This was completed some months ago. I'm posting it now for completeness.
Warning! Some of the combination work is heavy going, involving hypotheticals. If anyone wants to know how to solve V3, I'd recommend Afmob's walkthrough.
I first tried Ed's challenging CDK V3 soon after it first appeared in early 2007. At times I was struggling and without Ed's help, as discussed below, I would probably have given up. I thought I had finished it early last year and had intended to post my walkthrough but on checking I found that I'd incorrectly eliminated a combination in step 29. I've recently reworked the later steps because of that.
It's good to see that Afmob solved it using very different methods that I did.
It's hard to rate this puzzle the way I did it, particularly since some of the steps were done over a year ago, so I'll just agree with Afmob's rating of 1.75.
Here is my walkthrough, including Ed's hints and some discussion between us. A couple of steps use detailed analysis of remaining combinations. If you don't want to work through this analysis, I've provided summaries after these steps. I won't say enjoy, some of it is heavy going.
As with V2, the centre dot cells don’t necessarily form a remote nonet so there is no elimination between the centre dot cells except for ones in the same row/column.
Many thanks to Ed for his feedback on my earlier steps and the hint he gave me after step 27. In a couple of cases, steps 14a and 25, the feedback has been included and forms part of the walkthrough.
1. R12C1 = {17/26/35}, no 4,8,9
2. R1C23 = {29/38/47/56}, no 1
3. R3C12 = {39/48/57}, no 1,2,6
4. R34C7 = {18/27/36/45}, no 9
5. R4C56 = {18/27/36/45}, no 9
6. R5C34 = {49/58/67}, no 1,2,3
7. R5C67 = {29/38/47/56}, no 1
8. R67C3 = {17/26/35}, no 4,8,9
9. R6C45 = {17/26/35}, no 4,8,9
10. R7C89 = {13}, locked for R7 and N9, clean-up: no 5,7 in R6C3
11. 11(3) cage in N3, no 9
12. 24(3) cage in N7 = {789}, locked for N7, clean-up: no 1 in R6C3
13. 21(3) cage in N8 = {489/579/678}, no 1,2,3
14. 14(4) cage in N89, no 9; only remaining 1,3 in same cell -> no 8
14a. 14(4) must have 1/3 -> R8C6 = {13} (thanks Ed)
[I’d only got “Min R7C67 + R8C7 = 11 -> max R8C6 = 3”. I’d missed Ed’s better move because I hadn’t listed the combinations for the 14(4) cage.]
15. 45 rule on R1 1 innie R1C1 = 1 outie R2C7 + 3 -> R1C1 = {567}, R2C7 = {234}, clean-up: R2C1 = {123}
16. 45 rule on R9 2 outies R8C39 = 11 = [29/38/47/56/65], no 1 in R8C3, no 2,4 in R8C9
17. 45 rule on R4 1 outie R5C9 = 1 innie R4C7 + 6 -> R4C7 = {123}, R5C9 = {789}, clean-up: R3C7 = {678}
17a. 45 rule on N3 1 innie R2C8 = 1 outie R4C7 + 6 -> R2C8 = R5C9 = {789}
[Alternatively 17b. 45 rule on N3 2 innies R2C8 + R3C7 = 15]
18. 45 rule on R6 1 innie R6C3 = 1 outie R5C1 + 2 -> R6C3 = {36}, R5C1 = {14}, clean-up: no 6 in R7C3
18a. 45 rule on N7 1 outie R6C3 = 1 innie R8C2 + 2 -> R8C2 = R5C1 = {14}
[Alternatively 18b. 45 rule on N7 2 innies R7C3 + R8C2 = 6]
19. 45 rule on N8 3 innies R7C6 + R8C56 = 9 = {126/135/234}, no 7,8,9
19a. 5 of {135} must be in R7C6 -> no 5 in R8C5
20. 21(3) cage cannot have 4,5,6 in R8C4 because {89/79/78} would clash with R7C12 -> R8C4 = {789}
20a. Killer triple 7,8,9 in R7C1245, locked for R7
21. Only valid combinations for 15(4) cage in N7 are {1356/2346} = 36{15/24}
22. 45 rule on N12 2 innies R2C25 = 14 = {59/68}
23. 45 rule on N89 2 innies R8C58 = 10 = [19/28/37/46/64]
24. 45 rule on N1 3 innies R2C23 + R3C3 = 14, min R2C2 = 5 -> max R23C3 = 9, no 9 in R23C3
25. 45 rule on N4 3 innies R5C23 + R6C3 – 6 = 1 outie R4C4, min R5C23 + R6C3 = 9 (cannot be {124} because R6C3 only contains 3,6,
cannot be {134} which would clash with R5C1, thanks Ed) -> min R4C4 = 3
26. 45 rule on R4 3 innies R4C789 = 11 -> no 9 in R4C89
26a. 9 in R4 locked in 25(4) cage = 9{178/268/358/367/457}
[While reviewing the early steps, Ed commented
Just noticed a nice elim from this. I'll put it into tt since it ends up being potentially very helpful.
