SudokuSolver Forum

Est = Estimated rating by puzzle maker
E = Easy
H = Hard
M = Mike (mhparker)
Score = SudokuSolver v3.3 score, rounded to nearest 0.05
! indicates that the Score has changed at least 0.10 from the SS v3.2.1 score
** in the Afmob column indicates that these puzzles were made by him,
for these ones the estimate is his rating.

3x3::k:4096:4096:6658:3587:3587:6405:3846:3846:3846:4096:6658:6658:6658:3587:6405:6415:5136:5136:4370:4370:6658:8213:6405:6405:6415:5136:8218:4370:5660:8213:8213:3615:6415:6415:5136:8218:5660:5660:5660:8213:3615:1321:1321:8218:8218:3117:5660:8213:8213:3615:5170:5170:5172:8218:3117:3117:5688:8213:3898:3898:5170:5172:8218:5439:5688:5688:5688:4419:3898:5170:5172:5172:5439:5439:5688:4419:4419:3898:3918:3918:3918:

Thanks Afmob for A126, which I found more challenging than the estimated rating. The cage pattern could be very challenging with different cage totals so if there's a planned V2 I wouldn't be surprised if it was a Killer-X.

I'll rate it at 1.25 because, although my steps were technically at the 1.0 level, some of them took time to find.

Here is my walkthrough.

Prelims

a) R5C67 = {14/23}
b) 21(3) cage in N7 = {489/579/678}, no 1,2,3

1. 45 rule on C789 3 outies R456C6 = 17
1a. R5C6 = {1234} -> no 1,2,3,4 in R46C6

2. 45 rule on C6789 2 outies R37C5 = 12 = {39/48/57}, no 1,2,6

3. 45 rule on C89 2 outies R19C7 = 12 = {39/48/57}, no 1,2,6

4. 45 rule on N1 2 outies R2C4 + R4C1 = 14 = {59/68/77}, no 1,2,3,4

5. 45 rule on N2 2 innies R23C4 = 6 = [51], R4C1 = 9 (step 4), clean-up: no 7 in R7C5 (step 2)
5a. R4C1 = 9 -> R3C12 = 8 = {26/35}, no 4,7,8

6. 45 rule on C1234 2 innies R19C4 = 12 = {39/48}, no 2,6,7

7. 45 rule on N8 2 innies R78C4 =13 = {67} (cannot be {49} which clashes with R19C4), locked for C4 and N8
7a. 17(3) cage in N8 = {359/458}, no 1,2, 5 locked in R89C5, locked for C5 and N8, clean-up: no 7 in R3C5 (step 2)
7b. 1,2 in N8 locked in R789C6, locked for C6, clean-up: no 3,4 in R5C7

8. 2 in N2 locked in 14(3) cage = {239/248}, no 6,7
8a. R456C5 = {167} (hidden triple in C5), locked for N5
8b. 2 in C4 locked in R456C4, locked for 32(7) cage

9. 45 rule on N7 2 outies R6C1 + R8C4 = 10 -> R6C1 = {34}
9a. 45 rule on N4 3 remaining innies R4C3 + R6C13 = 14 = {347/356}, no 8, 3 locked for N4

10. 32(7) cage at R3C4 = {1234679/1235678} (cannot be {1234589} because R7C4 only contains 6,7)
10a. 45 rule on N5 R456C6 = 17 (step 1) -> R456C4 = 14 = {239} (cannot be {248} which clashes with 32(7) cage), locked for C4, N5 and 32(7) cage -> R5C6 = 4, R5C7 = 1
10b. 32(7) cage at R3C4 = {1234679} (only remaining combination), no 5, clean-up: no 6 in R46C3 (step 8)
10c. Naked pair {47} in R46C3, locked for C3, N4 and 32(7) cage -> R6C1 = 3, R7C4 = 6, R8C4 = 7, clean-up: no 5 in R3C2 (step 5a)
10d. R6C1 = 3 -> R7C12 = 9 = {18/27/45}, no 9
10e. 1 in N4 locked in R46C2, locked for C2, clean-up: no 8 in R7C1 (step 10d)

11. 17(3) cage in N8 (step 7a) = {458} (cannot be {359} because R9C4 only contains 4,8), locked for N8, clean-up: no 4,8 in R3C5 (step 2)
11a. Naked pair {39} in R37C5, locked for C5
11b. Naked triple {248} in 14(3) cage in N2, locked for N2
11c. 4 in R3 locked in R3C789, locked for N3, clean-up: no 8 in R9C7 (step 3)

12. 26(5) cage at R1C3 = {13589/24569/34568} (cannot be {14579/24578} because 4,7 only in R2C2, cannot be {23579} which clashes with R3C12), no 7
12a. 4 of {24569/34568} must be in R2C2 -> no 2,6 in R2C2
12b. 7 in N1 locked in 16(3) cage = {178/457} (cannot be {367} which clashes with R3C12), no 2,3,6,9
12c. 9 in N1 locked in 26(5) cage (step 12) = {13589/24569} [1/2 in C3]

13. 3 in N7 locked in 22(5) cage at R7C3 = {12379/13567/23467}, no 8
13a. 9 of {12379} must be in R789C3 (R789C3 cannot be {123} which clashes with R123C3), no 9 in R8C2

14. 45 rule on C12 2 innies R28C2 = 1 outie R5C3 + 2
14a. Min R28C2 = 5 -> no 2 in R5C3
14b. Max R5C3 = 8 -> max R28C2 = 10, no 9 in R2C2
14c. 9 in N1 locked in R1C123, locked for C3
14d. R9C2 = 9 (hidden single in C2), clean-up: no 3 in R1C7 (step 3)
14e. R9C2 = 9 -> R89C1 = 12 = [48/57/84], no 6, no 5 in R9C1

15. R9C789 = {267} (only remaining combination, cannot be {168} because R9C7 only contains 3,4,5,7, cannot be {258/348/357/456} which clash with R9C145) -> R9C7 = 7, R1C7 = 5 (step 3), R9C89 = {26}, locked for R9 and N9, clean-up: no 5 in R8C1 (step 14e)
15a. Naked pair {48} in R89C1, locked for C1 and N7, clean-up: no 1,5 in R7C12 (step 10d)
15b. Naked pair {17} in R12C1, locked for C1 and N1 -> R7C12 = [27], R1C2 = 8 (step 12b), R1C45 = [42], R2C5 = 8, R9C4 = 8, R89C1 = [84], R89C5 = [45], clean-up: no 6 in R3C2 (step 5a)
15c. R8C6 = 2 (hidden single in R8)

16. R3C1 = 5 (hidden single in N1), R3C2 = 3 (step 5a), R2C2 = 4, R5C1 = 6, R5C5 = 7, R37C5 = [93], R79C6 = [91], R9C3 = 3
16a. Naked triple {125} in R456C2, locked for C2 and N4 -> R5C3 = 8, R8C2 = 6

17. R1C789 = {159/357}, no 6
17a. Killer pair 1,7 in R1C1 and R1C89, locked for R1

18. 20(4) cage at R6C6 = {2459/3458} (cannot be {2369} because R6C6 only contains 5,8, cannot be {2468} because R8C7 only contains 3,9), no 6 -> R6C6 = 5, R4C6 = 8
18a. 3,9 of 20(4) cage must be in R8C7 -> no 9 in R6C7

19. 25(4) cage at R2C7 = {2689} (only remaining combination), -> R2C7 = 9, R8C7 = 3, R34C7 = {26}, locked in R234C7, locked for C7, clean-up: no 1 in R1C89 (step 17)
19a. Naked pair {37} in R1C89, locked for R1 and N3 -> R12C1 = [17], R123C6 = [637], R1C3 = 9
19b. Naked pair {26} in R3C37, locked for R3

20. 45 rule on N3 2 remaining outies R4C78 = 1 innie R3C9 + 7
20a. Max R4C78 = 13 -> no 8 in R3C9 -> R3C89 = [84]

21. 1 in R2 locked in R2C89, locked for 20(4) cage = {1568} (only remaining combination, cannot be {1478} because 4,7 only in R4C8) -> R4C8 = 5, R2C89 = {16}, locked for R2 and N3
21a. R23C3 = [26], R34C7 = [26], R46C5 = [16], R456C2 = [251], R4C4 = 3, R4C9 = 7, R1C89 = [73], R46C3 = [47]
21b. R5C8 = 3 (hidden single in R5)

22. 32(6) cage at R3C9 = {134789} (only remaining combination) -> R567C9 = [981]

and the rest is naked singles.

It's surprising that Afmob's new program took a long time to solve this puzzle. Despite my introductory comments, this wasn't a long solving path.

3x3:d:k:5121:5121:6658:4105:4105:4363:4367:4367:4367:5121:6658:6658:6658:4105:4363:4367:6161:6161:2819:2819:6658:7688:4363:4363:2835:2835:6161:2819:6150:7688:7688:4877:6162:6162:2835:6161:6150:6150:6150:7688:4877:6162:5397:5397:5397:3076:6150:7688:7688:4877:6162:6162:4628:4624:3076:3076:7175:7688:5132:5132:4628:4628:4624:4357:7175:7175:7175:3338:5132:4878:4624:4624:4357:4357:7175:3338:3338:5132:4878:4878:4878:

Andrew

We haven't had a "tag" solution for some time. Ed has suggested to me that we should start one for A126 V2 with me posting the starting steps, then he will add some more and then others are welcome to join in with further moves. As puzzle creator, Afmob's comments and suggestions will be very welcome after we've finished or if we get stuck.

Here are my starting steps

This is a Killer-X. If I manage to fix any cells on the diagonals I'll add "locked for D/" or "locked for D\". Even though this isn't necessary, I hope that others taking part in this "tag" will also do this. It makes it easier for those of us who do our own manual eliminations.

Prelims

a) 20(3) cage in N1 = {389/479/569/578}, no 1,2
b) 11(3) cage at R3C1 = {128/137/146/236/245}, no 9
c) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
d) R456C5 = {289/379/469/478/568}, no 1
e) R5C789 = {489/579/678}, no 1,2,3

1. 45 rule on C6789 2 outies R37C5 = 9 = {18/27/36/45}, no 9

2. 45 rule on C789 2 innies R46C7 = 7 = {16/25/34}, no 7,8,9

3. 45 rule on N3 2 outies R4C89 = 7 = {16/25/34}, no 7,8,9

4. 45 rule on N9 2 outies R6C89 = 10 = {19/28/37/46}, no 5

5. 45 rule on N1 2 outies R2C4 + R4C1 = 12 = [48/57/66/75/84/93], no 1,2,3 in R2C4, no 1,2 in R4C1
5a. 45 rule on N1 1 outie R2C4 = 2 innies R3C12 + 1
5b. Max R3C12 = 8, no 8

6. 45 rule on N7 2 outies R6C1 + R8C4 = 12 = {39/48/57}/[66], no 1,2
6a. 45 rule on N7 1 outie R8C4 = 2 innies R7C12 -> max R7C12 = 9, no 9

7. 45 rule on N2 2 innies R23C4 = 12 = [48/57/75/84/93], no 6, no 1,2,9 in R3C4, clean-up: no 6 in R4C1 (step 5)

8. 45 rule on N8 2 innies R78C4 = 12 = {39/48/57}, no 6, no 1,2 in R7C4, clean-up: no 6 in R6C1 (step 6)

9. 45 rule on C1234 2 innies R19C4 = 12 = {39/48/57}, no 1,2,6

10. Hidden triple {126} in R456C4, locked for N5 and 30(7) cage at R3C4
10a. R456C5 = {379/489}, no 5, 7 locked for C5 and N5, clean-up: no 2 in R37C5 (step 1)
10b. R456C6 = {359/458}, 5 locked for C6 and 24(5) cage at R4C6, clean-up: no 2 in R46C7 (step 2)
10c. R46C7 = {16} (cannot be {34} which clashes with R456C6), locked for C7 and N6, clean-up: no 4,9 in R6C89 (step 4)
10d. R5C789 = {489/579}, 9 locked for R5
10e. 11(3) cage at R3C7 = {128/137/236/245} (cannot be {146} because 1,6 only in R3C8)
10f. 1,6 of {128/137/236} must be in R3C8 -> no 3,7,8 in R3C8
10g. Max R4C9 = 5 -> min R2C89 + R3C9 = 19, no 1

11. 30(7) cage at R3C4 = {1234569}, no 7,8, clean-up: no 4,5 in R2C4 (step 7), no 7,8 in R4C1 (step 5), no 4,5 in R8C4 (step 8), no 7,8 in R6C1 (step 6)
11a. Naked quad {3459} in R46C13, locked for N4
11b. 11(3) cage at R3C1 = {137/146/236/245}
11c. 3 of {137/236} must be in R4C1 -> no 3 in R3C12

12. 3 in R5 locked in R5C56, locked for N5
12a. Hidden killer pair 4,5 in R5C56 and R5C789 for R5 -> R5C56 must contain one of 4,5 -> R5C56 = {345}
12b. R456C5 (step 10a) = {379/489}
12c. R5C5 = {34} -> no 4 in R46C5

13. 2 in C5 locked in R1289C5
13a. 45 rule on C1234 4 outies R1289C5 = 17 = {1259/1268/2456} (cannot be {2348} which clashes with R5C5), no 3
13b. R12C5 cannot be {49/58} which clash with R1289C5 -> no 3 in R1C4, clean-up: no 9 in R9C4 (step 9)
13c. 16(3) cage in N2 cannot be [448] -> no 4 in R1C4, clean-up: no 8 in R9C4 (step 9)

14. 18(3) cage at R6C8 = {189/279/369/378/468/567} (cannot be {459} because R6C8 only contains 2,3,7,8)
14a. 6 of {468/567} only in R7C8 -> no 4,5 in R7C8

15. 45 rule on N12 1 outie R4C1 = 1 innie R3C4
15a. 45 rule on N78 1 outie R6C1 = 1 innie R7C4


I've also got the following un-numbered steps which can be included later when they become useful. Currently they don't provide any eliminations.

Hidden killer pair 1,2 in 26(5) at R1C3 and 11(3) cage at R3C1 for N1 -> 26(5) cage at R1C3 must contain one of 1,2 = {13589/13679/14579/14678/23489/23579/23678/24569/24578} (cannot be {12689/34568}

17(4) cage in N2 = {1259/1268/1349/1367/1457/2348/2357/2456} (cannot be {1358} which clashes with R23C4)

20(4) cage in N8 = {1289/1379/1469/1478/1568/2369/2468/2567} (cannot be {2378/2459/3458/3467} which clash with R78C4)


Ed

Thanks for getting us started Andrew. Actually, you found rather a lot compared to my miserly extras. I have no problem if this one hangs around for a good while since I'm not planning a V2 for the next Assassin and solving time is scarce.

I'd rather we don't get into hypotheticals. Let it sit if needs.

16. "45" r1234: r3c4 + 7 = r4c189
16a. ->r4c189 = 10, 11, 12
16b. from candidates (2345) which sum to 14 =>from subtraction must have 5
16c. 5 locked for r4

17. r456c6 = h17(3) = {359/458}: 9 in {359} must be in r4c6 -> no 9 r6c6

18. CPE on 9 in 30(7)n2 -> no 9 in r7c3

Should be here (select, copy and paste into A126 V2 in SudokuSolver or Jsudoku)


Glyn

Not much time to participate but this one leapt out. Only possible if Uniqueness is assumed. Available if desperate
30(5) cage must contain {126} in r456c4. To avoid UR(16)r46c47 must have either 1 or 6 in r5c4 => r5c4<>2.
2's of row 5 locked in box 4 => r46c2<>2.

NOTE I'll thank Para here for pointing out that Uniqueness cannot be applied here due to the diagonals.


Para

You can't use that UR as R46C4 are placed on the diagonals.

Here's a placement.

19. 3 in N6 is either R4C89 = {34} or R6C89 = {37}
19a. 19(3) @ R4C5 = [937] + R4C3 blocks both options
19b. 19(3) @ R4C5 = [847] + R4C36 blocks both options
19c. 19(3) @ R4C5 combination [937/847] blocked: 19(3)= [739/748] -> R4C5 = 7

[edit]
Here's some more and 3 more placements (if i didn't make any mistakes)

20. 5 in N6 is either R4C89 = {25} or R5C789 = {579}
20a. h17(3) @ R4C6 = [854] + R4C247 blocks both options
20b. h17(3) @ R4C6 = [935/845/458] -> R6C6: no 4
20c. 4 in R6 locked for N4 -> R4C13: no 4
20d. Clean up: R2C4: no 8 -> R3C4: no 4
20e. 4 in C4 locked for N8
20f. CPE: 4 in 30(7) @ R3C4 -> R7C3: no 4
20g. Clean up: R3C5: no 5

21. 16(3) @ R1C4 = [9]{16}/[8]{26}/[7]{18/45}: {259} blocked by R23C4{5|9} -> R1C4: no 5; R12C5: no 9
21a. Clean up: R9C4: no 7

22. 13(3) @ R8C5 = [3]{28}/[4]{18}/[5]{26}: [3]{19} blocked by 16{3} @ R1C4(with R19C4 = 12) -> R89C5: no 5,9
22a. R6C5 = 9(hidden single); R5C5 = 3, R4C3 = 9 (hidden single)
22b. Naked triple {458} in R456C6 -> locked for C6
22b. Clean up: R8C4: no 3(3 locked for D/ and D\), R37C5: no 6

23. 11(3) @ R3C1 = {17/26}[3]/{24}[5]: R3C12: no 5

24. 17(4) @ R1C6 = [8]{126}/[4]{139}: {1367} blocked by R23C4, {2348} blocked because 4,8 only in R3C5: no 7; 1 locked in R123C6 for C6 and N2
24a. 7 in N2 locked for C4; CPE: R1C3: no 7
24b. Clean up: R7C5: no 8; R6C1: no 5; R7C4: no 5
24d. CPE on 5 in 30(7) @ R3C4: R3C3: no 5
24c. Of course then 20(4) @ R7C5 = [1]{379}/[5]{267}

25. 16(3) @ R1C4 = [8]{26}/[7]{45}: no 9
25a. Clean up: R9C4: no 3
25b. 3 in C4 locked for 30(7) @ R3C4
25c. 3 in N4 locked for C1

Moves not necessary with later post by me
26. Killer Quad {3458} in R6C13689 -> R6C2: no 8

27. Hidden killer pair {45} in R4C1689 -> R4C16 needs exactly one of {45}: R4C16 = [58/34]
27a. R3C45 = [54/38]: other combos blocked by N2
27b. R3C4 = R4C1 (I/O difference N12) -> distant naked pair R3C5 + R4C6 {48} -> R3C7: no 4,8(over D/)



Andrew

It's good to see that we now several participants in this "tag". Hopefully we'll get more as it progresses.

I like the way that Ed used the subtraction combo in step 16b. It's something I've seen in WTs by nd and udosuk. I must learn to look out for it since in a case like this it's simpler and clearer than a string of combinations.

