 -> R5C6 = {3468}

13. 45 rule on R1234 1 innie R4C5 = 1 outie R5C7 + 2, no 2,5,6 in R4C5, no 8,9 in R5C7

14. 45 rule on R6789 1 innie R6C5 = 1 outie R5C3 + 3, no 7,8,9 in R5C3, no 2,3 in R6C5

15. 45 rule on R12 4 innies R2C2369 = 26 = {2789/3689/4589/4679/5678}, no 1, clean-up: no 9 in R3C2, no 9 in R3C3

16. 45 rule on N3 3 innies R1C7 + R23C9 = 17 = {269/278/359/458} (cannot be {179/368/467} which clash with R3C78), no 1

17. 45 rule on R9 3 outies R8C569 = 16 = {169/178/259/268/349/358/457} (cannot be {367} because R8C5 only contains 1,2,4,5)
17a. 1 of {169/178} must be in R8C5 -> no 1 in R8C9, clean-up: no 7 in R8C9
17b. 8,9 of {169/268} must be in R8C6 -> no 6 in R8C6

18. 45 rule on N47 3(1+2) outies R3C1 + R69C4 = 19
18a. Max R3C1 + R9C4 = 14 -> min R6C4 = 5

19. 45 rule on N5 4 innies R46C46 = 14
19a. Min R6C46 = 6 -> max R4C46 = 8, no 8 in R4C4, no 7,8 in R4C6
19b. R46C46 = 14 and contains 1 = {1238/1247/1256/1346}
19c. 7 of {1247} must be in R6C4 -> no 7 in R4C4

20. 12(3) cage at R3C4 = {138/147/156/237/246/345}
20a. 7,8 of {138/147} must be in R3C4, 1 of {156} must be in R3C5 -> no 1 in R3C4
20b. 7 of {246} must be in R3C4, 2 of {246} must be in R3C5 -> no 2 in R3C4
20c. 7,8 of {138/147} must be in R3C4, 3 of {345} must be in R3C5 -> no 3 in R3C4

21. 45 rule on R6789 3 innies R6C345 = 18 = {279/378/459/468} (cannot be {189/369/567} which clash with R6C78), no 1
21a. 2,3 of {279/378} must be in R6C3, no 7 in R6C3
21b. 5 of {459} must be in R6C4, no 5 in R6C35, clean-up: no 2 in R5C3 (step 14)
21c. Killer pair 8,9 in R6C345 and R6C78, locked for R6

22. 31(5) cage at R4C5 = {34789/35689/45679} (cannot be {25789} because 2,5 only in R5C5), no 2
22a. 5 of {35689/45679} must be in R5C5 -> no 6 in R5C6
22b. R5C56 cannot be {56} which clashes with R5C12 -> no 6 in R5C6, clean-up: no 5 in R7C5 (step 12)
22c. 2 in R5 only in R5C789, locked for N6

23. Hidden killer pair 8,9 in R12C5 and R456C5 for C5, R12C5 contains one of 8,9 -> R456C5 must contain one of 8,9
23a. Hidden killer pair 8,9 in R5C12 and R5C456 for R5, R5C12 contains one of 8,9 -> R5C456 must contain one of 8,9
23b. Combining these hidden killer pairs 31(5) cage at R4C5 must either contain both of 8,9 or can contain only one of 8,9 if it’s in R5C5
23c. 31(5) cage at R4C5 (step 22) = {34789/35689} (cannot be {45679} which only contains one of 8,9 which cannot be in R5C5 because this is the only available position for 5), 3 locked for N5

24. 31(5) cage at R4C5 (step 23c) = {34789/35689}
24a. 4 of {34789} must be in R456C5 (R5C6 + R7C5 cannot be [43], IOD blocker) -> no 4 in R5C6, clean-up: no 3 in R7C5 (step 12)

25. 10(3) cage at R6C6 (step 7) = {127} (only remaining combination, cannot be {235} because 3,5 only in R7C6) -> R6C6 = 1, R7C56 = {27}, locked for R7 and N8, clean-up: no 4,9 in R7C23, no 4 in R89C5, no 1,6 in R8C7

26. Naked pair {15} in R89C5, locked for C5 and N5, clean-up: no 7 in R5C4 (step 11), no 6 in R78C4

27. R9C6 = 6 (hidden single in N8), R9C3 = 7, R9C4 = 8, R8C6 = 9, R5C4 = 9, clean-up: no 4 in R1C7, no 3 in R23C3, no 3 in R23C6, no 5 in R4C2, no 5 in R5C12, no 4 in R7C8

28. Naked pair {68} in R5C12, locked for R5 and N4 -> R5C6 = 3, R7C5 (step 12) = 2, R7C6 = 7, R3C5 = 3, clean-up: no 7 in R2C2, no 5 in R23C6, no 4 in R4C23, no 2 in R5C89, no 2,3,4 in R9C12

29. Naked pair {14} in R5C89, locked for R5 and N6 -> R5C357 = [572], R6C9 = 3, R7C9 = 9, clean-up: no 8 in R12C5, no 8 in R1C6, no 3,7 in R1C7, no 5 in R1C8, no 3 in R2C8, no 6 in R7C2, no 6 in R7C7, no 2 in R8C2, no 4 in R8C8, no 2,5 in R8C9, no 5 in R9C9

30. Naked pair {48} in R23C6, locked for C6 and N2 -> R1C6 = 2, R1C7 = 8, R4C6 = 5, R4C7 = 6 (cage sum), R6C4 = 6, R6C3 = 4 (cage sum), R46C5 = [48], R4C4 = 2, R3C4 = 7 (cage sum), R3C78 = [96], R6C78 = [59], R4C1 = 1, R3C1 = 5, R9C12 = [91], R89C5 = [15], R9C9 = 2, R8C9 = 6, R3C9 = 4, R5C89 = [41], R9C78 = [43], R23C6 = [48], R3C2 = 2, R2C2 = 8, R3C3 = 1, R2C3 = 9, R4C3 = 3, R4C2 = 9, R1C3 = 6, R1C2 = 4 (cage sum), R7C3 = 8, R7C2 = 3

and the rest is naked singles.