Nice puzzle for your first one Peter! Not too difficult but the combination of killer with noncon requires one to think a bit differently to make proper use of the noncon feature.
Here is my walkthrough.
Clean-up is used in various steps, using the combinations in steps 1 to 10 for further eliminations from these two cell cages; it is also used for the two cell split sub-cages that are produced by applying the 45 rule. In some of the later steps, clean-up is followed by further moves and sometimes more clean-up. Non-consecutive (noncon) eliminations have been given as separate sub-steps for clarity.
1. R1C34 = {29/38/47} (cannot be {56} which are consecutive), no 1,5,6
2. R12C5 = {29/38/47} (cannot be {56} which are consecutive), no 1,5,6
3. R12C8 = {16/25} (cannot be {34} which are consecutive), no 3,4,7,8,9
4. R12C9 = {17/26/35}, no 4,8,9
5. R23C1 = 10(2), no 5
6. R4C12 = {17/26/35}, no 4,8,9
7. R4C67 = {17/26/35}, no 4,8,9
8. R67C2 = {29/38/47} (cannot be {56} which are consecutive), no 1,5,6
9. R78C9 = {59/68}
10. R89C5 = {13}, locked for C5 and N8, clean-up: no 8 in R12C5
10a. Noncon, no 2 in R7C5, R8C46 and R9C46
11. 11(3) cage in N14, no 9
12. 9(3) cage in N69 = {126/135} (cannot be {234} which are consecutive) = 1{26/35}
13. 2 in N8 locked in R7C46, locked for R7, clean-up: no 9 in R6C2
13a. Only 2 remaining 2 in 9(3) cage in N69 in R6C7 -> no 6 in R6C7
14. 45 rule on R9 2 innies R9C15 = 9 -> R9C1 = {68}
14a. Noncon, no 7 in R8C1 and R9C2
15. 45 rule on C9 2 innies R39C9 = 7 = {16/25/34}, no 7,8,9
16. 45 rule on R123 2 outies R4C38 = 7 = {16/25/34}, no 7,8,9
17. Killer triple 1/2/3 in R4C123678 for R4
18. 16(3) cage in N36, valid combinations with R3C9 + R4C8 = {123456} are {169/259/268/349/358/457} (cannot be {367} because 6,7 would be consecutive) -> R3C8 = {789}
18a. Noncon, no 8 in R3C7 [Thanks Peter. Missed that one]
19. 45 rule on R789 2 outies R6C27 = 11 = [83] (only possible combination), R7C2 = 3, R7C78 = {15}, locked for R7 and N9, clean-up: no 5 in R4C1, no 4 in R4C3, no 5 in R4C6, no 9 in R78C9 = {68}, locked for C9 and N9, clean-up: no 2 in R12C9
19a. Noncon, no 7,9 in R5C2 and R6C13, no 2,4 in R5C7 and R6C68, no 4 in R7C13, no 2,4 in R8C2, no 7 in R6C9 and R8C8
19b. No 1 in R4C8 (from combinations in step 18), clean-up: no 6 in R4C3
20. 45 rule on C123 3 outies R169C4 = 20, no 1,2, clean-up: no 9 in R1C3
21. 45 rule on C1234 3 outies R347C5 = 20, no 2
22. 45 rule on C6789 2 innies R56C6 = 10, no 5, no 2,6,7,8 in R5C6
22a. R56C5 = 10, no 5,7,9, no 2 in R5C5
23. Combinations for R789C1 with R9C1 = {68} are {189/468} (cannot be {567} because 5,6 would be consecutive) -> R7C1 = {689}, R8C1 = {14}
[8 locked in R79C1. Thanks Peter. Missed that one too. I haven’t changed the walkthrough for that because it gets locked in the next step.]
24. 18(3) cage in N4 max R5C2 + R6C1 = 11 -> min R5C1 = 7, only valid combination {459} (cannot be {567} because 6,7 would be consecutive) -> R5C1 = 9, R5C2 + R6C1 = {45}, locked for N4, clean-up: no 1 in R23C1, no 3 in R4C1, no 2 in R4C8, no 1 in R6C6
24a. R79C1 = {68}, locked for C1 and N7 -> R8C1 = 4, R6C1 = 5, R5C2 = 4, clean-up: no 2 in R23C1, no 2 in R4C2, no 6 in R6C56
24b. Noncon, no 3 in R5C3, no 5 in R8C2
24c. R23C1 = {37}, locked for C1 and N1, clean-up: no 4,8 in R1C4, no 1 in R4C2
25. R4C3 = 3 (hidden single in N4) -> R3C23 = 8 = [26] (2 cannot be next to 3)
[I’d worked that out, then typed R3C23 = [62] and put that in my diagram! Thanks Peter for correcting me on this.], clean-up: no 9 in R1C4, no 5 in R4C7, R4C8 = 4
25a. Noncon, no 1 in R2C2, no 5 in R2C3, no 5,7 in R3C4, no 3 in R3C1, no 5 in R4C9 and R5C8, no 2 in R5C3
26. R1C1 = 1 (naked single) -> R4C12 = [26], clean-up: no 6 in R2C8, no 7 in R2C9
26a. R3C1 = 7 (naked single), R2C1 = 3, clean-up: no 5 in R1C9
26b. R4C67 = {17}, locked for R4 -> R4C9 = 9, R56C9 = [52] (only valid combination)
26c. R4C45 = {58}, locked for N5 -> R5C4 = 2, R56C5 = [64], clean-up: no 7 in R12C5 = {29}, locked for C5 and N2, R34C5 = {58}, locked for C5 -> R7C5 = 7
26d. Noncon, no 6,8 in R7C46
26e. R7C3 = 9, R7C4 = 4, R7C6 = 2 (naked singles), R8C4 = 6
26f. Noncon, no 5 in R8C3, no 1 in R7C7 -> R7C78 = [51]
27. 45 rule on N1 2 outies R1C4 + R4C3 = 6 -> R1C4 = 3, R1C3 = 8, R2C3 = 4
27a. Noncon, no 9 in R1C2, no 5 in R2C2 -> R12C2 = [59]
and the rest is naked singles, naked pairs, cage sums, simple and noncon elimination
If anyone is interested, there's a regular noncon with only 12 givens at
http://www.sudoku.org.uk/discus/message ... 1157689006
2818
4613:4613
2056
4864:4864
2820:4622:4613
3340
2075
2080
4121:4131:4644:4644:4390
3882:4131:4644
4390:4390:5160:5160
3882:4131:4662
4662:4664:4664:4409
4923:4923:4923
3657
