Ed wrote:
Put on your creative hat!
I certainly needed to do that!
This puzzle turned out to be almost a “one trick pony”, but it took me a long time to spot the key step; then it needed to be used in several different ways. Nice puzzle, Ed!
Prelims
a) R23C9 = {49/58/67}, no 1,2,3
b) R45C2 = {89}
c) R45C4 = {17/26/35}, no 4,8,9
d) R56C6 = {19/28/37/46}, no 5
d) R56C8 = {16/25/34}, no 7,8,9
e) R78C1 = {39/48/57}, no 1,2,6
f) 19(3) cage at R3C7 = {289/379/469/478/568}, no 1
g) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
h) 37(8) cage at R1C2 = {12345679}, no 8
i) 41(8) cage at R5C7 = {12356789}, no 4
1. Naked pair {89} in R45C2, locked for C2
1a. 45 rule on NR1C1 2 innies R14C2 = 13 = [49/58]
2. 45 rule on NR6C8 2 innies R69C8 = 8 = [17]/{26/35}, no 4,8,9, no 1 in R9C8, clean-up: no 3 in R5C8
3. 45 rule on C1234 2 innies R69C4 = 13 = {49/58/67}, no 1,2,3
4. 45 rule on C6789 2 innies R14C6 = 10 = {19/28/37/46}, no 5
5. Law of Leftovers (LoL) for C123 two outies R45C4 must exactly equal two innies R13C3
5a. R45C4 = {17/26/35} -> R13C3 = {17/26/35}, no 4,9
6. LoL for C789 two outies R56C6 must exactly equal two innies R79C7
6a. No 4 in R79C7 -> no 4 in R56C6, clean-up: no 6 in R56C6
6b. R56C6 = {19/28/37} -> R79C7 = {19/28/37}, no 5,6
7. 45 rule on NR1C1 + NR1C3 + NR4C3 2 innies R3C5 + R5C1 = 13 = {49/58/67}, no 1,2,3
8. 45 rule on NR3C7 + NR6C8 + NR7C5 2(1+1) innies R5C9 + R7C5 = 6 = {15/24}/[33], no 6,7,8,9
9. 45 rule on C1 1 innie R9C1 = 1 outie R7C2 + 1, no 1,9 in R9C1
10. 45 rule on C9 1 innie R1C9 = 1 outie R3C8 + 1, no 1,8,9 in R1C9
11. 45 rule on C9 3 innies R145C9 = 10 = {127/136/145/235}
11a. 4 of {145} must be in R1C9 (R45C9 cannot be {14} because 9(3) cage at R3C8 cannot be 4{14}), no 4 in R45C9, clean-up: no 2 in R7C5 (step 8)
12. 45 rule on NR1C1 + NR1C3 + NR4C3 + NR6C1 2 outies R78C4 = 1 innie R3C5
12a. Max R78C4 = 9, no 9 in R78C4
[45 rule on NR6C1 3(1+2) outies R5C1 + R78C4 = 13, min R5C1 = 4 -> max R78C4 = 9, no 9 in R78C4 is simpler.]
[However my original version of step 12 helps with this step …]
13. 40(7) cage at R3C5 = {1456789/2356789}
13a. 5 in 40(7) cage only in R3C5 => R78C4 = {14/23} (step 12) or R456C5 + R6C4, locked for NR2C6 or in R7C5 -> no 5 in R7C4 (a sort of killer locking-out cages)
14. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4 -> there must be a hidden 13(3) cage in R6789C4 but R69C4 = 13 (step 3) -> R78C4 + one of R69C4 must form a hidden 13(3) cage
14a. Looking at this LoL the other way round, R69C4 = 13, two cells of the 13(3) cage cannot total 13 -> R3C5 + one cell of the 13(3) cage must total 13
14b. 8 in NR1C3 only in 13(3) cage = {148/238} => R3C5 = {59} (step 14a) or 8 in R3C5 -> R3C5 = {589}, R5C1 = {458} (step 7)
15. 40(7) cage at R3C5 = {1456789/2356789}, 6,7 locked for NR2C6, no 6,7 in R23C6 + R78C4
15a. 8,9 in 40(7) cage only in R3C5 or R4C56 + R5C5 + R6C45, locked for NR3C7 -> no 8,9 in R3C6 (CPE using NR2C6)
16. R69C4 = 13 (step 3)
16a. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4, 13(3) cage cannot contain both of 6,7 -> no 6,7 in 13(3) cage, no 6,7 in R69C4, clean-up: no 3,4 in R4C6 (step 4)