An alternative way to do step 16 is
R4C1 = {345}, if R4C1 = {34} => R4C89 = {25} -> 5 locked in R4C189 for R5
I suppose that's technically a chain but it's very easy to see; I ought to have seen it earlier before I posted the starting steps.

I've edited my starting steps slightly, moving the original step 15 to step 10g so that I could add innies-outies for N12 and for N78. I think one of those has already been used in Para's step 27b.

Para's combination and permutation analysis has started to get us into the difficult part of the puzzle. Great stuff! I've sent Para a message off-forum with a few suggestions for simplication and clarification.


Andrew (further post)

I've continued using techniques similar to some of Para’s moves for the next few steps

28. 11(3) cage at R3C7 = {137/245} (cannot be {146} (eliminated in step 10e), cannot be {236} which clashes with 11(3) at R3C1 = {24}5), no 6
28a. {245} cannot be [254] => R4C89 = [43] => R3C7 clashes with 11(3) at R3C1 = {24}5
28b. {245} cannot be [524]=> R4C89 = [43] => R3C8 clashes with 11{3} at R3C1 = {24}5
28c. -> 11(3) cage at R3C7 = [245/542/713], no 2,5 in R3C8, no 4 in R4C8, clean-up: no 3 in R4C9

29. R7C45 = [35/41] other permutations blocked by combos in N8
29a. R6C1 = R7C4 -> 12(3) cage at R6C1 cannot be 3{45} which clashes with R7C45
29b. {345} in 12(3) cage at R6C1 can only be [453]
29b. -> no 4 in R7C1, no 4,5 in R7C2

30. Hidden killer pair 3,8 in 20(3) cage and 26(5) cage at R1C3 for N1 -> either 20(3) cage must be {389} or 26(5) cage at R1C3 must contain both of 3,8
30a. From the un-numbered starting steps 26(5) cage at R1C3 must contain one of 1,2
30b. 26(5) cage at R1C3 = {13589/14579/23489/23678/24569}
30c. 9 of {14579} must be in R2C4 (because {1459} clashes with 20(3) cage), 7,9 of all other combinations must be in R2C4 -> no 9 in R2C2

[When I checked through the "tag" walkthrough later I realised that the first part of my step 30 is flawed because I hadn't properly considered that the 20(3) cage might be {578} and the 26(5) cage {13679} with 7 in R2C4.

On looking further I found a short chain which seems to sort things out
20(3) cage = {578} => 26(5) cage = {13679} (only combination which doesn’t clash with {578}) with R2C4 = 7 => R1C4 = 8, R3C12 = {24} => R3C45 = [38] (step 27a) clashes with R1C4

Can now continue as if the basic assumption in step 30 was correct and the combinations in step 30b are correct.

In fact the above chain can simplify things further because it eliminates {578} from 20(3) cage which must therefore contain 9, locked for N1.]


And now some more placements

31. 26(5) cage at R1C3 = {13589/14579/23489/24569} (cannot be {23678} => R2C4 = 7 => R4C1 = 5 => R4C12 = {24} clashes with 26(5) cage) -> no 7 in R2C4
31a. R2C4 = 9, R8C4 = 8, R1C4 = 7, clean-up: R3C4 = 3, R4C1 = 3, R6C13 = [45], R79C4 = [45], R7C5 = 1, R3C5 = 8, R456C6 = [458], 4 locked for D/, 8 locked for D\, no 7 in R5C789
31b. Naked pair {25} in R4C89, locked for R4 and N6
31b. Naked pair {37} in R6C89, locked for R6
31c. Naked triple {489} in R5C789, locked for R5
31d. Naked pair {26} in R89C5, locked for C5 and N8
31e. R4C2 = 8 (hidden single in R4)

After this it's straightforward steps

32. 11(3) cage at R3C7 (step 28c) = [245/542] -> R3C8 = 4, R3C7 = {25}
32a. Naked quad {1267} in R3C1236 -> R3C79 = [59], 5 locked for D/, R4C8 = 2, R4C9 = 5

33. R34C9 = [95] = 14 -> R2C89 = 10 = [73/82]
33a. 1 in N3 locked in R1C89, locked for R1

34. R6C1 = 4 -> R7C12 = [26/53/62], no 7,8

35. R9C1 = 8 (hidden single in N7), locked for D/ -> R2C89 = [73], 7 locked for D/, R6C89 = [37]
35a. R8C1 + R9C2 = 9 = [27/54/63/72], no 1,9, no 6 in R9C2
35b. Naked pair {28} in R12C7, locked for C7 and N3
35c. Naked pair {16} in R1C89 -> R1C6 = 2, R12C7 = [82]

36. R1C1 = 9 (hidden single in C1), locked for D\, R7C7 = 7, locked for D\
36a. R1C2 + R2C1 = 11 = [56], R23C6 = [16], R12C5 = [45], R1C3 = 3, R2C23 = [48], 4 locked for D\, R3C3 = 2 (step 31), locked for D\, R7C3 = 6, locked for D/, R1C9 = 1, locked for D/, R6C4 = 2, locked for D/, R9C9 = 6, locked for D\, R4C4 = 1, locked for D\

37. R6C1 = 4 -> R7C12 = 8 = [53]

and the rest is naked singles.

Many thanks Afmob for a challenging variant!

It's hard to rate a puzzle like this when it has been solved as a "tag". At least 1.75 but possibly not 2.0, assuming that the rating of A74 Brick Wall is correct, so I'll go for Hard 1.75.


Ed

I really appreciate you saying this Andrew. I choose not to use those techniques since they go 3 ways (or use more than 2 elements eg multiple permutations, cage block, multiple nonets, multiple cages) to get contradictions...unless, of course, there is no other way. I'd personally give those sort of techniques a 2.0 rating...so very happy with Andrew's ratings summation. Thanks!

Is there another way Afmob?


Afmob

Great tag walkthrough! Especially Para's step 20 is easier than my method of eliminating 4 from R6C6. I used a forcing chain on 21(3) @ N6 to get the same result.

Here is an alternative for step 19 albeit I don't know whether it's easier:

19. 1,6 in R6 locked in R6C247
19a. 1,6 locked in Innies R6789 = 35(6+1) @ R6 -> Two numbers already set -> R6C4 + Four of R6C23456 = 28(4+1)
19b. 28(4+1) = 3+{4579} / 4+59{28/37} / 5+49{28/37} / 9+45{28/37} since other combos blocked by step 15a (or by Killer pairs of Outies N9)
19c. 28(4+1): R6C5 <> 7 since 7 must be @ R6C2 because R6C46 = (16) leaves R6C2 = (78)
(19d. R6C2 <> 8 because (126) only possible @ R6C247 [this could replace step 26])

After step 25 I took a different way which I think is easier than steps 30 and 31 since it uses no chains:

26. Innies+Outies R12: 13 = R3C29+R4C9 - R12C6: R12C6 <> 9 since R4C9 <= 5
26a. 17(4) @ N2: R3C6 <> 3 since 9 only possible there
26b. Outies R12 = 30(4+1): R3C9 <> 2,3 because R4C9 <= 5 and R3C356 <= 21 since R3C56 @ 17(4) <= 14 and R3C356 cannot be [886]
26c. Hidden Single: R3C4 = 3 @ R3
26d. R7C4 = 4, R6C3 = 5, R6C6 = 8, R4C1 = 3, R6C1 = 4
26e. Outie N1 = R2C4 = 9
26f. R8C4 = 8, R1C4 = 7, R9C4 = 5, R7C5 = 1, R4C6 = 4, R5C6 = 5

27. 16(3) @ N2 = {457} -> 4,5 locked for C5
27a. R3C5 = 8
27b. Naked pair (25) locked in R4C89 for R4+N6
27c. 11(3) @ N3 = {245} since R4C8 = (25) -> R3C8 = 4
27d. Hidden Single: R3C9 = 9 @ R3, R3C7 = 5 @ R3
27e. R4C8 = 2, R4C9 = 5

28. 12(3) @ N7 = 4[26/53/62], no 7,8 and R7C2 <> 5
28a. 28(5) @ N7 = 189{37/46} because 36{29/47} blocked by Killer pair (36) of 12(3) -> R8C2 = 9; 1 locked for C3+N7; R89C3 <> 6,7
28b. Killer pair (36) locked in 12(3) + 28(5) for N7
28c. 17(3) @ N7 = 8{27/45} -> 8 locked for R9

29. 19(4) @ N9 = 6{139/247} because {1279} blocked by R7C7 = (279) -> 6 locked for R9+N
29a. R9C5 = 2, R8C5 = 6
29b. Hidden Single: R1C1 = 9 @ N1, R8C8 = 5 @ D\
29c. 18(4) @ N9 = 25{38/47} because R6C9 = (37) -> 2 locked for C9+N9 and R78C9 <> 3,7
29d. R7C7 = 7, R6C8 = 3, R7C8 = 8 (cage sum)
29e. R7C3 = 6, R2C8 = 7, R2C9 = 3 (cage sum)

30. 17(4) @ N3 = {1268} -> R1C8 = 6, R1C9 = 1, {28} locked for C7

31. Rest is singles without considering diagonals.

I think the most difficult steps were step 19 and 20 and I'm wondering about their rating. I think they are not that complicated though probably not easy to find, so I would rate them (Hard) 1.5 but if the majority think they are tougher then this Killer is likely of rating 1.75. But at least in my opinion it's nowhere near a 2.0 Killer.


Para

I can't believe i didn't see this before. I was 1 step away from finishing this puzzle, namely step 27. A few more smple steps to make it to all singles after that. I started it from after step 25, because those old moves 26/27 were really not necessary

26. Innies N12: R2C124 = 11 = {17/26}[3]/{24}[5]

27a. {45} in N2 either in 16(3) @ R1C4 or R3C45
27b. R3C45 blocked by innnies N12 -> 16(3) @ R1C4 = [7]{45} -> R1C4 = 7, R12C5 = {45} -> locked for N2 and C5
27c. R2C45 = [93], R37C5 = [81], R9C4 = 5, R78C4 = [48], R6C3 = 5, R46C1 = [34], R456C6 = [458], R4C2 = 8(hidden), R3C9 = 9(hidden)
27d. 8 in N7 locked for C1

28. 11(3) @ R3C7 = {2[4]5} (only possible combinatinon) -> R3C8 = 4, R3C7 = {25}
28a. R3C7 = 5(hidden), R4C89 = [25], R8C8 = 5(hidden)

29. 5 in N1 locked within 20(3) @ R1C1 -> 20(3) = {569}: locked for N1
29a. R3C12 = {17}(last combo) -> locked for R3 and N1
29b. R3C36 = [26], R2C2 = 4, R12C5 = [45], R2C1 = 6, R1C12 = [95], R7c7 = 7, R6C89 = [37], R7C3 = 6

30. R7C8 = 8(last value in cage)
30a. R25C8 = [79]
30b. R7C12 = [53](last combo in cage)
30c. R8C9= 4(last value in cage)

And the rest is all naked singles.

Think this was the quickest and easiest way to the end.

note: 4 diagonal cages all starting in n2

3x3::k:2049:2049:2049:3842:4867:4356:5637:5637:5637:6150:6150:3842:7943:4867:6408:4356:3593:3593:6150:3842:7943:4867:4867:4867:6408:4356:3593:6150:7943:4874:4874:4107:4620:4620:6408:3593:7943:4874:4874:2573:4107:5902:4620:4620:6408:7943:7951:2573:2573:4107:5902:5902:7952:6408:7951:7951:7951:4113:4113:4113:7952:7952:7952:7951:4626:7951:4627:4627:4627:7952:2580:7952:4626:4626:5141:5141:5141:5141:5141:2580:2580:

Thanks for this fun Killer, Ed!

I think SudokuSolver's rating is right since at the time I found the Hidden Killer pair a lot of placements were already made so there weren't many candidates left to look for.

A127 Walkthrough:

1. R6789
a) Outies R9 = 3(2) = {12} locked for R8
b) 18(3) @ N7 = 9{18/27} because R8C2 = (12) -> 9 locked for R9+N7; R9C12 <> 1,2
c) Outies R789 = 9(2) <> 9
d) Innies+Outies N7: 4 = R6C2 - R9C3 -> R6C2 = (5678), R9C3 = (1234)
e) Killer pair (12) locked in 31(6) + R8C2 for N7
f) Outies N8 = 9(2) = [36/45]
g) Innies+Outies N7: 4 = R6C2 - R9C3 -> R6C3 = (78)
h) Outies R789 = 9(2) = [72/81]

2. R789
a) 31(6) @ N9 = 349{168/258/267} because 1289{47/56} blocked by R8C8 = (12)
and 567{139/148/238} blocked by R9C7 = (56) -> 3,4 locked for N9
b) 10(3) = {127} locked for N9 and 7 also locked for R9
c) 18(3) @ N7 = {189} -> R8C2 = 1; 8 locked for R9+N7
d) R8C8 = 2, R6C8 = 1, R9C8 = 7, R9C9 = 1
e) Outies R789 = R6C2 = 8
f) R9C2 = 9, R9C1 = 8
g) Innie N7 = R9C3 = 4
h) Innie N9 = R9C7 = 5
i) Naked triple (236) locked in R9C456 for N8
j) 18(3) @ N8 = {459} locked for R8+N8

3. R123+N6
a) 23(3) = {689} -> R5C6 = 8, {69} locked for R6
b) 8(3) = 1{25/34} -> 1 locked for R1+N1
c) 22(3) = 9{58/67} -> 9 locked for R1+N3
d) 14(4) = {2345} -> 2 locked for C9; CPE: R1C9 <> 5
e) 17(3) = 4{58/67} since (68,78) are Killer pairs of 22(3) and 22(3) sees all cells of 17(3)
f) Hidden Single: R3C7 = 1 @ N3
g) 19(5) must have 1 -> R2C5 = 1
h) 24(4) = 9{267/357/456} -> 9 locked for C1
i) 2,3 in N3 locked in 14(4) -> R4C9 <> 2,3
j) Outies N3 = 9(1+1) = {45} -> CPE: R4C6 <> 4,5

4. R123
a) Killer pair (45) locked in 8(3) + R1C6 for R1
b) 22(3) = {679} locked for R1+N3
c) 17(3) = {458} -> CPE: R3C456 <> 5
d) 19(5) = 123{49/67} -> 2,3 locked for N2
e) R1C4 = 8
f) Hidden Single: R3C3 = 8 @ N1, R2C7 = 8 @ N3, R4C8 = 8 @ N6
g) 17(3) = {458} -> CPE: R3C456 <> 4
h) 19(5) = {12367} -> 6,7 locked for R3+N2
i) 15(3) = 8{25/34}; R3C2 <> 3
j) Hidden Single: R3C1 = 9 @ R3
k) 6,7 in N1 locked in 24(4) = {2679} -> R2C12 = (67) and R4C1 = 2

5. C456
a) 31(5) = 89{167/347/356} -> R2C4 = 9
b) Naked pair (45) locked in R12C6 for C6
c) R8C6 = 9, R6C6 = 6, R6C7 = 9
d) Hidden Single: R5C7 = 2 @ N6
e) 18(4) = {2367} since {2457} blocked by R3C9 = (45)
-> 7 locked for R4 and 6 locked for N6

6. C123 !
a) ! Hidden Killer pair (14) in R1C1+31(5) for C1 since 31(5) cannot have both of (14)
-> R1C1 = (14) and 31(5) = 789{16/34} -> 7 locked for C1+N4
b) R2C1 = 6, R8C1 = 3
c) 31(5) = 789{16/34} -> R4C2 = (36)
d) 19(4) = {1459} because R4C2 = (36) blocks {1369}
e) Hidden Single: R4C2 = 6 @ N4, R6C3 = 3 @ N4
f) 10(3) = {235} -> R5C4 = 5, R6C4 = 2

7. Rest is singles.

Rating: 1.0. I used a Hidden Killer pair.

Thanks for the fun puzzle Ed!

I also used a hidden killer pair but not the same one that Afmob used. After going through his walkthrough I see that I didn't actually need to use it if I'd omitted step 5 and then used a killer pair after step 5a.

I'll rate A127 as (Hard?) 1.0 because although the steps were technically only 1.0 some of them felt hard and also there were so many hidden singles which IMHO are hard to spot. Afmob's walkthrough also felt like (Hard?) 1.0 to me.

