I originally solved this puzzle with 4 pairs of cages from A300 combined. I hadn’t spotted that the 10(2) cage R23C5 and the 6(2) cage R3C67 had also been combined. Thanks Afmob for pointing that out and telling me that my steps were valid as far as step 19d! I’ve re-worked from there; a few earlier steps, or parts of steps have been deleted and others renumbered.
Prelims
a) R23C1 = {49/58/67}, no 1,2,3
b) R34C8 = {29/38/47/56}, no 1
c) R34C9 = {18/27/46/45}, no 9
d) R4C45 = {18/27/46/45}, no 9
e) R4C67 = {89}
f) Disjoint cage R6C58 = {18/27/46/45}, no 9
g) R8C56 = {14/23}
h) R8C78 = {49/58/67}, no 1,2,3
i) R89C9 = {19/28/37/46}, no 5
j) R9C45 = {39/48/57}, no 1,2,6
k) 41(8) cage at R3C2 = {12356789}, no 4
l) 38(8) cage at R5C4 = {12345689}, no 7
m) 40(8) cage at R5C7 = {12346789}, no 5
1. Naked pair {89} in R4C67, locked for R4, clean-up: no 2,3 in R3C8, no 1 in R3C9, no 1 in R4C45
2. 45 rule on C123 1 outies R8C4 = 1 innie R1C3 + 4, R1C3 = {12345}, R8C4 = {56789}
[Now I’ll use some of the early steps from wellbeback’s walkthrough for A300. I hope that, if necessary, I’d have found this step if I hadn’t seen his walkthrough.]
3. R4C67 = {89}, 38(8) cage at R5C4 and 40(8) cage at R5C7 each contain both of 8,9 -> R7C4589 must contain both of 8,9 (cannot be in R7C67 because of CPEs in N5 and N6), locked for R7
3a. R7C4589 contains both of 8,9 -> the remaining parts of the 38(8) and 40(8) cages must each contain one of 8,9
3b. Killer pair 8,9 in R4C6 and 38(8) cage, locked for N5
3c. Killer pair 8,9 in R4C7 and 40(8) cage, locked for N6
3d. Clean-up: no 1 in R6C58
[Note that R7C45 and R7C89 must each contain one of 8,9.]
4. 7 in N5 only in R4C45 = {27} or R6C58 = [72] (locking cages) -> 2 in R4C45 or R6C8, CPE no 2 in R4C89, clean-up: no 9 in R3C8, no 7 in R4C9
5. 5 in N6 only in R4C89 or in R6C58 = [45] (locking cages) -> R4C45 = {27/36} (cannot be {45} because 5 in R4C89 or 4 in R6C5), no 4,5 in R4C45
[And another of the early steps from wellbeback’s walkthrough for A300.]
6. 38(8) cage at R5C4 = {12345689}
6a. R7C456 must contain at least one of 2,3 (they cannot both be in R5C456 + R6C46, which would clash with R4C45)
6b. R8C56 = {14} (cannot be {23} which clashes with R7C456, which contains at least one of 2,3), locked for R8 and N8, clean-up: no 9 in R8C78, no 8 in R9C45, no 6,9 in R9C9
6c. 38(8) cage at R5C4 = {12345689}, 4 locked for N5, clean-up: no 5 in R6C8
6d. 5 in N6 only in R4C89, locked for R4
[Extending step 4, which I missed when solving A300.]
7. 7 in N5 only in R4C45 = {27} or R6C58 = [72] (locking cages) -> 2 in R4C45 or R6C8, CPE no 2 in R6C46
7a. 7 in N5 only in R4C45 = {27} or R6C58 = [72] -> no 2 in R6C5 (locking-out cages), clean-up: no 7 in R6C8
8. 4 in N4 only in R4C12 + R5C1 + R6C12, locked for 28(6) cage at R4C1, no 4 in R7C1
8a. 4 in R7 only in R7C789, locked for N9 and 40(8) cage at R5C7, no 4 in R5C789 + R6C79, clean-up: no 6 in R8C9
9. 45 rule on N23 2 innies R3C89 = 1 outie R1C3 + 10
9a. Min R3C89 = 11, max R3C8 = 8 -> min R3C9 = 3, clean-up: no 7 in R4C9
9b. 7 in N6 only in R4C8 + R5C789 + R6C79, CPE no 7 in R7C8
10. 7 in N8 only in R8C4 + R9C456, CPE no 7 in R9C23
11. 13(3) cage at R9C6 = {139/157/238/256}
11a. Killer pair 3,5 in R9C45 and 13(3) cage, locked for R9, clean-up: no 7 in R8C9
12. R7C89 contains one of 8,9 (from step 3)
12a. Killer triple 7,8,9 in R7C89, R8C78 and R89C9, locked for N9
12b. Hidden killer triple 7,8,9 in R7C89, R8C78 and R8C89 for N9, R8C78 contains one of 7,8, R89C9 contains one of 7,8,9, R7C89 contains one of 8,9 -> no 7 in R7C9
[Steps 12a and 12b slightly simplified; thanks Afmob.]