16b. 6,7 in NR1C3 only in R13C3 + R123C4, locked for 37(8) cage at R1C1, no 6,7 in R45C3
17. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4
17a. R78C4 = R3C5 (step 12)
17b. R78C4 cannot total 8 (because 13(3) cage cannot contain both of 3,5 and 8 would be in R3C5 if R78C4 totalled 8) -> R3C5 = {59}, clean-up: no 5 in R5C1 (step 7)
17c. 8 in 40(7) cage only in R4C56 + R5C5 + R6C45, locked for NR2C6, no 8 in R2C6 + R78C4
18. LoL for C1234 four outies 13(3) cage at R1C5 + R3C5 must exactly equal four innies R6789C4
18a. 8 in NR1C3 only in 13(3) cage at R1C5 = {148/238}, no 5,9
18b. R6789C4 contains one of 8,9, 13(3) cage contains 8 -> no 9 in R3C5 -> R3C5 = 5, placed for NR1C3, R5C1 = 8 (step 7), R5C2 = 9, both placed for NR4C3, R4C2 = 8, R1C2 = 5 (step 1a), both placed for NR1C1, clean-up: no 3 in R13C3 (step 5a), no 2 in R1C6 (step 4), no 6 in R1C9 (step 10), no 8 in R2C9, no 4 in R3C8 (step 10), no 1 in R4C6 (step 4), no 1 in R5C9 (step 8), no 1,2 in R6C6, no 4 in R78C1, no 7 in R7C2 (step 9), no 6 in R9C1 (step 9), no 8 in R9C4 (step 3)
18c. LoL for C123 (step 5a) R13C3 = {17/26} -> R45C4 = {17/26}
18d. R78C4 = R3C5 (step 12), R3C5 = 5 -> R78C4 = {14/23}
[Cracked. The rest is fairly straightforward.]
19. R6C4 = 8 (hidden single in C4), R9C4 = 5 (step 3), placed for NR7C5, clean-up: no 2 in R5C6, no 3 in R6C8 (step 2), no 4 in R5C8, no 4 in R7C2 (step 9)
20. Killer pair 1,2 in R45C4 and R78C4, locked for C4
20a. 1,2 in 37(8) cage at R1C3 only in R1345C3, locked for C3
21. 45 rule on C1 2 remaining innies R69C1 = 6 = {24} (cannot be {15} because 1,5 only in R6C1), locked for C1 and NR6C1, R7C2 = {13} (step 9)
21a. 19(4) cage at R1C1 = {1369} (only remaining combination), locked for C1 and NR1C1
21b. Naked pair {57} in R78C1, locked for NR6C1
21c. Naked triple {136} in R789C2, locked for C2 and NR6C1
22. 5 in NR4C3 only in 15(3) cage at R6C2 = {357/456}, no 2
22a. R6C2 = {47} -> no 4,7 in R67C3
23. R78C4 (step 18d) = {14/23} = 5 -> R8C23 = 12 = [39], R7C2 = 1, R9C23 = [68], R9C1 = 2 (cage sum), R6C1 = 4, R6C2 = 7, placed for NR4C3, clean-up: no 1 in R45C4, no 3 in R5C6, no 2,6 in R6C8 (step 2), no 1,5 in R5C8
23a. Naked pair {26} in R45C4, locked for NR4C3 and C4 -> R78C4 = [41], both placed for NR2C6, R7C5 = 3, placed for NR7C5, R67C3 = [35], R78C1 = [75], R5C9 = 3 (step 8), placed for NR3C7, clean-up: no 7 in R56C6
23b. R56C6 = [19], placed for NR3C7, R9C6 = 7, placed for NR7C5, R9C8 = 3, R6C8 = 5 (step 8), R5C8 = 2, placed for NR3C7
24. R2C3 = 7 (hidden single in NR1C1), clean-up: no 6 in R3C9
24a. R13C3 = {26} (hidden pair in C3), locked for NR1C3
24b. Naked triple {379} in R123C4, locked for NR1C3
25. R45C4 = [26], R4C6 = 6, placed for NR2C6, R6C5 = 2, placed for NR2C6
25a. R23C6 = [53] = 8 -> R2C78 = 12 = {48}, locked for R2 and NR1C7, clean-up: no 9 in R23C9
25b. R23C9 = [67], placed for NR1C7
and the rest is naked singles, without using the nonets.
The practice version certainly helped in getting used to the cage patterns, both jigsaw and killer, but I'm not sure whether the key step for the main version can be used for the practice version; I found it was definitely an extra for the main version.