Here is my walkthrough

Prelims

a) R1C123 = {125/134}, 1 locked for R1 and N1
b) R1C789 = {589/679}, 9 locked for R1 and N3
c) 10(3) cage at R5C4 = {127/136/145/235}, no 8,9
d) 23(3) cage at R5C6 = {689}, CPE no 6,8,9 in R6C45
e) 10(3) cage in N9 = {127/136/145/235}, no 8,9
f) 19(5) cage in N2 must contain 1, locked for N2

1. 45 rule on R9 2 outies R8C28 = 3 = {12}, locked for R8
1a. 18(3) cage in N7 = {189/279}, R9C12 = {789}, 9 locked for R9 and N7

2. 45 rule on N7 1 outie R6C2 = 1 innie R9C3 + 4, no 1,2,3,4 in R6C2, no 6,7,8 in R9C3

3. 45 rule on N9 1 innie R9C7 = 1 outie R6C8 + 4, no 1,2,3,4 in R9C7, no 5,6,7,8,9 in R6C8

4. 45 rule on N8 2 outies R9C37 = 9 = [18/27/36/45], no 5 in R9C3, clean-up: no 9 in R6C2 (step 2)

5. Hidden killer pair 7,8 in 31(6) cage at R6C2 and R9C12 for N7 -> 31(6) cage at R6C2 must contain one of 7,8 within N7
5a. 31(6) cage at R6C2 = {145678/235678} contains both of 7,8 -> R6C2 = {78}, clean-up: no 1,2 in R9C3 (step 2), no 7,8 in R9C7 (step 4), no 3,4 in R6C8 (step 3)
[Ed pointed out that I missed CPE no 7,8 in R9C2 which fixes R9C2 a bit quicker]

6. Naked pair {12} in R68C8, locked for C8, CPE no 1,2 in R7C79
6a. Hidden pair {12} in R8C8 + R9C9 for N9 -> R9C8 = 7 (prelim e)
6b. Naked pair {89} in R9C12, locked for R9 and N7

7. R6C2 = 8 (hidden single in 31(6) cage at R6C2), R9C12 = [89], R9C3 = 4 (step 2), R9C7 = 5 (step 4), R6C8 = 1 (step 3), R8C8 = 2, R8C2 = 1, R9C9 = 1
7a. Naked triple {236} in R9C456, locked for N8

8. Naked pair {69} in R6C67, locked for R6 and 23(3) cage at R5C6 -> R5C6 = 8

9. R8C456 = {459} (only remaining combination), locked for R8 and N8
9a. Naked triple {178} in R7C456, locked for R7

10. 14(4) cage at R2C8 = {2345} (only remaining combination), 2 locked in R234C9, locked for C9, CPE no 5 in R1C9

11. Max R1C6 + R3C8 = 15 -> min R2C7 = 2
11a. R3C7 = 1 (hidden single in C7), R2C5 = 1 (hidden single in R2)

12. 45 rule on N3 2 outies R1C6 + R4C9 = 9 = [45/54/63/72], no 2,3 in R1C6

13. 45 rule on R1 3 innies R1C456 =15 = {258/267/348} (cannot be {357/456} which clash with R1C123)
13a. 4,5 of {258/348} must be in R1C6 -> no 4,5 in R1C45

14. 45 rule on C6789 4 remaining innies R3789C6 = 15
14a. Min R389C6 = 9 -> R7C6 cannot be 7 -> R7C6 = 1
14b. R3789C6 = {1239/1257/1347/1356}
14c. R8C6 = {459} -> no 4,5,9 in R3C6

15. 45 rule on C1234 4 remaining innies R3789C4 = 20 = {2468/2567/3458/3467} (cannot be {2369/2459} because R7C4 only contains 7,8, cannot be {2378} because R8C4 only contains 4,5,9), no 9
15a. R7C4 = {78} -> no 7,8 in R3C4

16. 15(3) diagonal cage at R1C4 = {258/267/348} (cannot be {249/357/456} which clash with R1C123 because all cells of 15(3) cage are common peers of R1C123), no 9
16a. 4 of {348} must be in R3C2 -> no 3 in R3C2

17. 17(3) diagonal cage at R1C6 = {458/467} (cannot be {278/368} which clash with R1C789 because all cells of 17(3) cage are common peers of R1C789), no 2,3

18. 2,3 of N3 locked in R2C89 + R3C9 for 14(4) cage, no 2,3 in R4C9, clean-up: no 6,7 in R1C6 (step 12)
[Alternatively 17(3) diagonal cage at R1C6 and 14(4) cage at R2C8 both contain 4 -> R1C6 + R4C9 must contain 4 = {45}]
18a. 2 in C7 locked in R45C7, locked for 18(4) cage at R4C6, no 2 in R4C6

19. R1C456 (step 13) = {258/348} (cannot be {267} because R1C6 only contains 4,5), no 6,7, 8 locked for R1 and N2, clean-up: no 5 in R1C8 (prelim b)
19a. Naked triple {679} in R1C789, locked for N3

20. 45 rule on N2 4 innies R12C46 = 26 = {4589/5678} (cannot be {2789/3689} because R1C6 only contains 4,5, cannot be {4679} because R1C4 only contains 2,3,8), no 2,3, 5 locked for N2 -> R1C4 = 8, R7C45 = [78]
20a. 7 of {5678} must be in R2C6, no 6 in R2C6

21. 15(3) diagonal cage at R1C4 (step 16) = {258/348}, no 6,7
21a. Naked quint {12345} in R1C123 + R2C3 + R3C2, locked for N1
21b. R3C3 = 8 (hidden single in N1), R2C7 = 8 (hidden single in R2), R4C8 = 8 (hidden single in R4), R8C9 = 8 (hidden single in R8)
21c. R2C12 + R3C1 = {679} = 22 -> R4C1 = 2, R5C7 = 2 (hidden single in C7)
21d. 9 in C3 locked in R45C3, locked for N4 and 19(4) cage at R4C3, no 9 in R4C4
21e. R2C4 = 9 (hidden single in C4)

22. Naked pair {67} in R2C12, locked for R2 and N1 -> R3C1 = 9
22a. Naked pair 4,5 in R12C6, locked for C6 -> R8C6 = 9, R6C67 = [69]

23. 9 in C3 locked in 19(4) cage at R4C3 = {1369/1459}, no 7
23a. 1 in R4 locked in R4C34, locked for 19(4) cage, no 1 in R5C3

24. 25(5) diagonal cage at R2C6 = {14578} (only remaining combination, cannot be {13678} because R2C6 only contains 4,5), no 3,6
24a. Naked triple {457} in R456C9, locked for C9 and N6
24b. Naked pair {23} in R23C9, locked for C9 and N3
24c. Naked pair {36} in R4C7 + R5C8, locked for 18(4) cage at R4C6 -> R4C6 = 7

25. R2C2 = 7 (hidden single in C2), R2C1 = 6

26. Naked pair {36} in R48C7, locked for C7 -> R1C7 = 7, R7C7 = 4

27. Naked pair {23} in R1C5 + R3C6, locked for N2 -> R3C45 = [67], R9C5 = 6 (hidden single in R9)
27a. Naked pair {45} in R2C68, locked for R2
27b. Naked pair {23} in R3C69, locked for R3

28. 10(3) cage at R5C4 = {127/145/235}
28a. 1 of {145} must be in R5C4 -> no 4 in R5C4
28b. 2,4 only in R6C4 -> R6C4 = {24}
28c. 3 of {235} must be in R6C3 (R56C4 cannot be [32] which clashes with R9C4)
-> no 3 in R5C4

29. 45 rule on N4 1 innie R6C3 = 1 remaining outie R4C4 + 2, no 4 in R4C4

30. 19(4) cage at R4C3 (step 23) = {1369/1459}
30a. 9 of {1369} must be in R5C3 (R5C23 cannot be {36} which clash with R5C8) -> no 3,6 in R5C3
30b. 4 of {1459} must be in R5C2 -> no 5 in R5C2

31. 31(5) diagonal cage at R2C4 = {16789/34789} (cannot be {35689} because R56C1 = {35} clashes with R7C1), no 5, 7 locked in R56C1, locked for C1 and N4 -> R78C1 = [53], R8C7 = 6, R7C89 = [39], R8C3 = 7, R1C89 = [96], R4C7 = 3, R5C8 = 6, clean-up: no 5 in R4C4, no 5 in R6C3 (both step 29)

and the rest is naked singles.

Thanks for the walk-throughs and rating feedback Afmob and Andrew. I missed Afmob's step 4c (a neat CPE) and Andrew's step 20 so made it harder than they did. Well done guys! I really enjoyed the sneaky cage clashes (eg Afmob step 3e ; Andrew's step 17) available with this cage shape.

Put a lot of time into finding a new scoring routine. Found a real good one (but of course it will change again!). A127 gets a 1.15. Perfect I reckon. One of the recent problem ones, A124, which you guys rated 1.0-H1.0 now gets 1.25 rather than 1.40. Getting there!

3x3::k:4352:2305:2305:1539:1539:8197:8197:8197:8197:4352:4352:2571:2571:5645:782:782:3600:8197:3858:3858:2836:2836:5645:10519:5400:3600:5400:2843:3858:2589:5645:5645:10519:5400:5400:5400:2843:2589:2589:10519:10519:10519:3626:3626:3372:7469:7469:7469:10519:5681:5681:3626:1588:3372:7469:3383:7469:10519:5681:2107:2107:1588:1588:4415:3383:2113:2113:5681:2884:2884:4678:4678:4415:4415:4415:4415:3148:3148:3150:3150:4678:

It was certainly that. Lots of prelims, must have been pretty close to a record number; maybe it was a record.

Thanks for a fun puzzle.

I'll rate it at 1.0. At first I found it a touch harder but then I realised that I'd missed a couple of simple things.

Here is my walkthrough. It would have been quicker if I'd spotted step 11 earlier.

Prelims

a) R1C45 = {15/24}
b) R1C23 = {18/27/36} (cannot be {45} which clashes with R1C23), no 4,5,9
c) R2C34 = {19/28/37/46}, no 5
d) R2C67 = {12}, locked for R2, clean-up: no 8,9 in R2C34
e) R23C8 = {59/68}
f) R3C34 = {29/38/47/56}, no 1
g) R45C1 = {29/38/47/56}, no 1
h) R56C9 = {49/58/67}, no 1,2,3
i) R78C2 = {49/58/67}, no 1,2,3
j) R7C67 = {17/26/35}, no 4,8,9
k) R8C34 = {17/26/35}, no 4,8,9
l) R8C67 = {29/38/47/56}, no 1
m) R9C56 = {39/48/57}, no 1,2,6
n) R9C78 = {39/48/57}, no 1,2,6
o) 10(3) cage in N4 = {127/136/145/235}, no 8,9
p) 6(3) cage at R6C8 = {123}, CPE no 1,2,3 in R89C8, clean-up: no 9 in R9C7
q) 32(5) cage at R1C6 = {26789/35789/45689}, no 1, must contain 8 and 9
r) 17(5) cage at R8C1 = {12347/12356}, no 8,9, must contain 1, 2 and 3
s) 41(5) cage at R3C6 = {2456789}, no 1,3

1. Killer pair 1,2 in R1C45 and R2C6, locked for N2, clean-up: no 9 in R3C3

2. Killer triple 1,2,3 in R7C67 and R7C89, locked for R7
2a. 2 in 41(5) cage at R3C6 locked in N5, no 2 in R4C45, no 2 in R6C56

3. 45 rule on R12 2 innies R2C58 = 13 = [49/58/85] (cannot be [76] which clashes with R2C34), no 3,6,7,9 in R2C5, no 6 in R2C8, clean-up: no 8 in R3C8

4. 45 rule on R89 2 innies R8C25 = 12 = [48/57/75/84/93], no 6, no 1,2,9 in R8C5, clean-up: no 7 in R7C2

5. 45 rule on R1 1 outie R2C9 = 1 innie R1C1 + 2, no 8,9 in R1C1

6. 45 rule on R9 1 innie R9C9 = 1 outie R8C1 + 4, no 6,7 in R8C1, no 1,2,3,4 in R9C9

7. 1,2 in R9 locked in R9C1234, locked for 17(4) cage at R8C1 -> no 1,2 in R8C1, clean-up: no 5,6 in R9C9 (step 6)
7a. 6 in R9 locked in R9C1234 -> 17(4) cage at R8C1 = {12356} (prelim r), no 4,7, clean-up: no 8 in R9C9 (step 5)
7b. R8C34 = {17/26} (cannot be {35} which clashes with R8C1)

8. 45 rule on N36 1 outie R1C6 = 2 innies R2C7 + R6C8 + 4
8a. Min R2C7 + R6C8 = 2 -> min R1C6 = 6

9. 45 rule on N47 1 innie R4C2 = 2 outies R89C4 + 2
9a. Min R89C4 = 3 -> min R4C2 = 5
9b. Max R89C4 = 7, no 7 in R8C4, clean-up: no 1 in R8C3
9c. 1 in N7 locked in R9C123, locked for R9 -> no 6 in R8C4 (step 9b), clean-up: no 2 in R8C3
9d. 2 in N7 locked in R9C123, locked for R9
9e. Min R89C4 = 4 -> min R4C2 = 6 (step 9)
9f. R78C2 = {49/58} (cannot be [67] which clashes with R8C3), clean-up: no 5 in R8C5 (step 4)

10. 45 rule on N9 2 innies R78C7 = 1 outie R6C8 + 9
10a. Min R78C7 = 10, no 2 in R8C7, clean-up: no 9 in R8C6

11. 45 rule on N6 2 outies R3C79 = 1 innie R6C8 + 3
11a. R6C8 = {123} -> R3C79 = 4,5,6 = {13/14/15/23/24}, no 6,7,8,9
11b. Killer pair 1,2 in R2C7 and R3C79, locked for N3

12. 32(5) cage at R1C6 = {35789/45689}, 5 locked in R1C789 + R2C9, locked for N3, clean-up: no 9 in R23C8
12a. R23C8 = [86], R2C5 = 5 (step 3), clean-up: no 3,4,6 in R1C1 (step 5), no 1 in R1C45, no 5 in R3C3, no 7 in R9C6, no 4 in R9C7
12b. R1C6 = 8 (hidden single for 32(5) cage, clean-up: no 1 in R1C23, no 3 in R3C3, no 3 in R8C7, no 4 in R9C5
12c. Naked pair {24} in R1C45, locked for R1 and N2 -> R2C67 = [12], clean-up: no 7 in R1C23, no 6 in R2C3, no 4 in R2C9 (step 5), no 7 in R3C3, no 6 in R7C6, no 7 in R7C7
12d. Naked pair {36} in R1C23, locked for R1 and N1, clean-up: no 7 in R2C4

13. Naked triple {579} in R1C789, locked for R1 and N3 -> R1C1 = 1, R2C9 = 3, R2C4 = 6, R2C3 = 4, clean-up: no 7 in R3C4
13a. Naked pair {79} in R2C12, locked for N1
13b. 6 in R9 locked in R9C123, locked for N7 -> R8C3 = 7, R8C4 = 1, clean-up: no 5 in R8C2 (step 4), no 8 in R7C2, no 4 in R8C67

14. Naked pair {14} in R3C79, locked for 21(5) cage at R3C7
14a. R3C79 = {14} = 5 -> R6C8 = 2 (step 11), R7C89 = [31], R3C79 = [14], clean-up: no 9 in R56C9, no 5,7 in R7C6, no 5 in R7C7, no 9 in R9C8
14b. R7C67 = [26], clean-up: no 5 in R8C6, no 9 in R8C7
14c. R5C8 = 1 (hidden single in C8)
14d. 2 in N5 locked in R5C45, locked for R5, clean-up: no 9 in R4C1

15. 2 in N9 locked in 18(3) cage = {279} (only remaining combination) -> R8C9 = 2, R9C9 = 7, R8C8 = 9, R8C1 = 3 (step 6), R9C4 = 5, R9C78 = [84], R8C7 = 5, R8C6 = 6, clean-up: no 8 in R45C1, no 6 in R56C9, no 4 in R7C2
15a. Naked pair {58} in R56C9, locked for C9 and N6 -> R1C9 = 9, R1C78 = [75], R4C89 = [76], R4C7 = 3 (cage sum), clean-up: no 4,5 in R5C1

16. 22(4) cage at R2C5 = {1579} (only remaining combination) -> R3C5 = 7, R4C45 = [91]
[Alternatively I could have used the fact that 22(4) cage at R2C5 and 22(4) cage at R6C5 can each only contain one of 1,3 -> 22(4) cage at R2C5 must contain 1. I’d spotted that a lot earlier but this was the earliest that I could use it.]
16a. R3C4 = 3, R3C3 = 8, R3C6 = 9, R9C56 = [93]

17. R4C2 = 8, R8C25 = [48], R7C2 = 9

and the rest is naked singles.

Thanks for providing us with a Killer right on time! And it was fun, too.

A128 Walkthrough:

1. R123+N6 !
a) 3(2) = {12} locked for R2
b) 10(2) <> 8,9
c) Innies+Outies N3: 1 = R1C6 - (R2C7+R3C79) -> R1C6 = (789); R3C79 <> 6,7,8,9
d) 7 locked in 32(5) @ N3 = 789{26/35}; R1C6 <> 7
e) Innies+Outies N3: 1 = R1C6 - (R2C7+R3C79):
- 1,4 locked in R2C7+R3C79 @ N3 -> R2C7+R3C79 = 14{2/3}
-> 4 locked for R3
f) ! Outies N6 = 9(2+2) = {14}+{13} / {24}+{12} (step 1e)
-> R3C79 <> 3 and 1 locked in R7C89 for R7+N9+6(3)
g) 3 locked in 32(5) @ N3 = {35789} -> 5 locked for N3
h) 14(2) = {68} locked for C8+N3
i) 32(5) = {35789} -> R1C6 = 8
j) Innies R12 = 13(2) = {58} because (67) is a Killer pair of 10(2)
-> R2C5 = 5, R2C8 = 8

2. R123
a) 6(2) = {24} locked for R1+N2
b) 9(2) = {36} locked for R1+N1
c) 17(3) = {179} -> R1C1 = 1, {79} locked for R2+N1
d) R2C3 = 4 -> R2C4 = 6, R2C6 = 1, R2C7 = 2
e) 15(3) = {258} because R3C12 = (258)
f) 21(5) = 14{259/268/358/367} because R3C79 = (14); R4C789 <> 1,4

3. R789+N5
a) Innies R89 = 12(2) = [48/57/84/93]
b) 1 locked in 8(2) @ R8 = {17} locked for R8
c) 13(2) = {49} locked for C2+N7 because {58} blocked by R34C2 = (258)
d) 41(7) must have 6 -> 6 locked for N5
e) 22(4) @ N2 = 57{19/28}
f) Hidden Single: R3C4 = 3 @ N2
g) Cage sum: R3C3 = 8
h) Hidden Single: R7C1 = 8 @ N7, R4C2 = 8 @ N4
i) 22(4) @ N2 = {1579} -> 1 locked for R4+N5
j) Innies+Outies R9: -4 = R8C1 - R9C9 -> R8C1 = (235); R9C9 = (679)

4. R789
a) 8(2) @ R7 <> 7; R7C6 <> 6
b) 7 locked in R9C789 @ N9 for R9
c) 17(5) = {12356} -> 3,6 locked for N7 and 6 also locked for R9
d) 2 locked in 17(5) @ R9 -> R8C1 <> 2
e) Outies R9 = 14(3) = 3{29/56} because R8C1 = (35) -> 3 locked for R8
f) Innies R89 = 12(2) = {48} -> R8C2 = 4, R8C5 = 8
g) 12(2) @ N8 = {39} locked for R9+N8
h) R9C9 = 7
i) 12(2) @ N9 = {48} -> R9C8 = 4, R9C7 = 8
j) 8(2) @ N9: R7C7 <> 5

5. R4567
a) 1 locked in 14(3) @ N6 = 1{49/67}
b) 3 locked in 22(4) @ R6C5 @ N5 for R6
c) R6C8 = 2
d) 21(5) = {13467} -> 3,6,7 locked for R4+N6
e) 6(3) = {123} -> 3 locked for N9
f) R7C7 = 6 -> R7C6 = 2
g) 29(5) = 189{47/56} -> 1,9 locked for R6+N4
h) 10(3) = {235} locked for N4
i) 11(2) = {47} -> R4C1 = 4, R5C1 = 7
j) 29(5) = {15689} -> R7C3 = 5
k) 22(4) @ N2 = {1579} -> R3C5 = 7

6. Rest is singles.

Rating: 1.0. I used Killer pairs.

3x3::k:4096:4096:8194:3843:3843:5125:5125:5125:1800:4096:8194:8194:8194:3843:4110:5125:6928:1800:2578:2578:8194:1813:4110:4110:6928:6928:6928:2578:2578:3357:1813:6943:2848:2848:6928:2851:2852:3357:3357:6943:6943:6943:4650:4650:2851:2852:6190:3119:3119:6943:3378:4650:4404:4404:6190:6190:6190:3129:3129:3378:4668:4404:4404:3135:6190:6465:3129:2371:4668:4668:4668:5703:3135:6465:6465:6465:2371:2371:4668:5703:5703:

Thanks Para

I enjoyed Boredom Killer #1, particularly for step 12a which was my first key breakthrough.

I'll rate BK #1 at 1.25. I hope that Ed and Mike find step 12a acceptable for this rating.

Here is my walkthrough for BK #1. Thanks Afmob and Para for pointing out the alternative for step 12.