12c. 7 in R7 only in R7C123, locked for N7
12d. 40(8) cage at R5C7 = {12346789}, 7 locked for N6, clean-up: no 4 in R3C8
12e. 9 in N9 only in R7C89 +R8C9, CPE no 9 in R56C9
13. 14(3) cage at R8C1 = {158/239/248/356} (cannot be {149} because 1,4 only in R9C1)
13a. 1,4 of {158/248} must be in R9C1 -> no 8 in R9C1
13b. 6 of {356} must be in R9C1 -> no 6 in R8C12
14. 13(3) cage at R9C6 (step 11) = {139/157/238/256}
14a. 8,9 in {139/238} must be in R9C6 -> no 3 in R9C6
14b. 8 of {238} must be in R9C6, 2 of {256} must be in R9C78 (R9C78 cannot be {56} which clashes with R8C78) -> no 2 in R9C6
14c. 2 in N8 only in R7C456, locked for R7 and 38(8) cage at R5C4, no 2 in R5C456
15. 2 in N5 only in R4C45 = {27}, locked for R4 and N5, clean-up: no 2 in R6C8
16. 45 rule on N23 3(1+2) outies R1C3 + R4C89 = 10
16a. 5 in R4 only in R4C89 -> the remaining two cells must total 5 -> no 5 in R1C3, no 6 in R4C89, clean-up: no 5 in R3C8, no 3 in R3C9, no 9 in R8C4 (step 2)
16b. R4C89 cannot total 7 (because it contains 5) -> no 3 in R1C3, clean-up: no 7 in R8C4 (step 2)
16c. 6 in R4 only in R4C123, locked for N4
17. 7 in N8 only in R9C456, locked for R9, clean-up: no 3 in R8C9
17a. 7 in N9 only in R8C78 = {67}, locked for R8 and N9, clean-up: no 2 in R1C3 (step 2)
17b. 13(3) cage at R9C6 (step 11) = {139/157/238/256}
17c. Killer pair 1,2 in R89C9 and 13(3) cage, locked for N9
17d. 1 in N9 only in R9C789, locked for R9
18. 40(8) cage at R5C7 = {12346789}, 1 locked for N6, clean-up: no 8 in R3C9
18a. 1 in R4 only on R4C123, locked for N4
19. R1C3 + R4C89 = 10 (step 16)
19a. 5 in R4 only in R4C89 -> R1C3 = 1, R4C89 = {45}, locked for R4 and N6, R8C4 = 5 (step 2), clean-up: no 8 in R3C8, no 6 in R3C9, no 5 in R6C5, no 7 in R9C45
19b. Naked pair {67} in R38C8, locked for C8 -> R6C8 = 3, R6C5 = 6
19c. Naked pair {45} in R34C9, locked for C9
19d. Naked pair {39} in R9C45, locked for R9 and N8
20. 41(8) cage at R3C2 = {12356789} -> R7C2 = 1
20a. Naked pair {36} in R4C23, locked for N4 -> R4C1 = 1
20b. Naked pair {36} in R4C23, CPE no 3,6 in R3C2
21. Naked triple {268} in R7C456, locked for R7, N8 and 38(8) cage at R5C4, no 8 in R5C456 + R6C46 -> R9C6 = 7
21a. Naked triple {349} in R7C789, locked for R7, N9 and 40(8) cage at R5C7, no 9 in R5C78 + R6C7, clean-up: no 1 in R9C9
21b. Naked pair {28} in R89C9, locked for C9 and N9
21c. 1 in C4 only in R56C4, locked for N5
22. R4C67 = [89] (hidden singles in N5 and N6)
23. R8C4 = 5 -> 23(4) cage at R8C3 = {4568} (only remaining combination, cannot be {3569} because 3,9 only in R8C3) -> R8C3 = 8, R9C23 = {46}, locked for N7-> R9C1 = 2
23a. 41(8) cage at R3C2 = {12356789}, 8 locked for C2, 3 locked for C3
24. 45 rule on N1 2 remaining innies R3C23 = 11 = [29/56/83/92], no 7 in R3C2, no 5,7 in R3C3
[There’s a larger amount of re-work from here.]