9 in r4c4 -> 9 cannot be in r5c23. Here's how.
a. 9 in r4c4 -> from step 25: R5C23 + R6C3 = 15.
i. 3 in r6c3 -> r5c23 = 12 but cannot be {39} -> no 9 in r5c23
ii. 6 in r6c3 -> r5c23 = 9 -> cannot have 9
b. 9 elsewhere in 25(4) must be in n4 -> no 9 in r5c23]
27. 45 rule on N47 2 outies R45C4 – 9 = 2 innies R58C2, max R45C4 = 17 -> max R58C2 = 8 -> max R5C2 = 7
At this stage I was struggling. Ed reviewed my earlier steps, including the first part of step 28, and then added
“Now, in case these things above don't unlock it, here's a big hint. The way to unlock this puzzle is combining steps 15 and 17b and seeing what this means for R1. Easy. If you want a harder way, do a similar thing for R9! If you want to make it a really easy puzzle, do both.”
Many thanks for the hint. A typical hint from Ed, just enough to provide help but still make one work to make progress. That’s how good hints ought to be! Not sure about the last sentence. There was still a lot of hard work.
28. 19(4) cage in N3 must contain {234} in R2C7, valid combinations at this stage are {1279/1369/1378/1459/1468/2359/2368/2458/2467/3457}
[When Ed reviewed this he told me that I had too many combinations, leaving me to work out which ones weren’t valid. I found that was because I hadn’t been looking at the effect of steps 15 and 17b.]
28a. There cannot be any combinations with {67}, {68} or {79} which would clash with R2C8 + R3C7, eliminating {1279/1468/2368/2467}
28b. There cannot be any combinations with 5,6,7 in R1 when 2,3,4 (respectively) are in R2C7 (step 15), eliminating {1369} and also limiting three of the other combinations to having a specific value in R2C7
28c. The remaining valid combinations, with [] indicating the value in R2C7, are {159[4]/178[3]/258[4]/259[3]/457[3]} -> no 3,6 in R1C789, R2C7 = {34}, R1C1 = {67} (step 15), clean-up: R2C1 = {12}
29. Consider each of these combinations and their effect on R1
For {1378}, R2C7 = 3, R1C789 = {178}, R1C1 = 6, R1C23 = {29), R1C456 = {345}
For {1459}, R2C7 = 4, R1C789 = {159}, R1C1 = 7, R1C23 = {38}, R1C456 = {246}
For {2359}, R2C7 = 3, R1C789 = {259}, R1C1 = 6, R1C23 = {38/47}, R1C456 = {138/147}
For {2458}, R2C7 = 4, R1C789 = {258}, R1C1 = 7, R1C23 is blocked
For {3457}, R2C7 = 3, R1C789 = {457}, R1C1 = 6, R1C23 = {29/38}, R1C456 = {138/129}
Summary of step 29: no {2458} combination in 19(4) cage in N3, no 5,6 in R1C23
[Ed said that he’d done similar analysis of hypotheticals but using 4 innies in R1, R1C1789 = 22 together with the restrictions from steps 15 and 17b.]