Prelims

a) R12C9 = {16/25/34}, no 7,8,9
b) R34C4 = {16/25/34}, no 7,8,9
c) R4C67 = {29/38/47/56}, no 1
d) R45C9 = {29/38/47/56}, no 1
e) R56C1 = {29/38/47/56}, no 1
f) R6C34 = {39/48/57}, no 1,2,6
g) R67C6 = {49/58/67}, no 1,2,3
h) R89C1 = {39/48/57}, no 1,2,6
i) 9(3) cage in N8 = {126/135/234}, no 7,8,9
j) 22(3) cage in N9 = {589/679}, 9 locked for N9
k) 10(4) cage at R3C1 = {1234}
l) 32(5) cage at R1C3 = {26789/35789/45689}, no 1, must contain 8,9
m) 18(5) cage at R7C7 = {12348/12357/12456}, no 9, must contain 1,2

1. 45 rule on N8 3 innies R78C6 + R9C4 = 24 = {789}, locked for N8, clean-up: no 7,8,9 in R6C6

2. 45 rule on N9 2 innies R7C89 = 1 outie R8C6 + 5
2a. R8C6 = {78} -> R7C89 = 12,13 = {48/58/67} (cannot be {57} which clashes with 22(3) cage), no 1,2,3
2b. R7C89 = 12,13 -> R6C89 = 4,5 = {13/23} (cannot be {14} which clashes with R7C89 = {48}), 3 locked for R6 and N6, clean-up: no 8 in R4C6, no 8 in R45C9, no 8 in R5C1, no 9 in R6C34
2c. 1,2,3 in N9 locked in R789C7 + R8C8 -> 18(5) cage at R7C7 (prelim m) = {12348/12357}no 6
2d. R8C6 = {78} -> no 7,8 in R789C7 + R8C8

3. 45 rule on R12 2 innies R2C68 = 1 outie R3C3
3a. Min R2C68 = 3 -> min R3C3 = 3
3b. Max R2C68 = 9, no 9

4. 45 rule on N1 1 outie R2C4 = 2 innies R3C12 + 3
4a. Min R3C12 = 3 -> min R2C4 = 6

5. 45 rule on N3 2 outies R1C6 + R4C8 = 9 = {18/27/45}/[36], no 9, no 6 in R1C6

6. 45 rule on N7 2 outies R6C2 + R9C4 = 16 = [79/88/97]

7. 45 rule on C123 3 outies R269C4 = 20 = {479/569/578}
7a. 4,5 only in R6C4 -> R6C4 = {45}, clean-up: no 4,5 in R6C3

8. 45 rule on N5 4 innies R46C46 = 18
8a. Max R4C4 + R6C46 = 15 -> min R4C6 = 3, clean-up: no 9 in R4C7
8b. Min R4C4 + R6C46 = 10 -> no 9 in R4C6, clean-up: no 2 in R4C7
[There may be candidate eliminations because of clashes between R4C6 and R7C6 but I’ll leave those until later.]

9. 45 rule on N12 4 innies R1C6 + R3C124 = 11
9a. Min R3C124 = 6 -> max R1C6 = 5, clean-up: no 1,2 in R4C8 (step 3)

10. 45 rule on N14 2 innies R6C23 = 1 outie R2C4 + 8
10a. Min R6C23 = 15 -> min R2C4 = 7
10b. R269C4 (step 7) = {479/578}, 7 locked for C4

11. Hidden killer pair 8,9 in R15C4 and R29C4 for C4 -> R15C4 must contain one of 8,9
11a. 45 rule on C1234 2 innies R15C4 = 1 outie R7C5 + 6
11b. Min R15C4 = 9 -> min R7C5 = 3
11c. Max R7C5 = 6 -> max R15C4 = 12, no 5,6 (because must contain 8 or 9)

12. 45 rule on N69 2 innies R4C78 = 1 outie R8C6 + 4, R8C6 = {78} -> R4C78 = 11,12
12a. R4C78 cannot be 11 (because the overlap of R4C67 with R4C78 would make R4C6 equal R4C8) -> R4C78 = 12 -> R8C6 = 8, clean-up: no 8 in R6C2 (step 6), no 5 in R6C6, no 5 in R789C7 + R8C8 (step 2c), no 4 in R9C1
12b. R4C78 = 12 = {48/57}, no 6, clean-up: no 3 in R1C6 (step 5), no 5 in R4C6
12c. R7C89 = R8C6 + 5 (step 2) -> R7C89 = 13 = {58/67}, no 4, R6C89 = 4 = {13}, locked for R6 and N6
[Afmob and Para both pointed out an alternative to steps 12 and 12a.
45 rule on N69 2 outies R48C6 = 1 innie R4C8, IOU no 7 in R8C6 -> R8C6 = 8
Their way is easier but IMHO my way is more interesting.]

13. 45 rule on C789 2 remaining outies R14C6 = 8 = [17/26/53], no 4, clean-up: no 7 in R4C7, no 5 in R4C8 (step 12b)

14. R46C46 = 18 (step 8) = {1467/2457/3456} (cannot be {2367} because R6C4 only contains 4,5), 4 locked for N5
[Again I’ll leave clashes between R4C6 and R7C6 until later. These cells get fixed in step 19b without needing to use the clash.]

15. 2 in R6 locked in R6C157
15a. 45 rule on R6789 3 innies R6C157 = 16 = {259/268}, no 4,7, clean-up: no 4,7 in R5C1
15b. 7 in R6 locked in R6C23, locked for N4
15c. 4 in R6 locked in R6C46, locked for N5, clean-up: no 3 in R3C4

16. 45 rule on N1 3 outies R2C4 + R4C12 = 13
16a. R2C4 = {789} -> R4C12 = 4,5,6 = {13/14/23/24}
16b. 13(3) cage in N4 = {139/148/238/256} (cannot be {346} which clashes with R4C12)
16c. Killer pair 1,2 in R4C12 and 13(3) cage, locked for N4, clean-up: no 9 in R56C1

17. Combined cage R5689C1 = 23(4) = {3569/3578/4568} (cannot be {3479} because 4,7,9 only in R89C1), 5 locked for C1

18. 45 rule on R1234 3 innies R4C359 = 19 = {289/379/469} (cannot be {478/568} which clash with R4C78), no 1,5, clean-up: no 6 in R5C9

19. 1 in R4 locked in R4C124
19a. 45 rule on R123 4 outies R4C1248 = 15 = {1248/1347} (cannot be {1257} because R4C12 cannot be {12}, cannot be {1356} because R4C8 only contains 4,7,8), no 5,6, 4 locked for R4, clean-up: no 1,2 in R3C4, no 7 in R4C6, no 8 in R4C8 (step 12b), no 7 in R5C9
19b. R4C1248 = 15 = {1347} (only remaining combination) -> R4C8 = 7, R4C7 = 5 (step 12b), R4C6 = 6, R6C6 = 4, R6C4 = 5, R4C4 = 3 (step 14), R3C4 = 4, R6C3 = 7, R6C2 = 9, R7C6 = 9, R9C4 = 7, R2C4 = 8 (step 10b), R1C6 = 2 (step 5), clean-up: no 5 in R2C9, no 6 in R5C1, no 4 in R5C9, no 6 in R7C9 (step 12c), no 5 in R8C1

20. Naked pair {29} in R45C9, locked for C9 and N6, clean-up: no 5 in R1C9
20a. R9C8 = 9 (hidden single in N9), R89C9 = [58/76], no 6 in R8C9, no 5 in R9C9, clean-up: no 3 in R8C1
20b. Killer pair 1,3 in R12C9 and R6C9, locked for C9

21. Naked triple {289} in R4C359, locked for R4
21a. Naked pair {14) in R4C12, locked for N4 and for 10(4) cage at R3C1
21b. Naked pair {23} in R3C12, locked for R3 and N1
21c. 1,8 in N1 locked in 16(3) cage = {178}, locked for N1, 8 locked for R1
21d. R8C1 = 9 (hidden single in C1), R9C1 = 3, R3C12 = [23], R5C1 = 5, R6C1 = 6, R6C7 = 8, R6C5 = 2
21e. R5C3 = 3 (hidden single in C3)

22. Naked pair {19} in R15C4, locked for C4
22a. R15C4 = {19} = 10 -> R7C5 = 4 (step 11a)
22b. Naked pair {26} in R78C4, locked for N8
22c. Naked pair {15} in R9C56, locked for R9 and N8 -> R8C5 = 3
22d. R7C7 = 3 (hidden single in N9)
22e. 1 in N9 locked in R8C78, locked for R8

23. R2C6 = 3 (hidden single in C6), clean-up: no 4 in R1C9
23a. R3C56 = 13 = [67], R5C46 = [91], R45C5 = [87], R9C56 = [15], R1C4 = 1, R4C3 = 2, R45C9 = [92], R5C2 = 8, R1C12 = [87], R2C1 = 1, R4C12 = [41], R7C1 = 7, clean-up: no 6 in R12C9, no 6 in R7C8 (step 12c)
23b. R12C9 = [34], R6C89 = [31]
23c. R1C3 = 4 (hidden single in R1), R2C78 = [72] (hidden singles in R2)

24. 1,8 in N3 locked in R3C789 -> 27(5) cage at R2C8 = {12789} (only remaining combination) -> R3C789 = [918]

and the rest is naked singles.

3x3::k:2816:2816:2816:4611:4611:5637:5637:5637:3592:5129:4106:4106:4106:4611:2318:3599:3599:3592:5129:4115:4106:2069:2069:2318:3599:4633:3592:5129:4115:4381:4381:2069:2592:2592:4633:4633:5156:4115:4115:5159:5159:5159:5162:5162:4633:5156:5156:2351:2351:3633:1330:1330:5162:4149:3638:5156:3384:3129:3633:3633:6716:5162:4149:3638:3384:3384:3129:2627:6716:6716:6716:4149:3638:4425:4425:4425:2627:2627:4174:4174:4174:

I struggled for some time with Boredom Killer #2 until I eventually found step 17. Then I realised that it is an interesting killer. With hindsight step 17 was available immediately after step 7 but the work between those steps wasn't completely wasted; some of it was useful.

I'll rate BK #2 at Hard 1.25, because of the difficulty I had in making progress, although it could be argued that on my actual steps it should be 1.25.

Here is my walkthrough for BK #2.

Prelims

a) R23C6 = {18/27/36/45}, no 9
b) R4C34 = {89}, locked for R4
c) R4C67 = {37/46}
d) R6C34 = {18/27/36/45}, no 9
e) R6C67 = {14/23}
f) R78C4 = {39/48/57}, no 1,2,6
g) R1C678 = {589/679}, 9 locked for R1 (this also does the prelim for R1C123)
h) R234C1 = {389/479/569/578}, no 1,2
i) 8(3) cage at R3C4 = {125/134}, CPE no 1 in R12C5
j) R5C456 = {389/479/569/578}, no 1,2
k) 10(3) cage in N8 = {127/136/145/235}, no 8,9
l) 26(4) cage at R7C7 = {2789/3689/4589/4679/5678}, no 1

1. 45 rule on R1 1 outie R2C5 = 1 innie R1C9 +6, R2C5 = {789}, R1C9 = {123}
1a. Max R1C9 = 3 -> min R23C9 = 11, no 1 in R23C9

2. 45 rule on R9 1 innie R9C1 = 1 outie R8C5 + 2, no 1,2 in R9C1

3. 45 rule on N3 1 outie R1C6 = 1 innie R3C8 + 5, no 5 in R1C6, R3C8 = {1234}

4. 45 rule on C789 2 outies R18C6 = 2 innies R46C7 + 11
4a. Min R46C7 = 4 -> min R18C6 = 15, no 2,3,4,5 in R8C6
4b. R18C6 = 15,16,17 -> R46C7 = 4,5,6 = [31/32/42], clean-up: no 3,4 in R4C6, no 1,2 in R6C6

5. 45 rule on C789 4 outies R1468C6 = 26 = {3689/4679}, 6,9 locked for C6, clean-up: no 3 in R23C6

6. 45 rule on C6789 3 innies R579C6 = 10 = {127/145/235}, no 8
6a. 7 of {127} must be in R5C6 -> no 7 in R79C6

7. R5C456 = {479/569/578} (cannot be {389} which clashes with R4C4), no 3
7a. Killer pair 8,9 in R4C4 and R5C456, locked for N5, clean-up: no 1 in R6C3
7b. Killer pair 6,7 in R4C6 and R5C456, locked for N5, clean-up: no 2,3 in R6C3

8. 14(3) cage at R6C5 = {149/158/239/248/257/347/356} (cannot be {167} because 6,7 only in R7C5)
8a. 6,7,8,9 only in R7C5 -> R7C5 = {6789}

9. 45 rule on N9 2 outies R6C9 + R8C6 = 1 innie R7C8 + 13
9a. Max R6C9 + R8C6 = 18 -> max R7C8 = 5
9b. Min R6C9 + R8C6 = 14 -> min R6C9 = 5

10. 45 rule on C123 4 outies R2469C4 = 18
10a. Min R4C4 = 8 -> max R269C4 = 10, no 8,9 in R29C4

11. 45 rule on C1 3 innies R156C1 = 11 = {128/137/146/236/245}, no 9

12. 45 rule on N7 1 innie R7C2 = 1 outie R9C4 + 1, no 1,9 in R7C2

13. 45 rule on N1 2 outies R2C4 + R4C1 = 1 innie R3C2 + 2
13a. Min R2C4 + R4C1 = 4 -> min R3C2 = 2

14. 45 rule on N23 2 innies R2C4 + R3C8 = 1 outie R4C5 + 5
14a. Min R2C4 + R3C8 = 6, no 1 in R2C4

15. 45 rule on R6789 2 innies R67C8 = 1 outie R5C1 + 8
15a. Min R67C8 = 9 -> min R6C8 = 4
15b. Max R67C8 = 14 -> max R5C1 = 6

16. 45 rule on N8 4 innies R7C56 + R8C6 + R9C4 = 23 = {1679/2489/2579/2678/3569/4568} (cannot be {1589/3479/3578} which clash with R78C4)
16a. 1 of {1679} must be in R7C6 -> no 1 in R9C4, clean-up: no 2 in R7C2 (step 12)

17. 1,2,3 in N5 locked in R4C5 + R6C456
17a. R6C456 cannot be {123} which clashes with R6C7 -> R6C456 must contain {13/23} -> R4C5 = {12}
17b. Killer triple 1,2,3 in R6C456 + R6C7, locked for R6

18. R4C5 = {12} -> R3C45 = {15/25/34}
18a. 45 rule on N2 4 innies R1C6 + R2C4 + R3C45 = 18 = {1359/1458/2349/2457/3456} (cannot be {1269/1278/1368/1467/2367} which aren’t consistent with R3C45, cannot be {2358} which clashes with R23C6)
18b. R1C6 = {6789} -> no 6,7 in R2C4
18c. R23C6 = {18/27} (cannot be {45} which clashes with R1C6 + R2C4 + R3C45)

19. 18(3) cage in N2 = {189/279/369/468/567} (cannot be {378} which clashes with R23C6, cannot be {459} which clashes with R1C6 + R2C4 + R3C45)
19a. 1 of {189} must be in R1C4, 8 of {468} must be in R2C4 -> no 8 in R1C4

20. R2469C4 = 18 (step 10) = {1269/1278/1359/1368/1458/2349} (cannot be {1467/2367/2457/3456} because R4C4 only contains 8,9, cannot be {2358} which clashes with R78C4)
20a. 1 of {1359/1458} must be in R6C4 -> no 5 in R6C4, clean-up: no 4 in R6C3

21. 5 in C6 locked in R579C6 (step 6) = {145/235}, no 7
21a. Naked quint {12345} in R4C5 + R5C6 + R6C456 locked for N5

22. 45 rule on R1 3 innies R1C459 = 12 = {138/237/246} (cannot be {147/345} which aren’t consistent with 18(3) cage in N2, cannot be {156} which clashes with R1C678), no 5
22a. 3 of {138/237} must be in R1C9 (R1C45 cannot be {37} which isn’t consistent with 18(3) cage in N2) -> no 3 in R1C45

23. 3,5 in N2 locked in R1C6 + R2C4 + R3C45 (step18a) = {1359/3456}, no 2,7,8, clean-up: no 2,3 in R3C8 (step 3)
23a. 3,4 of {3456} must be in R3C45 -> no 4 in R2C4
23b. R3C45 (step 18) = {15/34}
23c. Killer pair 1,4 in R3C45 and R3C8, locked for R3, clean-up: no 8 in R2C6

24. R2469C4 (step 20) = {1359/1368/1458/2349} (cannot be {1269/1278} because R2C4 only contains 3,5), no 7, clean-up: no 8 in R7C2 (step 12)
24a. 1 of {1359/1368/1458} must be in R6C4, 3 of {2349} must be in R2C4 -> no 3 in R6C4, clean-up: no 6 in R6C3

25. 45 rule on C1234 3 innies R135C4 = 15 = {168/249} (cannot be {159/258/348/357/456} which clash with R2469C4, cannot be {267} because no 2,6,7 in R3C4), no 3,5,7, clean-up: no 1,4 in R3C5 (step 23b)
25a. R3C4 = {14} -> no 1,4 in R1C4
25b. 8,9 can only be in R5C4 -> R5C6 = {89}

26. Naked pair {89} in R45C4, locked for C4 and N5, clean-up: no 3,4 in R78C4
26a. Naked pair {57} in R78C4, locked for C4 and N8 -> R2C4 = 3, R3C5 = 5, R3C4+R4C5 = 3 = [12], R3C8 = 4, R1C6 = 9 (step 18a or step 3), R6C4 = 4, R6C56 = [13], R5C6 = 5, R6C3 = 5, R6C7 = 2, clean-up: no 3 in R1C9 (step 1), no 8 in R3C6
26b. Naked pair {27} in R23C6, locked for C6 and N2 -> R1C4 = 6, R12C5 = [48], R1C9 = 2 (step 22 or step 1), R4C6 = 6, R4C7 = 4, R5C5 = 7, R5C4 = 8 (step 7), R4C34 = [89], R789C6 = [481], R9C4 = 2, clean-up: no 7 in R1C78 (prelim g), R9C1 = {58} (step 12)
26c. Naked pair {58} in R1C78, locked for R1 and N3
26d. Naked triple {137} in R1C123, locked for N1
26e. R7C5 = 9 (hidden single in C5)

27. R1C9 = 2 -> R23C9 = 12 = [93]

28. R234C1 = {479/578} (cannot be {389} because R2C1 only contains 4,5,6, cannot be {569} because R4C1 only contains 3,7) -> R4C1 = 7, R23C1 = [49/58], R6C12 = [69]
28a. R2C4 + R4C1 = R3C2 + 2 (step 13), R2C4 + R4C1 = 10 -> R3C2 = 8, R3C1 = 9, R2C1 = 4
28b. Naked pair {26} in R23C3, locked for C3 and N1 -> R2C2 = 5

29. R6C12 = [69] = 15 -> R5C1 + R7C2 = 5 = [23]

and the rest is naked singles and a cage sum.

