Thanks for a fun puzzle Ed!
Afmob wrote:By the way, I finally got the status "Addict" which more fits I think
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Congratulations! It won't take you too long to reach Expert and Master, which are also appropriate!
Afmob's steps 2d and 3b are the sort of steps that are so easy not to spot; I missed them. Using an innie pair and an outie pair to do a 45 isn't a particularly common step. Steps 4a and 5c were also interesting. With those steps, together with Afmob saying that step 5a was difficult to spot, I felt that it should have been rated 1.25 rather than (Easy) 1.25.
Gary's R7C126 = 10 is useful although both Afmob and I got the same cage eliminations using different steps; however the only possible combinations in R7C126 do lock 5 for R7 very quickly.
I used one, fairly easy to spot, contradiction move so I'll rate this puzzle 1.25.
Ed commented that SS had two key moves that gave this puzzle a low rating. I'll be interested to see what they were. I don't think I found either of them.
Here is my walkthrough
Prelims
a) R23C9 = {15/24}
b) R34C3 = {16/25/34}, no 7,8,9
c) R4C56 = {17/26/35}, no 4,8,9
d) R6C45 = {29/38/47/56}, no 1
e) R67C7 = {49/58/67}, no 1,2,3
f) R78C1 = {18/27/36/45}, no 9
g) 11(3) cage in N2 = {128/137/146/236/245}, no 9
h) R3C567 = {289/379/469/478/568}, no 1
i) 8(3) cage at R6C2 = 1{25/34}, CPE no 1 in R45C2
j) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
k) 20(3) cage in N8 = {389/479/569/578}, no 1,2
l) R9C123 = {127/136/145/235}, no 8,9
m) 28(4) cage in N4 = {4789/5689}, 8,9 locked for N4
1. 45 rule on N1 2 outies R4C23 = 11 = {56}/[74], clean-up: no 4,5,6 in R3C3
1a. 17(3) cage at R3C1 = {179/269/278/359/368/458/467}
1b. 5 of {359/458} must be in R4C2 -> no 5 in R3C12
2. Killer pair 4,5 in R4C23 and 28(5) cage, locked for N4
2a. Killer pair 6,7 in R4C23 and 28(5) cage, locked for N4
[Alternatively 45 rule on N14 3 innies R5C3 + R6C23 = 6 = {123} or another alternative hidden triple {123} in R5C3 + R6C23. Take your pick!
]
3. 8(3) cage at R6C2 = 1{25/34}
3a. 4,5 only in R7C2 -> R7C2 = {45}
3b. 1 locked in R6C23, locked for R6 and N4
3c. R78C1 = {18/27/36} (cannot be {45} which clashes with R7C2), no 4,5
[I should also have spotted that R7C2 = {45} eliminates 4 from R9C123]
4. Naked triple {123} in R356C3, locked for C3
5. 45 rule on N9 2 outies R6C78 = 13 = {49/58/67}, no 2,3
6. 45 rule on N7 2 innies R7C23 = 1 outie R8C4 + 10, max R7C23 = 14 -> max R8C4 = 4
6a. Max R8C34 = 13 -> min R8C2 = 3
7. 45 rule on R1234 2 innies R4C19 = 11 = {47/56}/[83/92], no 1,8,9 in R4C9
8. 45 rule on R6789 2 innies R6C19 = 10 = {46}/[73/82], no 5,9, no 7,8 in R6C9
9. 45 rule on N23 1 outie R4C4 = 1 innie R3C8 + 1, no 1 in R4C4, no 9 in R3C8
10. 45 rule on N78 1 outie R6C6 = 1 innie R7C2 + 3 -> R6C6 = {78}
11. Hidden killer pair 5,9 in R6C45 and R6C78. Neither can have both 5 and 9 -> R6C45 = {29/56}, R6C78 = {49/58}, clean-up: no 6,7 in R7C7
11a. R4C56 = {17/35} (cannot be {26} which clashes with R6C45), no 2,6
12. 45 rule on R89 2 outies R67C6 = 1 innie R8C1 + 4
12a. Min R67C6 = 8 -> no 1,2,3 in R8C1, clean-up: no 6,7,8 in R7C1
12b. Min R8C1 = 6 -> min R67C6 = 10, no 1 in R7C6
12c. Max R8C1 = 8 -> max R67C6 = 12, no 6,7,8,9 in R7C6