30. If R2C7 = 3, R34C7 <> [63] => R2C8 + R3C7 => {78} -> 19(4) cage in N3 cannot have 178[3] or 457[3] combinations.
Remaining valid combinations are {159[4]/259[3]} -> R1C789 = {159/259}, no 4,7,8 -> 5,9 locked for R1 and N3, clean-up: no 2 in R1C23, no 6 in R3C7 (step 17b), no 3 in R4C7
30a. R2C8 + R3C7 = {78}, locked for N3
30b. R5C9 = {78} (step 17a)
31. 17(3) cage in N6 must have R5C9 = {78}, valid combinations {278/368/458/467}, no 1
31a. R4C789 = 11 (step 26), R4C7 = {12} -> 17(3) cage combination {278} can only have 7 in R5C9 (cannot have [227] in R4C789) -> no 7 in R4C89
32. R3C12 = {39/57} (cannot be {48} which clashes with R1C23)
33. Killer pair 3,7 in R1C23 and R3C12, locked for N1 -> R1C1 = 6, R2C1 = 2, clean-up: no 8 in R2C5 (step 22)
33a. 1 in N1 locked in R23C3, locked for C3 and 18(4) cage -> no 1 in R23C4
34. R2C7 = 3 (step 15) -> R1C789 = {259} (step 30), locked for R1 and N3, clean-up: no 8 in R5C6
34a. 1 in R1 locked in R1C456, locked for N2
34b. 1 in C7 locked in R46C7, locked for N6
35. 18(4) cage in N12 must contain 1 = 1{278/359/368/458/467} (cannot be {1269} because no 2,6,9 in R23C3)
35a. 3 of {1359} must be in R3C4 -> no 9 in R3C4
36. 9 in C3 locked in R45C3, locked for N4
36a. 14(3) cage in N4 must have R5C1 = {14}, valid combinations are {158/167/248/347}, no 1,4 in R6C12
37. 4,9 in R6 locked in 21(4) cage = 49{17/26/35}, no 8
38. 8 in R6 locked in R6C12, locked for N4 -> 14(3) cage = 8{15/24}, no 3,6,7, clean-up: no 5 in R5C4
38a. R6C123 = 8{26/35} (step 18)
39. 25(4) cage = 9{178/268/358/367/457} (step 26a), any combinations with 8 must have R4C3 = 9, R4C4 = 8 -> cannot be {2689} because no 2,6 in R4C1 -> no 2 in 25(4) cage
39a. 25(4) cage = 9{178/358/367/457}
40. 2 in N4 locked in R56C2, locked for C2
41. Consider 14(4) cage in N89 = {1247/1256/2345} (only combinations because 1,3 only in R8C6)
If R8C6 = 1 => R8C2 = 4 => R7C3 = 2 (step 18b) => R7C67 = {456} => only valid combination for 14(4) cage in N89 = {1256}, no 7
If R8C6 = 3 => only valid combination for 14(4) cage in N89 = {2345}, no 7
-> 14(4) cage in N89 = 25{16/34}, no 7
41a. 2 of {1256} must be in R8C7 -> no 6 in R8C7
42. 45 rule on N9 1 innie R8C8 = 2 outies R78C6 + 1
42a. Min R78C6 = 5 (from combinations in step 41) -> min R8C8 = 6, clean-up: no 6 in R8C5 (step 23)
43. R7C6 + R8C56 (step 19) = {126/135/234}
43a. If {126} => R7C6 = 6, R8C56 = [21], R8C2 = 4, R7C3 = 2 (step 18b), R78C7 = [45] which gives wrong cage total in R78C67 -> R7C6 + R8C56 cannot be {126}
43b. R7C6 + R8C56 = {135/234}, no 6, 3 locked in R8C56 for R8 and N8, clean-up: no 8 in R8C9 (step 16)
44. R8C1 = {789}, R8C4 = {789} -> R8C89 must contain one of 7,8,9 -> R9C789 must contain two of 7,8,9. Combinations for the 26(4) cage in N9 are {2789/4589/4679/5678}, in the case of {5678} either 5 or 6 must be in R8C9
Here’s a discussion with Ed relating to the next step
Andrew “I looked at R9 but could only see how to make progress by doing hypotheticals on the five pairs of values for R8C39 (the discussion took place before I found step 43 which eliminated one pair of values for R8C39). This did provide progress by eliminating at least one of those pairs. Did you use hypotheticals in that way or did you have a more direct way to use r9?”