Like Andrew I had some difficulty finding the next (important) move but after using some Killer triples I managed to crack it. I have to say that Andrew's Killer triple in step 17 was quite neat.

Boredom #2 Walkthrough:

1. R1234
a) Innies+Outies R1: 6 = R2C5 - R1C9 -> R2C5 = (789), R1C9 = (123)
b) 22(3) = 9{58/67} -> 9 locked for R1
c) Innies+Outies N3: 5 = R1C6 - R3C8 -> R1C6 <> 5; R3C8 = (1234)
d) 17(2) = {89} locked for R4
e) 10(2) <> 1,2
f) Innies+Outies N1: -18 = R2C4 - (R23C1+R3C2) -> R2C4 <> 7,8,9
g) Innies+Outies N2: -10 = R4C5 - (R1C6+R2C4) -> R2C4 <> 1

2. N9
a) Innies+Outies N9: 13 = R6C9+R8C6 - R7C8 -> R6C9+R8C6 <> 1,2,3,4; R7C8 <> 6,7,8,9

3. C456 !
a) 20(3) <> 3 because {389} blocked by R4C4 = (89)
b) Killer pair (89) locked in R4C4 + 20(3) for N5
c) Innies C6789 = 10(3) <> 8,9; R79C6 <> 6,7 because R5C6 >= 4
d) Outies C789 = 26(4) <> 1; R4C6 <> 3,4 since R6C6 <= 4
e) 10(2): R4C7 <> 6,7
f) Killer pair (67) locked in R4C6 + 20(3) for N5
g) 14(3) must have one of (6789) -> R7C5 = (6789)
h) Outies C123 = 18(4) = {1269/1278/1359/1368/1458/2349/2358} since R4C4 = (89); R9C4 <> 8,9
i) ! Innies C1234 = 15(3) <> {159} since it's a Killer triple of Outies C123
j) Innies C1234 = 15(3): R1C4 <> 1 because R3C4 <> 6,8

4. C456 !
a) 9 locked in Outies C789 = 26(4) = 9{278/368/467} <> 5 because R4C6 = (67)
b) ! Innies N8 = 23(4): R9C4 <> 1 because R7C6 <> 6,7,9 and {1589} is blocked by Killer triple (589) of 12(2)
c) ! R4C5 <> 1 since it sees all 1 of C4
d) 1 locked in R6C45 @ N5 for R6
e) 5(2) = {23} locked for R6
f) Hidden pair (23) in R4C5+R6C6 for N5 -> R4C5 = (23)
g) 8(3) = 1{25/34} -> 1 locked for R3+N2; R3C45 <> 2,3
h) 9(2) @ N2 = {23/67} because {45} blocked by R3C45 = (145)
i) Naked quad (2367) locked in R2346C6 for C6
j) 14(3) = 1{49/58} since (67) only possible @ R7C5 -> R7C5 = (89)

5. C456
a) Naked pair (89) locked in R7C5+R8C6 for N8
b) 12(2) = {57} locked for C4+N8
c) 10(3) = {136} -> R9C6 = 1; {36} locked for C5+N8
d) R7C6 = 4, R5C6 = 5, R6C5 = 1 -> R7C5 = 9, R6C4 = 4 -> R6C3 = 5, R3C4 = 1, R4C5 = 2 -> R3C5 = 5
e) Hidden Single: R1C5 = 4 @ C5
f) 18(3) = {468} -> R2C5 = 8, R1C4 = 6
g) R5C5 = 7 -> R5C4 = 8, R4C6 = 6 -> R4C7 = 4

6. R123
a) 22(3) = {589} -> R1C6 = 9; {58} locked for R1+N3
b) 11(3) = {137} locked for R1+N1
c) 16(4) @ R2C2 = {2356} -> R2C2 = 5, R2C4 = 3; {26} locked for C3+N1
d) R1C9 = 2
e) 14(3) @ R1C9 = {239} -> R2C9 = 9, R3C9 = 3
f) R2C1 = 4
g) 20(3) = {479} -> R3C1 = 9, R4C1 = 7
h) R3C2 = 8
i) 16(4) @ R3C2 = {1348} -> 1,3 locked for N4

7. N7
a) Innies+Outies N7: -1 = R9C4 - R7C2 -> R9C4 = 2, R7C2 = 3
b) 14(3) = {158} locked for C1+N7
c) 13(3) = {247} -> R7C3 = 7, R8C3 = 4, R8C2 = 2

8. Rest is singles.

Rating: (Hard?) 1.25. I used Killer triples.

3x3::k:3328:3585:3585:4867:4867:4867:7174:7174:2312:3328:3585:4107:4867:3853:4867:3087:7174:2312:4370:3585:4107:4107:3853:3087:3087:7174:3610:4370:4370:6941:4126:4126:4126:3617:3610:3610:4388:6941:6941:6941:2344:3617:3617:3617:6188:4388:4388:4388:3888:2344:5938:6188:6188:6188:3126:3126:3888:3888:2344:5938:5938:3645:3645:4415:2112:2112:3888:7747:5938:2373:2373:3399:4415:4415:7747:7747:7747:7747:7747:3399:3399:

Next one in the line . This Killer was quite fun and the solution path flowed well. Thanks Para!

Boredom #3 Walkthrough:

1. R1234
a) Innies+Outies N3: 4 = R3C6 - R3C9 -> R3C6 <> 1,2,3,4 and R3C9 <> 6,7,8,9
b) 28(4) = 89{47/56} -> 8,9 locked for N3
c) 9(2) = {27/36} because (45) is a Killer pair of 28(4)
d) 12(3): R23C7 <> 7 since R3C6 >= 5
e) Innies N2 = 11(2): R3C4 <> 1,7,8,9
f) Innies+Outies N1: -2 = R3C4 - R3C1 -> R3C1 <> 1,2,3,9
g) Innies R1234 = 7(2) <> 7,8,9; R4C7 <> 5,6

2. R123+N46
a) Outies N4 = 16(1+1) = [79/88]
b) Innies+Outies N1: -2 = R3C4 - R3C1 -> R3C4 = (56)
c) Innies N2 = 11(2) = {56} locked for R3+N2
d) 15(2) = {78} locked for C5+N2
e) Naked pair (78) in R3C15 locked for R3
f) Innies+Outies N3: 4 = R3C6 - R3C9 -> R3C9 = (12)
g) Outies N6 = 7(1+1) = [16/25]
h) Naked pair (56) in R35C6 locked for C6
i) 16(3) @ N1 can only have one of (56) -> R2C3 <> 5,6

3. R789 !
a) Innies N7 = 8(2) <> 4,8,9
b) Innies N9 = 9(2) <> 9
c) Innies R89 = 13(2) <> 1,2,3; R8C4 <> 7,8
d) Outies R9 = 15(3)
e) ! Hidden Killer triple (123) in 8(2) + 9(2) + Outies R9 for R8 since each of them can only have one of (123)
-> 9(2) <> 4,5

4. C789
a) Innies+Outies C89: 12 = R16C7 - R58C8 -> R16C7 <> 1,2,3,4,5 and R58C8 <> 5,6,7,8
b) Innies+Outies C89: 21 = R168C7 - R5C8: -> R5C8 <> 4
c) 9(2): R8C7 = (678)
d) 12(3): R2C7 <> 1 since R3C7 <> 5,6
e) 1 locked in R3C79 @ N3 for R3
f) Innies N3 = 8(3) = 1{25/34}
g) Innies N7 = 9(2) <> 4,5 since (45) is a Killer pair of Innies N3
h) 4 locked in 13(3) @ N9 = 4{18/27/36} <> 5,9

5. R789
a) Hidden pair (59) in R7C89 @ N9 locked for R7 -> R7C89 = (59)
b) 12(2) = {48} locked for R7+N7
c) Innies N7 = 8(2): R9C3 <> 3

6. C123 !
a) ! Killer triple (478) locked in 13(2) + R37C1 for C1
b) 7 locked in R123C1 @ C1 for N1
c) 16(3) = {169/259/268/358} <> 4 because R3C4 = (56)

7. R123 !
a) Innies+Outies N23: 9 = R23C3 - R3C9 -> R2C3 <> 9 (IOU @ R3)
b) Innies N1 = 18(3): R3C3 <> 2 since 9 only possible there
c) 16(3) = {169/259/358} because R3C3 = (39)
d) ! 16(3) <> 1 because 16(3) = [196] + R3C8 = 4 blocked by Killer pair (46) of 12(3)
-> 16(3) = 5{29/38} -> R3C4 = 5; R2C3 <> 3
e) R3C6 = 6, R5C6 = 5
f) Innie N1 = R3C1 = 7
g) Innie N3 = R3C9 = 2
h) 9(2) = {36} locked for N3+C9

8. N569
a) 13(3) = 4{18/27} because 3,6 only possible @ R9C8
b) 6 locked in R789C7 @ N9 for C7
c) 14(4) = {2345} -> {234} locked for N6
d) 14(3) = {257} -> 5,7 locked for R4+N6
e) Innie N5789 = R5C4 = 9
f) 16(3) = {268} locked for R5+N5
g) 9(3) = {234} because R56C5 = (134) -> R7C5 = 2, {34} locked for C5+N5

9. N36
a) 7 locked in 27(4) @ R5 = {3789} -> R5C3 = 3; {78} locked for R5+N4
b) R3C3 = 9 -> R2C3 = 2
c) Innies N7 = 8(2) = {17} locked for C3+N7
d) 15(4) = {1347} because R6C4+R7C3 = (17) -> R8C4 = 4, R7C4 = 3
e) 8(2) = [26/35]

10. Rest is singles.

Rating: (Easy) 1.5. I used Killer triples and a not so obvious Killer pair.

Boredom Killer #3 took me quite a long time. Afmob commented that it flowed well. It did for me for about 20 steps but then I was struggling until I found step 34, which is clearly one of the key moves. After that it was simple because I'd already done all the hard work.

I'll rate BK #3 at least Hard 1.5 the way I solved it. If I'd found step 34 a lot earlier I think it would be 1.5.

Here is my walkthrough

Prelims

a) R12C1 = {49/58/67}, no 1,2,3
b) R12C9 = {18/27/36/45}, no 9
c) R23C5 = {69/78}
d) R7C12 = {39/48/57}, no 1,2,6
e) R7C89 = {59/68}
f) R8C23 = {17/26/35}, no 4,8,9
g) R8C78 = {18/27/36/45}, no 9
h) R567C5 = {126/135/234}, no 7,8,9
i) 14(4) cage in N1 = {1238/1247/1256/1346/2345}, no 9
j) 28(4) cage in N3 = {4789/5689}, no 1,2,3, 8,9 locked for N3, clean-up: no 1 in R12C9
k) 27(4) cage at R4C3 = {3789/4689/5679}, no 1,2
l) 14(4) cage at R4C7 = {1238/1247/1256/1346/2345}, no 9
m) 19(5) cage in N2 must contain 1, locked for N2

1. 45 rule on N3 3 innies R2C7 + R3C79 = 8 = {125/134}, no 6,7
1a. R12C9 = {27/36} (cannot be {45} which clashes with R2C7 + R3C79)

2. 45 rule on N4 2 outies R3C1 + R5C4 = 16 = [79/88/97]

3. 45 rule on N1 1 innie R3C1 = 1 outie R3C4 + 2, R3C4 = {567}

4. 45 rule on N3 1 outie R3C6 = 1 innie R3C9 + 4, no 2,3,4 in R3C6

5. 45 rule on N7 2 innies R79C3 = 8 = {17/26/35}, no 4,8,9

6. 45 rule on N9 2 innies R79C7 = 9 = {18/27/36/45}, no 9

7. 45 rule on N2 2 innies R3C46 = 11 = {56}, locked for R3 and N2, clean-up: no 9 in R23C5, no 9 in R3C1 (step 3), no 3,4 in R3C9 (step 4), no 7 in R5C4 (step 2)
7a. Naked pair {78} in R3C15, locked for R3
7b. Naked pair {78} in R23C5, locked for C5 and N2
7c. Max R3C9 = 2 -> min R4C89 = 12, no 1,2 in R4C89
7d. R79C7 (step 6) = {18/27/36} (cannot be {45} which clashes with R23C7)

8. 12(3) cage at R2C7 = {156/345} (cannot be {246} which clashes with R2C7 + R3C79), no 2
8a. 1 of {156} must be in R3C7 -> no 1 in R2C7
8b. 1 in N3 locked in R3C79, locked for R3
8c. 2 in N3 locked in R123C9, locked for C9

9. 45 rule on R89 2 innies R8C46 = 13 = {49/58/67}, no 1,2,3

10. 45 rule on R1234 2 innies R4C37 = 7 = [34/43/52/61], no 7,8,9 in R4C3, no 5,6,7,8 in R4C7
10a. 27(4) cage at R4C3 = {3789/4689/5679}, 9 locked for R5
10b. 3 of {3789} must be in R4C3 -> no 3 in R5C23

11. 45 rule on N6 2 outies R3C9 + R5C6 = 7 = [16/25]
11a. Naked pair {56} in R35C6, locked for C6, clean-up: no 7,8 in R8C4 (step 9)
11b. 14(4) cage at R4C7 = {1256/1346/2345} (cannot be {1238/1247} because R5C6 only contains 5,6), no 7,8

12. 45 rule on N5789 2 innies R5C46 = 14 = [86/95]
12a. 27(4) cage at R4C3 (step 10a) = {3789/4689/5679}
12b. 5 of {5679} must be in R4C3 (R5C234 cannot be {579} which clashes with R5C46 = [95]), no 5 in R5C23

13. Combined cage R8C2378 = 17(4) = {1268/1358/1367/2357} (cannot be {1457/2456} which clash with R8C46, cannot be {2348} which clashes with R8C78), no 4, clean-up: no 5 in R8C78

14. 4 in N9 locked in 13(3) cage = {148/247/346}, no 5,9
14a. 2 of {247} must be in R9C8 -> no 7 in R9C8

15. R7C89 = {59} (hidden pair in N9), locked for R7, clean-up: no 3,7 in R7C12, no 3 in R9C3 (step 5)
15a. Naked pair {48} in R7C12, locked for R7 and N7, clean-up: no 1 in R9C7 (step 6)

16. 45 rule on R9 3 outies R8C159 = 15 = {168/249/258/267/357} (cannot be {159/348} which clashes with R8C2378, cannot be {456} which clashes with R8C46)
16a. 8 of {168} must be in R8C9 -> no 1 in R8C9
16b. 4 of {249} must be in R8C9 -> no 4 in R8C5

17. 16(3) cage at R2C3 = {169/259/268/358/367/457} (cannot be {178/349} because R3C4 only contains 5,6}
17a. R3C4 = {56} -> no 5,6 in R2C3
17b. 7,8 of {358/367/457} must be in R2C3 -> no 3,4 in R2C3

18. Killer triple 7,8,9 in R12C1, R12C3 and R3C1, locked for N1
18a. 14(4) cage in N1 = {1256/1346/2345}
18b. Killer triple 4,5,6 in R12C1 and 14(4) cage, locked for N1

19. 28(4) cage in N3 = {4789/5689}
19a. 5 of {5689} must be in R1C7 (R123C8 cannot be {589} which clashes with R7C8) -> no 6 in R1C7, no 5 in R12C8
19b. 5 in N3 locked in R12C7, locked for C7

20. 15(4) cage at R6C4 = {1239/1248/1257/1347/1356/2346}
20a. 9 of {1239} must be in R8C4 -> no 9 in R6C4

21. 23(4) cage at R6C6 = {1679/2678/3479} (cannot be {2489} because 4,8,9 only in R68C6)
21a. 6 of {1679/2678} must be in R7C7 -> no 1,2 in R7C7, clean-up: no 7,8 in R9C7 (step 6)
21b. 3,7 of {3479} must be in R7C67 -> no 3 in R6C6

22. 14(4) cage at R4C7 (step 11b) = {1256/1346/2345}
22a. 4 of {1346} must be in R45C7 (R45C7 cannot be {13} which clashes with R23C7), 4 of {2345} must be in R45C7 (R45C7 cannot be {23} which clashes with R79C7) -> no 4 in R5C8

23. R4C456 = {178/259/268/349/367/457} (cannot be {169/358} which clash with R5C46)
23a. 45 rule on R123 4 outies R4C1289 = 22 = {1489/1579/2389/2578/3469} (cannot be {3568/4567} which clash with R4C37, cannot be {2479} which clashes with R4C456, cannot be {1678/2569/3478} which clash with 17(3) cage at R3C1)
23b. 5 of {1579/2578} must be in R4C89 (5 cannot be in 17(3) cage at R3C1 because {1579/2578} don’t contain 4), no 5 in R4C12
23c. 6 of {3469} must be in R4C12 (6 cannot be in 14(3) cage at R3C9 because {3468} doesn’t contain 7), no 6 in R4C89

24. Killer triple 4,7,8 in R12C1, R3C1 and R7C1, locked for C1
24a. 7 in C1 locked in R123C1, locked for N1
24b. 17(3) cage at R3C1 = {179/278/467} (cannot be {269} because R3C1 only contains 7,8, cannot be {368} which clashes with 27(4) cage at R4C3), no 3
24c. 2 of {278} must be in R4C1 (R34C1 cannot be {68/78} which clash with R12C1 + R7C1), no 2 in R4C2
24d. 4 of {467} must be in R4C2 -> no 6 in R4C2
24e. 17(3) cage in N7 = {179/269/359}
24f. 7 of {179} must be in R9C2 -> no 1 in R9C2
24g. R8C159 (step 16) = {168/249/258/267/357}
24h. 4,7,8 only in R8C9 -> R8C9 = {478}

25. Hidden killer pair 4,9 in R8C46 and R8C5 + R9C456 for N8 -> 30(6) cage at R8C5 must contain both of 4,9 or neither of them
25a. Hidden killer pair 5,8 in R8C46 and R8C5 + R9C456 for N8 -> R8C5 + R9C456 both of 5,8 or neither of them, but 30(6) cage at R8C5 can contain 5 in R9C3 without containing 8
25b. 30(6) cage at R8C5 = {134589/134679/135678/234579} (cannot be {123789/125679/234678} which contain only one of 4,9, cannot be {124689} which contains 8 but not 5)
25c. 5 of {234579} must be in R9C3 (step 25a) -> no 2 in R9C3, clean-up: no 6 in R7C3 (step 5)

26. 15(4) cage at R6C4 (step 20) = {1239/1248/1257/1347/2346} (cannot be {1356} which clashes with R3C4)
26a. 5 of {1257} must be in R8C4 -> no 5 in R6C4

27. Combined cage R5C234678 = 34(6) = {136789/235789/245689/345679} (cannot be {145789} because 14(4) cage at R4C7 cannot be 4{145})
27a. 45 rule on R6789 3 outies R5C159 = 11 = {128/137/146/245} (cannot be {236} which clashes with R5C234678)
27b. 7 of {137} must be in R5C9 -> no 3 in R5C9