25. 41(8) cage at R3C2 = {12356789} -> R34C3 = {36}, locked for C3
25a. R9C23 = [64] -> R4C2 = 3, R34C3 = [36], R3C2 = 8 (step 24), R8C12 = [39], clean-up: no 5 in R23C1
26. 41(8) cage at R3C2 = {12356789}, 2 locked for N4, 9 locked for C3 and N4
27. 18(4) cage at R1C3 contains 1 = {1269/1368/1467} (cannot be {1278} which clashes with R4C3), 6 locked for C3 and N2
27a. R7C6 = 6 (hidden single in R7)
28. 12(3) cage at R1C9 = {129/138/237} (cannot be {147} which clashes with R6C9, cannot be {156} which clashes with R56C9, ALS block, cannot be {246/345} because 2,4,5 only in R2C8), no 4,5,6
28a. 9 of {129} must be in R1C9 -> no 9 in R2C89
28b. 2, 8 of {129/138} must be in R2C8 -> no 1 in R2C8
28c. R5C9 = 6 (hidden single in C9)
29. 2 in N1 only in 20(4) cage at R1C1 = {2459/2567}
29a. 6,9 only in R1C1 -> R1C1 = {69}
29b. 5 in C1 only in R567C1, locked for 28(6) cage at R4C1, no 5 in R6C2
30. R3C89 = R1C3 + 10 (step 9), R1C3 = 1 -> R3C89 = 11 = [65/74]
30a. 1 in R3 only in R3C567, locked for 16(4) cage at R2C5, no 1 in R2C5
30b. 16(4) cage = {1249/1258/1267/1456} (cannot be {1348} because 3,8 only in R2C5, cannot be {1357} which clashes with R3C89), no 3
30c. 7 of {1267} must be in R2C5 (R3C567 cannot contain both of 6,7 which would clash with R3C8) -> no 7 in R3C57
30d. 8 of {1258} must be in R2C5, 4 of {1456} must be in R2C5 (R3C567 cannot contain both of 4,6 which would clash with R3C89), no 5 in R2C5
31. 9 in N3 only in R1C89, locked for R1 -> R1C1 = 6, clean-up: no 7 in R23C1
31a. Naked pair {49} in R23C1, locked for C1 and N1
31b. R6C2 = 4 (hidden single in N4)
32. 45 rule on R12 2 innies R2C15 = 1 outie R3C4 + 6
32a. R2C15 cannot total 8,10,15 -> no 2,4,9 in R3C4
32b. R3C4 = {67} -> R2C15 = 12,13 = [48]/{49}, no 2,7 in R2C5, 4 locked for R2
32c. Naked pair {67} in R3C48, locked for R3
33. 2 in C6 only in R123C6, locked for N2
33a. 16(4) cage at R2C5 (step 30b) = {1249/1258}
33b. 9 of {1249} must be in R23C5 (R23C5 cannot be [41] which clashes with R8C5) -> no 9 in R3C6
[Thanks Afmob for pointing out detail errors here and in step 38a; step 33 moved forward to make step 33b work.]
34. 18(4) cage at R1C3 (step 27) = {1368/1467}, no 9
34a. 4 of {1467} must be in R1C4 -> no 7 in R1C4
35. 45 rule on N2 4 remaining outies R1C78 + R23C7 = 22 = {1489/2479/2569/3478/3568} (cannot be {1678/4567} which clash with R3C8, cannot be {2389} which clashes with R2C8, cannot be {2578/3459} which clash with R3C89, cannot be {1579} which clashes with 12(3) cage at R1C9)
35a. Hidden killer pair 3,4 in R123C7 and R7C7 for C7, R7C7 = {34} -> R123C7 must contain one of 3,4 -> R1C78 + R23C7 = {1489/2479/3478/3568} (cannot be {2569} which doesn’t contain 3 or 4)
35b. R1C78 + R23C7 = {1489/2479/3568} (cannot be {3478} because 3,7,8 in C7 only in R12C7 and both of 3,4 in R123C7 would clash with R7C7)
35c. 9 of {1489/2479} must be in R1C8 -> no 2,4 in R1C8
36. 18(4) cage at R1C3 (step 34) = {1368/1467}, R3C89 (step 30) = [65/74]
36a. Consider combinations for 16(4) cage at R2C5 (step 33a) = {1249/1258}
16(4) cage = {1249}, caged X-Wing for 4,9 in R23, no other 4,9 in R23 => R3C89 = [65] => R3C4 = 7 => 18(4) cage = {1467}
or 16(4) cage = {1258} => R2C5 = 8 => 18(4) cage = {1467}
-> 18(4) cage = {1467} -> R1C4 = 4, R23C4 = {67}, locked for C4 and N2 -> R4C45 = [27], R7C45 = [82]
37. 3 in N2 only in R1C56 + R2C6, locked for 34(6) cage at R1C5, no 3 in R12C7
37a. 3 in N3 only in R12C9, locked for C9 -> R7C789 = [349], R4C8 = 5 -> R3C8 = 6
38. R1C8 = 9 (hidden single in C8)
38a. 9 in N2 only in R23C5, locked for C5 -> R9C45 = [93], R56C4 = [31], R6C9 = 7, R12C9 = [31], R2C8 = 8 (cage sum)
and the rest is naked singles.