Ed “Yeah, I used the hypo's you've mentioned, not including the 15(3) in R9”
Andrew “but there is also interaction with R67C3 = [35/62] and of course with R8C39.”
Ed “True.”
Andrew “Since sending yesterday's message I haven't made any more progress and can't see how to proceed except to use those hypotheticals. However some of the steps that I made after doing R1/N3 should help to make the hypotheticals a bit simpler. I had a look at doing two hypotheticals for R7C3 rather than more of them for R8C39 but that looks very messy and appears that it doesn't produce as much useful "output information". ”
The second part of Ed’s hint suggests that a similar approach is needed for R9. The interactions between R8C2 + R7C3 and the 15(4) cage are already built into the latter which must be 36{15/24} (step 21). Other useful interactions are provided by R8C39 = 11 (step 16) and by R67C3 = [35/62]. Values for R9C789 must be consistent with step 44.
45. Consider the combinations for R8C39 and their effect on R9
For R8C39 = [29], R9C123 = {346}, R9C789 = {278}, R9C456 = {159}
For R8C39 = [47], R9C123 = [362], R9C789 is blocked
For R8C39 = [56], R9C123 = [163] (6 cannot be in R9C3 because R67C3 = [62] when R8C3 = 5), R9C789 = {479/578}, R9C456 = {258/249}
For R8C39 = [65], R9C123 = {234} (cannot be {135} because R67C3 = [35] when R8C3 = 6), R9C789 = {678}, R9C456 = {159}
46. Summarising the results of step 45
R8C39 = [29/56/65], no 4 in R8C3, no 7 in R8C9
R9C123 = [163]/{234}/{346}, no 5, no 1 in R9C2
R9C456 = {159/249/258} -> no 6,7 in R9C456
R9C789 = {278/479/578/678}
46a. 5 in N7 locked in R78C3, locked for C3, clean-up: no 8 in R5C4
47. 6 in N8 locked in R7C45, locked for R7
47a. 21(3) cage in N8 (step 13) = {678}, locked for N8
47b. 8 in R9 locked in R9C789, locked for N9, clean-up: no 2 in R8C5 (step 23)
48. 14(4) cage in N89 (step 41) = {2345} (only remaining combination) -> R8C6 = 3, clean-up: no 6 in R4C5, no 8 in R5C7, no 7 in R8C8 (step 23)
48a. Naked pair {14} in R8C25, locked for R8
49. 8 in R9 locked in R9C789 (step 46) = {278/578/678} (cannot be {479} which doesn’t contain 8), no 4,9
49a. 9 in N9 locked in R8C89, locked for R8
50. R7C7 = 4 (hidden single in N9), clean-up: no 7 in R5C6
51. Combined cage R5C3467 = 24 = {2679/4569}, 6,9 locked for R5
51a. R5C67 = {29/56} (cannot be [47] which clashes with combined cage), no 4,7
52. 15(3) cage in N2 = {249/258/267/456} (cannot be {348/357} which clash with R1C456), no 3
52a. 8 of {258} must be in R23C6 (R23C6 cannot be [52] which clashes with R7C6), no 8 in R3C5
53. 45 rule on N2 3 innies R2C45 + R3C4 = 18 = {279/369/459/567} (cannot be {378/468} which clashes with R1C456), no 8
53a. 2,3 of {279/369} must be in R3C4