28. Hidden killer triple 4,7,8 in R9C2, R9C3456 and R9C89 for R9, R9C3456 must contain two of 4,7,8 (step 25b) -> R9C2 + R9C89 must contain one of 4,7,8
28a. 13(3) cage in N9 (step 14) = {148/247/346} must contain one of 4,7,8 in R9C89 except for {346} which has 4 in R8C9
28b. 17(3) cage in N7 (step 24d) = {179/269/359} can only be {179} when 13(3) cage in N9 = {346} with R8C9 = 4 -> R8C159 (step 16) = {249/258/267/357} (cannot be {168}), no 1
28c. 1 in R8 locked in R8C2378 (step 13) = {1268/1358/1367}
28d. R8C78 = {18/36} (cannot be {27} which isn’t consistent with R8C2378)

29. 2 in N9 locked in R9C78, locked for R9
29a. 17(3) cage in N7 = {179/269/359}
29b. 2 of {269} must be in R8C1 -> no 6 in R8C1

30. 17(4) cage in N4 = {1259/1349/1358/2348/2357/2456} (cannot be {1268} which clashes with 17(3) cage at R3C1, cannot be {1367/1457} which clash with 27(4) cage at R4C3)
30a. 17(4) cage cannot be {1259}, here’s how
17(4) cage = {1259} => R4C12 = [64] clashes with R4C37 = [34]
30b. -> 17(4) cage in N4 = {1349/1358/2348/2357/2456}
30c. Hidden killer pair 1,2 in R4C12 and 17(4) cage for N4 -> R4C12 must contain one of 1,2
30d. 17(3) cage at R3C1 (step 24b) = {179/278} (cannot be {467} which doesn’t contain 1 or 2), no 4,6
30e. 1 of {179} must be in R4C1 (R34C1 cannot be [79] which clashes with 17(3) cage in N7 = [917] because R9C1 must be 1 when R4C2 is 1), no 1 in R4C2, no 9 in R4C1
30f. R4C12 = [19/27/28]

31. R4C456 (step 23) = {268/349/367/457} (cannot be {178/259} which clash with R4C12), no 1

32. 1 in N5 locked in R5C5 + R6C456
32a. 45 rule on R789 4 outies R5C5 + R6C456 = 15 = {1239/1248/1257/1347} (cannot be {1356} which clashes with R5C6), no 6
32b. R567C5 = {126/135/234}
32c. 1 of {135} must be in R56C5 (R56C5 cannot be {35} which isn’t consistent with R5C5 + R6C456), no 1 in R7C5

33. 15(4) cage at R6C4 (step 26) = {1239/1248/1257/1347/2346}
33a. 4 of {1248/1347/2346} must be in R8C4 (R7C34 + R8C4 cannot be {236} because R8C5 is a common peer), no 4 in R6C4

34. 45 rule on C89 2 outies R16C7 = 2 innies R58C8 + 12
34a. Max R16C7 = 17 -> max R58C8 = 5, no 5,6,8 in R58C8, clean-up: no 1,3 in R8C7
34b. Min R58C8 = 3 -> min R16C7 = 15, no 4,5 in R1C7, no 1,2,3,4 in R6C7

35. R2C7 = 5 (hidden single in N3), R3C6 = 6, R3C7 = 1 (step 8), R3C9 = 2, R5C6 = 5, R5C4 = 9 (step 12), R3C4 = 5, R3C1 = 7 (step 3), R23C5 = [78], R23C3 = [29/83] (step 17), clean-up: no 6,8 in R1C1, no 7 in R1C9, no 6 in R2C1, no 6 in R4C3 (step 10)
35a. Naked pair {36} in R12C9, locked for C9 and N3, clean-up: no 3,6 in R9C8 (step 14)
35b. 4 in N3 locked in R123C8, locked for C8
35c. 4 in N9 locked in R89C9, locked for C9

36. R3C9 = 2 -> R4C89 = 12 = [39/57/75], no 8, no 9 in R4C8

37. R6C8 = 6 (hidden single in C8)

38. R5C6 = 5 -> R4C7 + R5C78 = 9 = {234} (only remaining combination), locked for N6, clean-up: no 9 in R4C9 (step 36)
38a. Naked pair {57} in R4C89, locked for R4 and N6, clean-up: no 2 in R4C7 (step 10)
38b. Naked pair {34} in R4C37, locked for R4
38c. Naked triple {268} in R4C456, locked for R4 and N5 -> R4C12 = [19], clean-up: no 7 in R9C2 (step 24e)
38d. 2 in N6 locked in R5C78, locked for R5

39. R567C5 = {234} (only remaining combination) -> R7C5 = 2, R4C5 = 6, R56C5 = {34}, locked for C5 and N5, clean-up: no 6 in R9C3 (step 5)
39a. Naked pair {17} in R6C46, locked for R6
39b. Naked pair {89} in R6C89, locked for R6 and N6 -> R5C9 = 1

40. 9 in N7 locked in R89C1, locked for C1, clean-up: no 4 in R12C1
40a. R12C1 = [58], R7C12 = [48], R2C3 = 2, R3C3 = 9 (step 35), R23C8 = [94], R3C2 = 3, R7C89 = [59], R4C89 = [75], R1C78 = [78], R6C79 = [98], clean-up: no 6 in R8C2, no 5 in R8C3, no 2 in R9C7 (step 6)

41. Naked pair {36} in R79C7, locked for C7 and N9 -> R8C78 = [81], R4C37 = [34], R5C78 = [23], R56C1 = [62], R56C5 = [43], R5C23 = [78], R9C8 = 2, clean-up: no 5 in R8C2, no 7 in R8C3, no 5 in R9C3 (step 5)

and the rest is naked singles and a cage sum.

3x3::k:6656:6656:6656:3843:3843:2821:4102:4102:2568:2569:6656:3339:3339:3843:2821:2821:2568:2568:2569:5395:3339:3339:2838:5655:5655:5655:2586:2569:5395:5395:5662:2838:3872:3872:5655:2586:1828:1828:4390:5662:5662:5662:3872:3627:3627:2861:4142:4390:4390:4145:5662:3635:3635:4661:2861:4142:4142:4142:4145:4667:4667:3635:4661:5439:5439:5185:5185:2371:4667:4667:4166:4661:5439:1609:1609:5185:2371:2371:4166:4166:4166:

Thanks for so many Killers, but wouldn't it be better if you used some of those for future Assassins?

Edit: Let's get back to business.

Boredom #4 offered lots of Killer subsets move and I used a lot of them but sometimes I later realized they weren't needed (e.g. I used Killer triples in R89 to get the same result as step 1b).

Boredom #4 Walkthrough:

1. R6789
a) 16(2) = {79} locked for C5
b) Innies+Outies R9: -14 = R8C58 - R9C14
-> R8C58 = {12} locked for R8 and R9C14 = {89} locked for R9
c) 7 locked in R9C789 @ R9 for N9; 16(4) = 7{126/135/234}
d) Innies+Outies R89 : R7C67 = R8C9 -> R7C67 <> 9
e) Innies+Outies R6789: 2 = R5C3 - R6C6 -> R5C3 <> 1,2 and R6C6 <> 8,9
f) R8C3 <> 8,9 because it sees all 8,9 of R9

2. R123
a) 16(2) = {79} locked for R1+N3
b) Hidden Single: R2C2 = 9 @ R2, R3C6 = 9 @ N2
c) 11(2) <> 2,4
d) 26(4) = 89{36/45} -> 8 locked for R1+N1
e) Innies+Outies R1: 3 = R2C5 - R1C69 -> R2C5 = (68) and R1C69 <> 5,6
f) Killer pair (68) locked in R2C5+11(2) for C5
g) Hidden Killer pair (56) in 26(4) + 15(3) for R1 since 26(4) can only have one of (56)
-> 15(3) = {168/258/458} <> 3
h) Innies+Outies R12: 1 = R3C34 - R2C1 -> R2C1 <> 1
i) 10(2): R4C9 <> 1,3
j) R2C3 <> 7 since it sees all 7 of N2
k) R3C4 <> 1 since it sees all 1 of N1
l) Outies R12 = 11(3+1) -> R4C1 <> 6,7 and R3C3 <> 7 because R34C1 cannot be [11]

3. C3456
a) 9(3): R9C6 <> 1,2 since 6 only possible there
b) 15(3) @ N2: R1C4 <> 1,2 because 8{16/25} blocked by Killer pairs (58,68) of 11(2)
c) Innies C1234 = 12(3) <> 8,9 because R1C4 >= 4
d) 9 locked in R6C45 @ N5 for R6
e) 9 locked in R45C3 @ N4 for C3
f) Innies C6789 = 16(3) <> 1 because R9C6 <> 1,7,8

4. R456
a) 11(2) @ N4: R7C1 <> 2
b) Innies+Outies R6789: 2 = R5C3 - R6C6 -> R5C3 <> 3
c) Innies+Outies R1234: R4C4 = R5C7 <> 8,9

5. R123 !
a) ! Innies+Outies R1: 14 = R2C567 - R1C9: R2C6 <> 6,8 (IOU @ N3)
b) 8 locked in R23C5 @ N2 for C5
c) 11(2): R3C5 <> 3
d) ! Killer triple (568) locked in 15(3) + R3C5 for N2

6. C456 + R5 !
a) ! Innies C1234 = 12(3) <> 7 because {147} blocked by R23C4 @ 13(4) since R23C4 cannot be {23} because 7 only possible there
b) Innies+Outies R1234: R4C4 = R5C7 <> 7
c) ! Hidden Killer triple (789) in R5C36 + 14(2) for R5 since 14(2) can only have one of (89)
-> R5C36 = (789)
d) Innies+Outies R6789: 2 = R5C3 - R6C6 -> R6C6 = (567)
e) Innies C6789 = 16(3) = {358/367/457}; R6C6 <> 7 and R9C6 = (34)
f) 9(3) = 3{15/24} -> 3 locked for R9+N8
g) Innies+Outies R6789: 2 = R5C3 - R6C6 -> R5C3 <> 9
h) 9 in R5 locked in 14(2) = {59} locked for R5+N6
i) Hidden Single: R4C3 = 9 @ N4
j) R6C4 <> 7,8 since it sees all 7,8 of R5

7. C789
a) 16(4) = {1267} locked for N9
b) 10(2) <> 1
c) Innies+Outies C9: 7 = R25C8 - R9C9: R9C9 = (1267):
-> R25C8 = 8/9/13/14(2) = [35/45/49/59] -> R2C8 = (345)
d) 18(3) <> 5 because (67) only possible @ R6C9 and {459} blocked by R5C9 = (59)
e) 18(3) must have one of (167) -> R6C9 = (167)

8. R789
a) Innies+Outies R89: R7C67 = R8C9: R8C9 = (3489)
- R8C9 <> 3 because R7C7 >= 3
- R7C67 = 4/8/9(2) = [13/18/45/53/54/63] -> R7C6 <> 2,7,8
b) 18(4) <> 7 because {1467} unplaceable
c) 2 in R7 locked in 16(4) -> R6C2 <> 2

9. C123
a) 7(2) <> 2
b) 2 locked in R79C2 @ C2 for N7
c) 17(3): R6C3 <> 2 because R6C4 <> 7,8
d) 2 locked in R23C3 @ C3 for N1+13(4)
-> 13(4) = 12{37/46}
e) 13(4): R2C34+R3C3 <> 4 because R3C4 <> 1,2,6

10. R123
a) 11(3) <> 7 because R2C4 = (137)
b) 7 in N2 locked in 13(4) = {1237} -> 7 locked for C4
c) Hidden Single: R7C5 = 7 @ N8, R6C5 = 9

11. C456 !
a) ! Hidden pair (78) in R45C6 for N5 locked for C6 -> R4C6 = (78)
b) 2 in R12C6 @ C6 locked for N2+11(3)
c) 15(3) @ N2 = 6{18/45} -> 6 locked for N2
d) 11(2): R4C5 <> 5
e) 22(5) = 258{16/34} because R6C6 = (56) and other combos blocked by R4C5 = (36)
-> R5C6 = 8; 2 locked for N5
f) R4C6 = 7, R5C3 = 7
g) 15(3) @ N5 = {267} -> 2,6 locked for C7+N6
h) 17(3) = {467} -> 4,6 locked for R6
i) Hidden Single: R6C1 = 2 @ R6
j) Cage sum: R7C1 = 9

12. R789
a) 21(3) = {678} -> R9C1 = 8, {67} locked for R8+N7
b) R6C6 = 5, R8C6 = 4, R9C6 = 3
c) 20(3) = {389} -> R9C4 = 9, R8C3 = 3, R8C4 = 8
d) R8C9 = 9
e) 18(3) = {189} -> R6C9 = 1, R7C9 = 8

13. Rest is singles.

Rating: 1.5. I used Killer triples and combo analysis.

Boredom Killer #4 took me even longer than #3. I think I started it about a week after I posted my walkthrough for #3 and have been looking at it on and off since then, eventually getting the first breakthrough yesterday (step 17) and finishing it today.

Congratulations to Afmob for solving it so quickly and without needing to use any chains!

I used a few short contradiction moves. The interactions between the 22(5) cage in N5 and the 5 innies in R5 reminded me of J-C's A118 that had a 7-cell cage at R4C3.

I'll rate BK#4 as 1.5 to Hard 1.5 the way I solved it.

Here is my walkthrough. As I've commented at the end of step 4, I found Afmob's step 1b but only well after I'd done step 4.

Thanks Afmob for a couple of comments. The second one would have avoided my last chain.

Prelims

a) R3C89 = {19/28/37/46}, no 5
b) R1C78 = {79}, locked for R1 and N3, clean-up: no 1,3 in R4C9
c) R34C5 = {29/38/47/56}, no 1
d) R5C12 = {16/25/34}, no 7,8,9
e) R5C89 = {59/68}
f) R67C1 = {29/38/47/56}, no 1
g) R67C5 = {79}, locked for C5, clean-up: no 2,4 in R34C5
h) R9C23 = {15/24}
i) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
j) 10(3) cage in N3 = {136/145/235}, no 8
k) R234C1 = {127/136/145/235}, no 8,9
l) 21(3) cage at R3C2 = {489/579/678}, no 1,2,3
m) 21(3) cage in N7 = {489/579/678}, no 1,2,3
n) 20(3) cage at R8C3 = {389/479/569/578}, no 1,2
o) 9(3) cage in N8 = {126/135/234}, no 7,8,9
p) 26(4) cage in N1 = {2789/3689/4589/4679/5678}, no 1
q) 13(4) cage at R2C3 = {1237/1246/1345}, no 8,9

1. 26(4) cage in N1 = {3689/4589/5678} (cannot be {2789/4679} because 7,9 only in R2C2), no 2, 8 locked for N1
1a. 7,9 only in R2C2 -> R2C2 = {79}
1b. 8 locked in R1C123, locked for R1
1c. 9 in N1 locked in R23C2, locked for C2

2. R3C6 = 9 (hidden single in N2)
2a. R2C2 = 9 (hidden single in N1)
2b. R1C123 = {368/458}

3. Max R1C45 = 11 -> min R2C5 = 4
3a. 15(3) cage in N2 = {168/258/456} (cannot be {348} which clashes with R1C123), no 3
3b. {456} can only be {45}6 (R1C45 cannot be {46/56} which clash with R1C123), no 4,5 in R2C5
3c. Killer pair 5,6 in R1C123 and R1C45, locked for R1
3d. Killer pair 6,8 in R2C5 and R34C5, locked for C5
3e. 1 of {168} must be in R1C5 -> no 1 in R1C4

4. 45 rule on R89 3 innies R8C679 = 18
4a. Max R9C14 = 17 -> min R8C1234 = 24 (combining 21(3) and 20(3) cages)
4b. R8C679 cannot be {189/279} (which clash with all 4-cell combinations that total 24 or more), no 1,2 in R8C679
4c. R8C59 = {12} (hidden pair in R8)
4d. R8C679 = {369/378/459/468/567}
4e. 45 rule on R8 4 remaining innies R8C1234 = 24 -> R9C14 = 17 = {89}, locked for R9
4f. R8C1234 = {3489/3579/3678/4569/4578}
4g. 4 of {3489/4569/4578} must be in R8C12 (other combinations for R8C12 or R8C34 clash with 21(3) or 20(3) cage), no 4 in R8C34
4h. 7 in R9 locked in R9C789, locked for N9
4i. Min R8C67 = 9 -> max R7C67 = 9, no 9 in R7C7
[Much more direct after step 4 is 45 rule on R8 2 outies R9C14 = 2 remaining innies R8C58 + 14 -> R9C14 = 17 = {89}, locked for R9, R8C58 = 3 = {12}, locked for R8. I only spotted this a long time after doing my original version of step 4.]