13. 45 rule on N69 1 outie R3C8 = 1 innie R5C7, no 9 in R5C7
14. 45 rule on C123 2 innies R57C3 = 1 outie R8C4 + 8, min R57C3 = 9 -> min R7C3 = 6
15. 45 rule on N5 5 innies R4C4 + R5C456 + R6C6 = 26 and must contain 4 = {14678/23489/34568} (cannot be {14579/24569/24578} which clash with R6C45)
16. Killer pair 5,7 in R4C23 and R4C56, locked for R4, clean-up: no 4,6 in R3C8 (step 9), no 4,6 in R4C19 (step 7), no 4,6 in R5C7 (step 13)
17. 7 in N6 locked in R5C789, locked for R5
18. R6C6 = R7C2 + 3 (step 10)
18a. 45 rule on N14 R7C2 = R5C3 + 2
18b. -> R6C6 = R5C3 + 5
19. R4C4 + R5C456 + R6C6 (step 15) = {14678/23489/34568}
19a. 8 of {23489} must be in R6C6 => R5C3 => 3 (step 18b) => R4C4 = 3 => R3C8 = 2 (step 9) => R5C7 = 2 (step 13) -> R4C4 + R5C456 + R6C6 cannot be {23489}
19b. R4C4 + R5C456 + R6C6 = {14678/34568}, no 2,9, 6 locked for N5, clean-up: no 1,8 in R3C8 (step 9), no 1,8 in R5C7 (step 13), no 5 in R6C45
20. Naked pair {29} in R6C45, locked for R6, clean-up: no 8 in R6C1 (step 8), no 4 in R6C78, no 4,9 in R7C7
20a. Naked pair {58} in R6C78, locked for R6 and N6 -> R6C6 = 7, R7C2 = 4 (step 10), clean-up: no 5 in R3C8 (step 13), no 6 in R4C4 (step 9), no 1 in R4C56, no 3 in R6C9 (step 8)
21. R4C2 = 7 (hidden single in R4), R4C3 = 4 (step 1), R3C3 = 3, R5C3 = 2, R6C23 = [31], R6C19 = [64]; clean-up: no 2 in R23C9, no 3 in R7C1
22. Naked pair {35} in R4C56, locked for R4 and N5 -> R4C4 = 8, R3C8 = 7 (step 9), R5C7 = 7 (step 13), R4C19 = [92]
22a. Naked pair {16} in R4C78, locked for N6
23. R9C1 = 3 (hidden single in C1), R9C23 = 7 = [16/25]
24. Naked pair {15} in R23C9, locked for C9 and N3
25. R4C4 = 8 -> R123C4 = 11
25a. 45 rule on N2 3 innies R2C6 + R3C56 = 23 = {689}, locked for N2
26. R3C567 = {289/469} -> R3C7 = {24}, 9 locked in R3C56, locked for R3 and N2
27. R4C2 = 7 -> R3C12 = 10 = {28}/[46], no 1
27a. Killer pair 2,4 in R3C12 and R3C7, locked for R3
28. R123C4 = 11 (step 25) = {137/245}
28a. R3C4 = {15} -> no 1,5 in R12C4
29. R2C678 = {369/468}, no 2, 6 locked for R2
30. R1C789 = {369/468}, no 2, 6 locked for R1 and N3 -> R2C6 = 6 (step 29)
31. R3C7 = 2 (hidden single in N3), clean-up: no 8 in R3C12 (step 27) -> R3C12 = [46]
32. 18(3) cage in N1 = {189/279}, no 5, 9 locked for N1
32a. 1,2 only in R2C2 -> R2C2 = {12}
32b. 9 locked in R12C3, locked for C3
33. Naked pair {12} in R29C2, locked for C2
33a. Naked pair {58} in R15C2, locked for C2 -> R8C2 = 9
33b. R8C34 = 7 = [52/61]
33c. Naked pair {56} in R89C3, locked for C3
34. R7C345 = {178/268/358/367} (cannot be {169/259} because R7C3 only contains 7,8), no 9
35. 9 in R7 locked in R7C89, locked for N9
35a. R6C8 = [829] (only remaining permutation), R5C89 = [93], R67C7 = [58], R7C3 = 7, R78C1 = [18], R5C12 = [58], R9C23 = [25] (step 23), R12C2 = [51], R23C9 = [51], R3C4 = 5, R8C34 = [61] (step 33b)
35b. R3C4 = 5 -> R12C4 = {24} (step 28), locked for C4 and N2 -> R5C4 = 6, R6C45 = [92], R7C4 = 3, R7C56 = [65], R9C4 = 7, R8C56 = [42], R5C56 = [14], R4C56 = [53], R1C6 = 1, R8C78 = [35], R89C9 = [76], R1C9 = 8, R12C3 = [98]
36. R1C789 (step 30) = {468}, 4,6 locked for R1 and N3
and the rest is naked singles and a couple of cage sums
7 5 9 2 3 1 6 4 8
2 1 8 4 7 6 9 3 5
4 6 3 5 8 9 2 7 1
9 7 4 8 5 3 1 6 2
5 8 2 6 1 4 7 9 3
6 3 1 9 2 7 5 8 4
1 4 7 3 6 5 8 2 9
8 9 6 1 4 2 3 5 7
3 2 5 7 9 8 4 1 6