53b. 6 of {567} must be in R2C5 (R23C4 cannot be {67} which clashes with R78C4)
53c. Combining steps 53a and 53b -> no 6 in R3C4
54. 18(4) cage in N12 (step 35) = 1{278/368/458} (cannot be {1359} because 3,5,9 only in R23C4, cannot be {1467} which clashes with R78C4), no 9
54a. 1,8 of {1458} must be in R23C3 -> no 4 in R23C3
54b. 2 of {1278} must be in R3C4 -> no 7 in R3C4
55. R2C23 + R3C3 = 14 (step 24) = {158} (only remaining combination) -> R2C2 = 5, R2C5 = 9 (step 22), R23C3 = {18}, locked for N1, clean-up: 3 in R1C23, no 7 in R3C12
55a. Naked pair {47} in R1C23, locked for R1
55b. Naked pair {39} in R3C12, locked for R3
55c. Naked triple {138} in R1C456, locked for N2
56. 18(4) cage in N12 (step 54) = 1{278/458}, no 6
56a. 5 of {1458} must be in R3C4 -> no 4 in R3C4
57. 45 rule on R789 4 innies R7C3 + R8C258 = 16, R8C25 = {14} = 5 -> R7C3 + R8C8 = 11 = [29/56]
57a. If R7C3 = 2 => R6C3 = 6 -> no 6 in R8C3
57b. If R7C3 = 5 => R8C8 = 6 -> no 6 in R8C3
57c. -> no 6 in R8C3
58. Naked pair {25} in R78C3, locked for N7
58a. Naked pair {25} in R8C37, locked for R8
58b. 6 in N7 locked in R9C23, locked for R9
59. 6 in C7 locked in R56C7, locked for N6
59a. 17(3) cage in N6 (step 31) = {278/458}, no 3, 8 locked for N6
59b. R4C789 = {128/245}, 2 locked for R4 and N6, clean-up: no 7 in R4C56, no 9 in R5C6
60. 45 rule on N36 2 innies R25C8 = 2 outies R56C6 + 2
60a. Min R25C8 = 10 -> min R56C6 = 8, no 1 in R6C6
61. 7 in R4 locked in R4C1234
61a. 25(4) cage (step 39a) = 9{178/367/457} (cannot be {3589} which doesn’t contain 7)
61b. 8 of {1789} must be in R4C4
61c. 3,6 of {3679} must be in R4C4 (R4C123 cannot contain both 3,6 which would clash with R6C3)
61d. 4,5 of {4579} must be in R4C4 (R4C123 cannot contain both 4,5 which would clash with 14(3) cage in N4)
61e. -> no 7,9 in R4C4
62. R4C3 = 9 (hidden single in R4), clean-up: no 4 in R5C4
62a. 7 in R4 locked in R4C12, locked for N4, clean-up: no 6 in R5C4
63. R1C3 = 7 (hidden single in C3), R1C2 = 4, R8C25 = [14], R5C1 = 1 (step 18a), R6C3 = 3 (step 18), R7C3 = 5, R7C6 = 2, R8C37 = [25], R56C2 = [28], R6C1 = 5, clean-up: no 5 in R4C6, no 6 in R5C6, no 9 in R5C7
63a. R5C67 = [56], R5C3 = 4, R4C4 = 9, R4C12 = [76], R4C4 = 3 (step 61a), R78C1 = [98], R7C2 = 7, R8C4 = 7, R3C12 = [39], R9C123 = [436], R8C8 = 6 (step 57), R8C9 = 9, R2C4 = 4, R3C4 = 5 (step 54), clean-up: no 1 in R6C5
64. R9C5 = 5 (hidden single in R9), clean-up: no 4 in R4C6
65. Naked pair {18} in R4C56, locked for R4 and N5 -> R4C7 = 2, R5C5 = 7, R5C89 = [38], R1C7 = 9, R2C8 = 8 (step 17a), R3C7 = 7, R3C56 = [26], R2C6 = 7, R23C3 = [18], R2C9 = 6, R6C7 = 1, R9C7 = 8, R6C45 = [26], R7C45 = [68], R4C56 = [18], R1C456 = [831], R9C46 = [19], R6C6 = 4, R7C89 = [13], R3C89 = [41], R4C89 = [54], R1C89 = [25], R9C89 = [72], R6C89 = [97]