5. 45 rule on R12 3 innies R2C134 = 12
5a. Max R2C34 = 10 -> min R2C1 = 2
5b. 45 rule on R12 4 outies R34C1 + R3C34 = 11
5c. Min R3C134 = 6 -> max R4C1 = 5
5d. Max R3C134 = 10 can only be {127} when R234C1 = {27}1 -> no 7 in R3C3
5e. R2C134 = 12 = {147/237/246/345} (cannot be {156} which clashes with 10(3) cage in N3)

6. 45 rule on C1234 3 innies R145C4 = 12 = {129/147/156/237/246/345} (cannot be {138} because no 1,3,8 in R1C4), no 8

7. 9(3) cage in N8 = {126/135/234}
7a. 1,2 of {135/234} must be in R8C5, 6 of {126} must be in R9C6 -> no 1,2 in R9C6

8. 45 rule on C6789 3 innies R569C6 = 16 = {268/358/367/457} (cannot be {178} because no 1,7,8 in R9C6), no 1

9. 8 in R2 locked in R2C567
9a. 45 rule on R2 5 innies R2C56789 = {12678/13578/14568/23568} (cannot be {23478} which clashes with R2C134
9b. Cannot be {12678}, here’s how
7 of {12678} must be in R2C6, R1C6 + R2C7 must be [31] => R2C89 = {26} would make 10(3) cage in N3 = 2{26}
9c. -> R2C56789 = {13578/14568/23568}, 5 locked for R2

10. 45 rule on R1234 1 innie R4C4 = 1 outie R5C7, no 8 in R5C7

11. 45 rule on R6789 1 outie R5C3 = 1 innie R6C6 + 2, no 1,2,3 in R5C3, no 8 in R6C6
11a. R569C6 (step 8) = {268/358/367/457}
11b. 8 of {268} must be in R5C6 -> no 2 in R5C6

12. 21(3) cage at R3C2 = {489/579/678}
12a. 4 of {489} must be in R3C2 -> no 4 in R4C23
12b. 9 of {579} must be in R4C3 -> no 5 in R4C3

13. 45 rule on C5 5 innies R12589C5 = 18 = {12348/12456}
13a. 15(3) cage in N2 = {168/258/456}
13b. 2 of {258} must be in R1C5 (R12C5 cannot be {58} which clashes with R12589C5), no 2 in R1C4
[Afmob pointed out that it’s easier to say R12C5 cannot be {58} which clashes with R34C5]

14. R145C4 (step 6) = {147/156/246/345} (cannot be {129/237} because R1C4 only contains 4,5,6), no 9, clean-up: no 9 in R5C7 (step 10)
14a. 9 in N5 locked in R6C45, locked for R6, clean-up: no 2 in R7C1
14b. 9 in C1 locked in R789C1, locked for N7

15. 3 in N7 locked in R7C123 + R8C3
15a. 45 rule on N7 4 innies R7C123 + R8C3 = 18 = {1359/1368/2349/2367} (cannot be {2358/3456} which clash with R9C23)
15b. 9 of {1359/2349} must be in R7C1 -> no 4,5 in R7C1, clean-uo: no 6,7 in R6C1

16. Min R7C67 = 4 (cannot be {12} which clashes with R7C23) -> max R8C67 = 14 -> min R8C9 = 4 (step 4)

17. R6C6 cannot be 7, here’s how
R6C6 = 7 => no 7 in R4C4 + R5C46 => no 7 in R5C7 (step 10), R5C3 = 9 (step 11) => no 7 in R5
17a. no 7 in R6C6, no 9 in R5C3 (step 11)
17b. 9 in R5 locked in R5C89 = {59}, locked for R5 and N6, clean-up: no 1 in R3C9, no 5 in R4C4 (step 10), no 2 in R5C12, no 3 in R6C6 (step 11)
17c. R4C3 = 9 (hidden single in R4), clean-up: no 6 in R34C2 (prelim l)

18. 2 in R5 locked in R5C457, R4C4 = R5C7 (step 10) -> 2 locked in R4C4 + R5C45, locked for N5, clean-up: no 4 in R5C3 (step 11)

19. 17(3) cage at R5C3 = {179/269/278/368/458/467} (cannot be {359} because R5C3 only contains 6,7,8)
19a. 9 of {179} must be in R6C4 -> no 1 in R6C4
19b. 8 in R5 locked in R5C36, CPE no 8 in R6C4
19c. 8 in C4 locked in R789C4, locked for N8

20. R569C6 (step 8) = {358/367/457}
20a. 7,8 only in R5C6 -> R5C6 = {78}
20b. 6 of {367} must be in R6C6 -> no 6 in R9C6

21. 9(3) cage in N8 = {135/234}, 3 locked for N8
21a. R8C5 = {12} -> no 1,2 in R9C5
21b. Killer pair 4,5 in R9C23 and R9C56, locked for R9

22. 16(4) cage in N9 = {1267} (only remaining combination), locked for N9, clean-up: no 7 in R7C6 (step 4i)

23. R678C9 = {189/369/378/468} (cannot be {279/567} because 2,6,7 only in R6C9, cannot be {459} which clashes with R5C9), no 2,5
23a. 1,6,7 only in R6C9 -> R6C9 = {167}
23b. 5 in N9 locked in R7C78 + R8C7, CPE no 5 in R7C6

24. 18(4) cage at R7C6 = {1359/1458/2349/3456} (cannot be {1269/1278} because 1,2 only in R7C6, cannot be {1368} which clashes with R678C9 because 1,6 only in R78C6, cannot be {1467/2367} because 1,2,6,7 only in R78C6, cannot be {2358} because R8C679 cannot be {58}5 and no 7 in R8C9, cannot be {2457} because no 6 in R8C9), no 7

25. 7 in R8 locked in R8C1234 (step 4f) = {3579/3678/4578}
25a. {3579} can only be {57}[39] -> no 9 in R8C1
25b. {3678} can only be {67}[38] -> no 6 in R8C34
25c. 20(3) cage at R8C3 = {389/578}
25d. 3 of {389} must be in R8C3, 8 of {578} must be in R9C4 -> no 8 in R8C3
25e. 8 locked in R89C4, locked for C4

26. Hidden killer quad 1,2,6,7 in R12C9, R34C9, R6C9 and R9C9 for C9 -> R12C9 must have one of 1,2,6
26a. 10(3) cage in N3 = {136/145/235}
26b. 2 of {235} must be in R12C9 -> no 2 in R2C8

27. R8C679 (step 4d) = {369/459/468}
27a. 8 of {468} must be in R8C7 (R8C67 cannot be [64] because R7C67 cannot total 8) -> no 8 in R8C9

28. R678C9 (step 23) = {189/369/468} (cannot be {378} because R8C9 only contains 4,9), no 7
28a. 3,8 only in R7C9 -> R7C9 = {38}

29. 18(4) cage at R7C6 (step 24) = {1359/1458/3456} (cannot be {2349} which clashes with R8C9), no 2
29a. 8 of {1458} must be in R7C7 (R8C67 cannot be [48/58]), no 8 in R8C7
29b. 8 in N9 locked in R7C789, locked for R7, clean-up: no 3 in R6C1

30. 2 in C6 locked in R12C6, locked for N2 and 11(3) cage at R1C6, no 2 in R2C7
30a. 11(3) cage at R1C6 = {128/236/245}, no 7
30b. 15(3) cage in N2 (step 13a) = {168/456}, 6 locked for N2, clean-up: no 5 in R4C5
30c. 6 of {236} (in 11(3) cage) can only be in R2C7 -> no 3 in R2C7

31. 7 in C6 locked in R45C6, locked for N5 -> R6C5 = 9, R7C5 = 7, clean-up: no 7 in R5C7 (step 10), no 4 in R6C1

32. 7 in C4 locked in R23C4 -> 13(4) cage at R2C3 = {1237} (only remaining combination), no 7 in R2C3
32a. R2C134 (step 5e) = {147/237}, cannot be {246} because R2C4 only contains 1,3,7), no 6
32b. 1 of {147} must be in R2C3 -> no 1 in R2C4
[Afmob pointed out that I missed 2 of 13(4) cage locked in R23C3, locked for C3 and N1, and 1 in 13(4) cage locked in R2C3 + R3C34, CPE no 1 in R3C1. Then the chain in step 33 would be avoided. I may have been careless with my manual eliminations of 2 from N2 in step 30 and still thought that 2 was in all four cells of the 13(4) cage. I missed a few CPEs that were in Afmob's walkthrough but I think this was the only important one that I missed.]

33. R234C1 = {127/136/145/235}
33a. Cannot be {127}, here’s how
R234C1 = {127} -> R3C2 = {45} => R1C123 = {368} => 4,5 can only be in R3C2
-> R234C1 = {136/145/235}, no 7
33b. 4 of {145} must be in R2C1 -> no 4 in R34C1

34. R3C2 = 7 (hidden single in N1), R4C2 = 5 (step 12), clean-up: no 6 in R7C1, no 1 in R9C3

35. R2C4 = 7 (hidden single in C4)
35a. 2 in 13(4) cage at R2C3 locked in R23C3, locked for C3 and N1, clean-up: no 4 in R9C2

36. R234C1 (step 33a) = {136/145} (cannot be {235} which clashes with R1C123), no 2
36a. 5,6 only in R3C1 -> R3C1 = {56} -> R4C1 = 1, clean-up: no 6 in R5C12, no 1 in R5C7 (step 10)

37. Naked pair {34} in R5C12, locked for R5 and N4, clean-up: no 3,4 in R4C4 (step 10)

38. Naked triple {126} in R5C457, locked for R5, clean-up: no 4 in R6C6 (step 11)
38a. Naked triple {126} in R4C4 + R5C45, locked for N5 -> R6C6 = 5, R5C3 = 7 (step 11), R5C6 = 8, R4C5 = 3, R3C5 = 8, R2C5 = 6, R6C4 = 4, R4C6 = 7, R1C4 = 5, R1C5 = 4 (step 30b), R9C5 = 5, R9C3 = 4, R9C2 = 2, R9C6 = 3, R8C5 = 1 (step 21), R8C8 = 2, R5C5 = 2, R45C4 = [61], R3C4 = 3, R5C7 = 6, R6C9 = 1, clean-up: no 4 in R3C9, no 2 in R4C9

39. Naked triple {368} in R1C123, locked for R1 and N1 -> R23C1 = [45], R5C12 = [34], R7C1 = 9, R9C1 = 8, R89C4 = [89], R6C1 = 2, R1C1 = 6, R8C12 = [76], R6C23 = [86], R1C23 = [38], R7C2 = 1, R7C4 = 2, R7C3 = 5 (cage sum)

and the rest is naked singles.

3x3::k:5383:5383:5383:6913:2307:5634:2566:2566:2566:3080:4356:4356:6913:2307:5634:4357:4357:3337:3080:4356:6913:6913:2307:5634:5634:4357:3337:3080:4362:6913:5132:5132:5132:5634:3339:3337:3346:5392:4362:2061:5391:3086:3339:4113:4883:3346:5392:2061:4362:5391:3339:3086:4113:4883:5652:3346:5392:5391:5391:5391:4113:4883:5653:5652:3346:3607:3607:4118:5912:5912:4883:5653:5652:5652:3607:3607:4118:5912:5912:5653:5653:

Thanks Afmob for a challenging puzzle. It took me quite a long time and I found it harder than the estimated rating.

I'll rate A129 at least 1.25 the way I solved it, mainly because of step 20.

Here is my walkthrough.

Prelims

a) 8(2) diagonal cage at R5C4 = {17/26/35}, no 4,8,9
b) 12(2) diagonal cage at R5C6 = {39/48/57}, no 1,2,6
c) R89C5 = {79}, locked for C5 and N8
d) R1C123 = {489/579/678}, no 1,2,3
e) R123C5 = {126/135/234}, no 7,8,9
f) R1C789 = {127/136/145/235}, no 8,9
g) R4C456 = {389/479/569/578}, no 1,2
h) 21(3) diagonal cage at R5C2 = {489/579/678}, no 1,2,3
i) 13(4) diagonal cage at R5C1 = {1237/1246/1345}, no 8,9, CPE no 1 in R789C1
j) 14(4) cage at R8C3 = {1238/1247/1256/1346/2345}, no 9

1. 45 rule on N1 3 innies R23C1 + R3C3 = 7 = {124}, locked for N1
1a. R1C123 = {579/678}, 7 locked for R1 and N1
1b. R1C789 = {136/145/235}
1c. Killer pair 5,6 in R1C123 and R1C789, locked for R1

2. 45 rule on N1 1 outie R4C1 = 1 innie R3C3 + 5, R4C1 = {679}
2a. 3 in C1 locked in R56789C1, CPE no 3 in R78C2

3. 45 rule on N3 1 innie R3C7 = 1 outie R4C9 + 5, R3C7 = {6789}, R4C9 = {1234}

4. 45 rule on R123 4 outies R4C1379 = 13 = {1237/1246} (cannot be {1345} because no 1,3,4,5 in R4C1), no 5,8,9, 1,2 locked for R4, clean-up: no 4 in R3C3 (step 2)
4a. R4C1 = {67} -> no 6,7 in R4C37
4b. 4 in N1 locked in R23C1, locked for C1
4c. 1,2 in C2 locked in R789C2, locked for N7
4d. Min R89C3 = 7 -> max R89C4 = 7, no 8 in R89C4
4e. Min R789C1 = 14 -> max R9C2 = 8

5. 45 rule on R1234 2 innies R4C28 = 12 = {39/48/57}, no 6
5a. R4C456 = {389/569/578} (cannot be {479} which clashes with R4C28), no 4

6. Hidden killer pair 1,2 in R23C1 and R56C1 for C1 -> R56C1 must contain one of 1,2
6a. R56C1 contains one of 1,2 -> R78C2 cannot contain more than one of 1,2
6b. Hidden killer pair 1,2 in R78C2 and R9C2 for C2 -> R9C2 = {12}, R78C2 must contain one of 1,2
6c. 13(4) diagonal cage at R5C1 must contain both of 1,2 = {1237/1246}, no 5
6d. 3 of {1237} must be in R56C1 -> no 7 in R56C1 (because R56C1 must contain one of 1,2)
6e. 4 of {1246} must be in R78C2 -> no 6 in R78C2 (because R78C2 must contain one of 1,2)

7. Max R34C3 = 6 -> min R123C4 = 21 -> R123C4 = {579/678/589/679/689/789} (cannot be {489} when [24] in R34C3), no 1,2,3,4
7a. Killer pair 8,9 in R1C123 and R1C4, locked for R1

8. 45 rule on C1234 2 innies R47C4 = 8 = [35/53/62/71], no 8,9 in R4C4, no 4,6,8 in R7C4

9. 45 rule on C6789 2 innies R47C6 = 13 = [58/76/85/94], no 3,6 in R4C6, no 1,2,3 in R7C6

10. 45 rule on C5 2 outies R7C46 = 1 innie R4C5 + 1, min R7C46 = 5 -> no 3 in R4C5

11. Hidden killer triple 1,2,3 in R123C5 and R567C5 for C5, R123C5 must contain two of 1,2,3 -> R567C5 must contain one of 1,2,3
11a. 21(5) cage at R5C5 = {12468/13458}
11b. R567C5 contains one of {123} -> R7C4 = {123}, clean-up: no 3 in R4C4 (step 8)
11c. R4C456 (step 4a) = {569/578}, 5 locked for R4 and N5, clean-up: no 7 in R4C28 (step 5), no 3 in R6C3, no 7 in R6C7

12. Hidden killer triple 1,2,3 in R123C5 and R123C6 for N2, R123C5 must contain two of 1,2,3 -> R123C6 must contain one of 1,2,3
12a. 22(5) cage at R1C6 must contain two of 1,2,3 -> R4C7 = {123}, 22(5) cage at R1C6 cannot be {12379}

13. 45 rule on C12 3 outies R127C3 = 1 innie R4C2 + 16
13a. Max R127C3 = 24 -> max R4C2 = 8, clean-up: no 3 in R4C8 (step 5)
13b. Min R4C8 = 4 -> max R5C7 + R6C6 = 9, no 9 in R5C7 + R6C6

14. 17(3) diagonal cage at R4C2 = {278/359/368/458/467} (cannot be {179/269} because R4C2 only contains 3,4,8), no 1
14a. 5 of {359} must be in R5C3 -> no 9 in R5C3
14b. 5 of {458} must be in R5C3, 4 of {467} must be in R4C2 -> no 4 in R5C3

15. 9 in N4 locked in R56C2, locked for C2 and 21(3) diagonal cage at R5C2, no 9 in R7C3
15a. 21(3) diagonal cage at R5C2 = {489/579}, no 6
15b. 6 in C2 locked in R123C2, locked for N1
15c. 9 in N7 locked in R789C1, locked for C1

16. R1C123 (step 1a) = {579/678}
16a. 9 of {579} must be in R1C3 -> no 5 in R1C3
16b. 17(3) cage in N1 = {359/368}
16c. 9 of {359} must be in R2C3 -> no 5 in R2C3

17. 13(3) diagonal cage at R4C8 = {139/148/238/247/346} (cannot be {157/256} because R4C8 only contains 4,8,9), no 5

18. 45 rule on C123 5 innies R34689C3 = 1 outie R6C4 + 12
18a. Min R34689C3 = 15 -> min R6C4 = 3

19. 22(4) cage in N7 = {1579/2389/2569}
19a. Hidden killer pair 5,8 in R1C1 and R789C1 for C1 -> R1C1 = {58}
19b. R1C123 (step 1a) = {579/678}
19c. R1C1 = {58} -> no 5,8 in R1C23

20. R789C1 “see” all cells of 13(4) cage at R5C1, 13(4) cage (step 6c) = {1237/1246}
20a. 3 in C1 locked in R56C1 + R789C1 -> if R789C1 contains 7 it must also contain 3
20b. 22(4) cage in N7 = {2389/2569} (cannot be {1579}), no 1,7
20c. R9C2 = 2
20d. 1 in C2 locked in R78C2, locked for 13(4) cage at R5C1, no 1 in R56C1
[Steps 20a and 20b can either be considered as a fairly difficult CPE or as an implied chain.]

21. R4C1 = 7 (hidden single in C1), R23C1 = {14} (hidden pair in C1), locked for N1
-> R3C3 = 2, clean-up: no 8 in R4C56 (step 11c), no 1,6 in R5C4
21a. Naked pair {56} in R4C45, locked for R4 and N5 -> R4C6 = 9, clean-up: no 3 in R4C2 (step 5), no 3 in R6C7
21b. Naked pair {48} in R4C28, locked for R4, clean-up: no 9 in R3C7 (step 3)
21c. 2 in R4 locked in R4C79, locked for N6
21d. 21(3) diagonal cage at R5C2 (step 15a) = {489/579}
21e. 7 of {579} must be in R7C3 -> no 5 in R7C3

22. 3 in C2 locked in R23C2, locked for N1
22a. 17(3) cage in N1 (step 16b) = {359/368}
22b. R2C3 = {89} -> no 8 in R23C2
22c. 8 in C2 locked in R456C2, locked for N4
22d. 4 in N4 locked locked in R456C2, locked for C1

23. Naked pair {17} in R78C2, locked for C2 and N7 -> R1C2 = 6, R1C13 = [87] (step 1a), R1C4 = 9, R2C3 = 9, clean-up: no 3 in R789C1 (step 20b)
23a. Naked triple {569} in R789C1, locked for C1 and N7
23b. Naked pair {23} in R56C1, locked for N4 -> R4C3 = 1, clean-up: no 7 in R5C4
23c. Naked pair {35} in R23C2, locked for C2
23d. Naked pair {23} in R5C14, locked for R5, clean-up: no 9 in R6C7
23e. Naked pair {23} in R4C79, locked for N6

24. 27(5) cage at R1C4 = {12789} (only remaining combination) -> R23C4 = {78}, locked for C4 and N2

25. 17(3) diagonal cage at R4C2 (step 14) = {368/458} -> R4C2 = 8, R4C8 = 4, clean-up: no 8 in R5C6

26. 3 in N7 locked R89C3, locked for 14(4) cage at R8C3, no 3 in R89C4
26a. 14(4) cage at R8C3 = {1238/1346/2345}
26b. Killer triple 1,2,3 in R5C4, R7C4 and R89C4, locked for C4 -> R6C4 = 4, R5C3 = 5 (step 25), R6C3 = 6, R5C4 = 2, R5C6 = 7, R6C7 = 5, R56C1 = [32], R56C2 = [49], R7C3 = 8
26c. 14(4) cage at R8C3 = {1346} (only remaining combination) -> R89C4 = {16}, locked for C4 and N8 -> R4C45 = [56], R7C4 = 3
26d. Naked pair {18} in R56C5, locked for C5 and N5 -> R6C6 = 3, R5C7 = 6 (step 17)

27. R123C5 = {234} (only remaining combination), locked for C5 and N2 -> R1C6 = 1, R7C56 = [54], R89C6 = [28]

28. R1C789 = {235} (only remaining combination), locked for R1 and N3 -> R1C5 = 4, R23C5 = [23], R23C2 = [35], R23C6 = [56]
28a. Naked pair {23} in R14C7, locked for C7

29. R89C6 = [28] = 10 -> R89C7 = 13 = {49}, locked for C7 and N9
29a. Naked pair {17} in R7C27, locked for R7
29b. Naked pair {26} in R7C89, locked for R7 and N9 -> R7C1 = 9

30. 17(3) cage in N3 = {179} (only remaining combination) -> R3C8 = 9, R2C78 = {17}, locked for R2 and N3 -> R23C1 = [41], R23C4 = [87], R3C7 = 8, R23C9 = [64], R7C89 = [62], R4C79 = [23], R1C789 = [325]

31. R5C9 = 9 (hidden single in R5)
31a. R5C9 + R7C8 = [96] = 15 -> R6C9 + R8C8 = 4 = [13]

and the rest is naked singles.

As suggested by Andrew, here is how I cracked A129 using only (Naked and Hidden) Killer pairs.

A129 Walkthrough snippet:

1. R1234
a) Innies N1 = 7(3) = {124} locked for N1
b) 21(3) = 7{59/68} -> 7 locked for R1+N1
c) 12(3) = {129/147/246} because R23C1 = (124) -> R4C1 = (679)
d) Outies R123 = 13(4) = 12{37/46} because R4C1 >= 6 -> 1,2 locked for R4; R4C379 <> 6,7
e) Innies R1234 = 12(2) <> 6
f) 12(3) = 4{17/26} -> 4 locked for C1+N1
g) Innies+Outies N3: -5 = R4C9 - R3C7 -> R3C7 = (6789)

2. C123!
a) 1,2 locked in R789C2 for N7
b) R78C2 <> 3 since it sees all 3 of C1
c) 13(4): R78C2 <> 6 because {1246} blocked by R23C1 = (124)
d) Hidden Killer pair (12) in R56C1 @ 13(4) for C1 since 12(3) <> 9
e) ! Hidden Killer pair (12) in R9C2 for N8 since R78C2 @ 13(4) cannot be {12}
-> R9C2 = (12) -> 22(4) = {1579/1678/2389/2569/2578}
f) From step 2e und 2f -> 13(4) must have 1 and 2 -> 13(4) = 12{37/46}
g) ! 13(4): R78C2 <> 2 because (27) is a Killer pair of 22(4) and 13(4) = {16}{24}
blocked by Killer pair (16) of 12(3)
h) Hidden Single: R9C2 = 2 @ N7

Rating: (Hard) 1.0.

3x3:d:k:4097:4097:4097:6915:3334:6919:3586:3586:3586:3337:5125:5125:6915:3334:6919:2564:2564:4362:3337:5125:6915:6915:3334:6919:6919:2564:4362:3337:3863:6915:2824:2824:2824:6919:4374:4362:5648:4111:3863:1035:6680:3084:4374:3342:4113:5648:4111:1035:3863:6680:4374:3084:3342:4113:5396:5648:4111:6680:6680:6680:3342:4113:6165:5396:5648:5138:5138:3853:4115:4115:4113:6165:5396:5396:5138:5138:3853:4115:4115:6165:6165:

I'm still in almost-retired mode, but here is a "walkthrough snippet" for A129v2:

4/2 @ r5c4={13} (PP @ r5c123+r6c456)
11/3 @ r4c4 can't have 9
Innies @ c6789: r47c6=14=[59|68|86]
11/3 @ r4c4: r4c45 can't have {5678}
Innies @ c1234: r47c4=6=[15|24|42]

All 5 cells of 26/5 @ r5c5 can see 15/2 @ r8c5={69|78}
Also 26/5 @ r5c5 must include at least 2 of {6789}
=> 2 cells of 26/5 must be {69|78}=15
=> the 3 remaining cells must be from {12345}=26-15=11={245}
Now r7c4 is from {245} & r7c6 is from {689}
=> r567c5 must have 2 cells from {245} & 1 cell from {679}
=> at least one of r56c5 must be from {245}
=> 11/3 @ r4c4 can't be {245}
=> r4c6 can't be 5

Innies @ c6789: r47c6=14={68} (NP @ c6, PP @ r56c5+r7c3)
=> r7c6 & 15/2 @ r8c5 form KNP {68} @ n8
Innies @ c5: r4567c5=17 from {1234579} must have 1|3
=> r4c5 must be from {13}
=> r4c5+r5c4={13} (NP @ n5)
Innies @ c1234: r47c4=6={24} (NP @ c4, PP @ r56c5+r7c7)
=> r56c5={57|59} (5 @ c5,n5 locked)
=> r56c5 & 15/2 @ r8c5 form KNP {79} @ c5
=> r7c45={24} (NP @ r7,n8)

HP @ n5: /46={68} (NP @ d/)
12/2 @ r5c6=[48|75|93]
Innie-outies @ c12: r4c2=r127c3-18 can't exceed 24-18=6
Innies @ r1234: r4c28=12=[39|48|57]
Innie-outies @ c12: r127c3=r4c2+18
=> r127c3 from 21..23 must be from {456789}
15/3 @ r4c2=[348|456|528|546]
=> r5c3 must be from {245}

Critical Step:
Innie-outies @ r1234: r5c3+r6c4=r4c8+3
But r5c3 can't be 3 => r4c8 & r6c4 can't be equal
=> r4c68+r6c4 can't be [688]
=> r4c8 can't be 8
=> Innies @ r1234: r4c28=[39|57]
=> 15/3 @ r4c2=[348|528|546] blocking 12/2 @ r5c6 to be [48]
=> 12/2 @ r5c6=[75|93]

HP @ n5: \46={24} (NP @ d\)
Innie-outies @ n3: r3c7=r4c9+4
=> r3c7 from {579}, r4c9 from {135}
=> r4c259={135} (NT @ r4)
=> /357={579} (NT @ d/, PT @ \37)
Innie-outies @ n1: r4c1=r3c3+4
=> r3c3=3, r4c1=7

The rest is easy stuff!

Nice and short walkthrough, udosuk!

I used an odd-even move instead of a (very) small chain. I am not sure about the rating for this particular move (step 5b), so I'd like to hear your thoughts about it.

A129 V2 Walkthrough:

1. C456 !
a) ! 26(5) = 245{69/78} since other combos blocked by Killer pairs (68,79,89) of 15(2)
b) Innies C1234 = 6(2) = [15/24/42]
c) Innies C6789 = 14(2) = [59/68/86]
d) 26(5) must have 2,4,5 -> at least one of them must be @ R56C5
e) ! 11(3) = {128/146/236} <> 5,7 because R4C6 = (568) and {245} blocked by Killer triple (245) of R56C5
f) Innies C6789 = 14(2) = {68} locked for C6; CPE: R7C3+R56C5 <> 6,8
g) Killer pair (79) locked in 15(2) + 26(5) for C5
h) Hidden Killer pair (13) in 13(3) + R4C5 for C5 since 13(3) <> 9
-> R4C5 = (13) and 13(3) = {148/238/346} <> 5
i) 11(3): R4C4 <> 1 because (24) only possible there
j) Innies C1234 = {24} locked for C4; CPE: R7C7+R56C5 <> 2,4

2. C456
a) 26(5) must have 2,4 -> R7C45 = {24} locked for R7+N8
b) Hidden pair (68) in R4C6+R6C4 @ N5 locked for D/; R6C4 = (68); CPE: R4C2 <> 6,8
c) 2 locked in R4C4+R6C6 @ N5 for D\; CPE: R4C8 <> 2
d) Naked pair (13) locked in R4C5+R5C4 for N5
e) 26(5) must have 5 -> 5 locked for N5
f) 12(2): R6C7 = (358)
g) 15(3) <> 9 since R6C4 >= 6

3. R1234
a) Innies N1 = 9(3) <> 7,8,9
b) Innies N3 = 21(3) <> 1,2,3
c) Innies+Outies N1: 4 = R4C1 - R3C3 -> R3C3 <> 6; R4C1 = (5789)
d) Innies+Outies N3: -4 = R4C9 - R3C7 -> R3C7 <> 4; R4C9 = (135)
e) Innies R1234 = 12(2) = [39/48/57/75]

4. C123 + D/
a) Innies+Outies C12: 18 = R127C3 - R4C2; R4C2 >= 3 -> R127C3 <> 1,2,3 and R4C2 <> 7
b) Naked triple (579) locked in R3C7+R5C5+R7C3 for D/; CPE: R3C3+R7C7 <> 5,7,9
c) Innies+Outies N1: 4 = R4C1 - R3C3 -> R4C1 <> 9

5. R1234 !
a) Innies R1234 = 12(2): R4C8 <> 5
b) ! 27(5) @ R1C6 must have an even number of even candidates and R123C6 cannot have 2 and 4
since it's a Killer pair of 13(3) @ N2 -> R4C7 must have even candidates -> R4C7 = (2468)
c) Outies R123 = 22(4): R4C3 <> 1 since R4C179 <= 20
d) 17(3) @ R4C8: R5C7 <> 9 because R4C8+R6C6 >= 9

6. C789
a) 16(4) @ R8C6: R89C7 <> 9 since R89C6 <> 2,4
b) 9 locked in R13C7 @ C7 for N3
c) 17(3) @ N3 = 8{36/45} because R4C9 = (135) -> 8 locked for C9+N3; R23C9 <> 5
d) Hidden Single: R4C5 = 1 @ R4
e) R5C4 = 3, R6C3 = 1
f) 8 locked in Innies N3 = 8{49/67}

7. R1234 !
a) 13(3) @ N2 = 3{28/46} -> 3 locked for N2
b) ! Outies N2 = 22(4): R4C3 <> 9 because {2479} blocked by R4C4 = (24)
c) Hidden Single: R4C8 = 9 @ R4
d) Innie R1234 = R4C2 = 3
e) 15(3) = {348} -> R6C4 = 8, R5C3 = 4
f) R4C6 = 6 -> R4C4 = 4

8. C789
a) R4C9 = 5, R6C7 = 3 -> R5C6 = 9, R7C6 = 8
b) Innie N3 = R3C7 = 9
c) 13(3) = {148} because R7C7 = (16) -> R7C7 = 1, R6C8 = 4, R5C8 = 8
d) R4C7 = 2
e) 16(4) @ R5C9 = {1357} -> R6C9 = 7, R5C9 = 1; {35} locked for C8+N9
f) Hidden Single: R1C9 = 3 @ C9
g) 14(3) = 3{47/56}; R1C7 = (45)
h) 27(5) = {24579} -> 4,5,7 locked for C6+N2

9. N4
a) 16(3) = {259} -> R7C3 = 5, R5C2 = 2, R6C2 = 9
b) 27(5) = {13689} -> R3C3 = 3, R4C3 = 8; {169} locked for C4+N2

10. Rest is singles.

Rating: At least (Hard) 1.25.

I love the logic of the technique itself, it's very nice and elegant. If you've seen me working with BossaNova or KenKen puzzles before you'd know I'm a big digger of parity (odd-even) tricks.

However, the application of your move for this particular puzzle which requires some cage blocking action from an adjacent cage reduces the elegancy a little. As a matter of fact I can't see your move being any more elegant (i.e. non-chain-like) than my critical move in my walkthrough. Also you didn't specifically eliminate a minor (obvious) combo in that move. Just for the sake of it this is how I'd write out for that step:

27/5 @ r1c6 with r123c6 from {1234579} & r3c7 from {579}:
27/5 @ r1c6 can't be {13579}=25, so must have at least two even digits.
(It can't have only one even digit since the sum would then be even not odd.)
r123c6 can't have both {24} since 13/3 @ r1c5 must have at least one of {24}.
Thus r123c6+r3c7 can have at most one even digit.
Hence r4c7 must be even.

Also, have to say your step 7b also doesn't feel any more elegant than my critical step (i.e. I can't see it as any less "chainy" than any of my moves).


Perhaps I can rewrite my critical step using a bit of odd-even analysis:

Critical Step:
Innie-outies @ r1234: r5c3+r6c4=r4c8+3
But r5c3 can't be 3 => r4c8 & r6c4 can't be equal i.e. can't be [88]
Also, r4c6 from {68} blocks r4c8+r6c4 to be [86]
Thus r4c8 & r6c4 can't be of the same parity
Hence r5c3=r4c8+3-r6c4 must be even, i.e. can't be 5
15/3 @ r4c2 with r5c3 from {24} & r6c4 from {68}
This cage must have at least one odd digit
=> r4c2 must be from {35}
...

See if this feels less "chainy" to you.

Another variant from my backlog of unfinished puzzles. Thanks Afmob for a challenging variant.

When I first tried this puzzle I didn't get very far. It was only when I came back to it recently that I found the next step, the first one in Afmob's optimised walkthrough. The solving path seems narrow at first but the posted walkthroughs show that there are then several ways to make the key breakthrough and fix R4C28.

Rating Comment. I'll rate my walkthrough for A129V2 at Easy 1.5. I used a couple of contradiction moves, steps 19b and 26a, each of which made an important elimination from R4C2.

It's hard to know how to rate this move, which I also used. I don't think it was the hardest move in either of our walkthroughs; I felt that the ratings were determined by other steps in each case.


Here is my walkthrough for A129 V2.

Prelims

a) 4(2) diagonal cage at R5C4 = {13}, CPE no 1,3 in R5C123 + R6C456
b) 12(2) diagonal cage at R5C6 = {39/48/57}, no 1,2,6
c) R89C5 = {69/78}
d) 20(3) cage in N1 = {389/479/569/578}, no 1,2
e) 10(3) cage in N3 = {127/136/145/235}, no 8,9
f) R4C456 = {128/137/146/236/245}, no 9

1. 45 rule on N1 3 innies R23C1 + R3C3 = 9 = {126/135/234}, no 7,8,9
1a. 45 rule on N1 1 outie R4C1 = 1 innie R3C3 + 4, no 6 in R3C3, no 1,2,3,4 in R4C1

2. 45 rule on N3 3 innies R23C9 + R3C7 = 21 = {489/579/678}, no 1,2,3
2a. 45 rule on N3 1 innie R3C7 = 1 outie R4C9 + 4, no 4 in R3C7, no 6,7,8,9 in R4C9

3. 45 rule on R1234 2 innies R4C28 = 12 = {39/48/57}, no 1,2,6

4. 45 rule on C1234 2 innies R47C4 = 6 = {15/24}

5. 45 rule on C6789 2 innies R47C6 = 14 = [59/68/86]

6. R4C456 = {128/146/236/245} (cannot be {137} which clashes with R5C4), no 7
6a. R4C6 = {568} -> no 5,6,8 in R4C45, clean-up: no 1 in R7C4 (step 4)

7. 45 rule on C12 3 outies R127C3 = 1 innie R4C2 + 18
7a. Max R127C3 = 24 -> no 7,8,9 in R4C2, clean-up: no 3,4,5 in R4C8 (step 3)
7b. Min R4C2 = 3 -> min R127C3 = 21, no 1,2,3

8. 45 rule on C9 3 innies R156C9 = 1 outie R9C8 + 4
8a. Min R156C9 = 6 -> min R9C8 = 2

9. 45 rule on C123 5 innies R34689C3 = 1 outie R6C4 + 12
9a. Min R34689C3 = 15 -> no 2 in R6C4
9b. Min R4C2 + R6C4 = 7 -> max R5C3 = 8

[This is how far I got when this variant originally appeared. Back then I didn’t spot the next step, even though I did something similar in C12 for the original Assassin.]

10. 26(5) cage at R5C5 = {24569/24578} (all other combinations clash with R89C5 because all cells of the 26(5) cage “see” R89C5), no 1,3
10a. 8 of {24578} must be in R7C6 -> no 8 in R567C5
10b. Combined cage 26(5) at R5C5 + R89C5 = {2456789}, 7 locked for C5

11. R123C5 = {139/148/238/346} (cannot be {256} which clashes with 26(5) cage at R5C5, ALS block), no 5

12. 5 in C5 only in R567C5, locked for 26(5) cage at R5C5, no 5 in R7C4, clean-up: no 1 in R4C4 (step 4)

13. Naked pair {24} in R49C4, locked for C4, CPE no 2,4 in R7C7 using D\
13a. Min R4C2 + R6C4 = 8 -> max R5C3 = 7
[Having looked at the posted walkthroughs by udosuk and Afmob, I realise that I missed CPEs for R56C5 in steps 13 and 15.]

14. R4C456 (step 6) = {128/146/236} (cannot be {245} which clashes with 26(5) cage at R5C5, ALS block because 26(5) must have at least one of 2,4,5 in R56C5), no 5, clean-up: no 9 in R7C6 (step 5)
14a. 1,3 only in R4C5 -> R4C5 = {13}
14b. Naked pair {13} in R4C5 + R5C4, locked for N5, clean-up: no 9 in R6C7

15. Naked pair {68} in R47C6, locked for C6, CPE no 6,8 in R7C3 using D/, clean-up: no 4 in R6C7
15a. Killer pair 6,8 in R7C6 and R89C5, locked for N8

16. 26(5) cage at R5C5 (step 10) = {24569/24578}
16a. 6 of {24569} must be in R7C6 -> no 6 in R56C5

17. Killer pair 7,9 in 26(5) cage at R5C5 and R89C5, locked for C5
[Alternatively 9 in combined cage 26(5) at R5C5 + R89C5 only in R56789C5, locked for C5.]

18. R4C6 + R6C4 = {68} (hidden pair in N5), locked for D/, clean-up: no 2,4 in R4C9 (step 2a)

19. 15(3) cage at R4C2 = {258/348/456} (cannot be {267} because 2,7 only in R5C3, cannot be {357} because R6C4 only contains 6,8), no 7
19a. R6C4 = {68} -> no 6 in R5C3
19b. 2 of {258} must be in R5C3, 4 of {348/456} must be in R5C3 (cannot be [456] => R4C6 = 8 clashes with R4C28 = [48]) -> no 4 in R4C2, no 5 in R5C3, clean-up: no 8 in R4C8 (step 3)

20. Naked triple {135} in R4C259, locked for R4, clean-up: no 1 in R3C3 (step 1a)

21. R23C1 + R3C3 (step 1) = {135/234} (cannot be {126} because R234C1 cannot be {16}6), no 6 in R23C1, 3 locked for N1
21a. Killer pair 4,5 in 20(3) cage and R23C1 + R3C3, locked for N1

22. 17(3) cage at R4C8 = {179/269/278/359/467} (cannot be {368/458} because R4C8 only contains 7,9)
22a. 1 of {179} must be in R5C7, 9 of {269} must be in R4C8 -> no 9 in R5C7
22b. 6,8 of {269/278} must be in R5C7 -> no 2 in R5C7
22c. 3,6 of {359/467} must be in R5C7 -> no 4,5 in R5C7
22d. 1,6,8 of {179/278/467} must be in R5C7 -> no 7 in R5C7

23. 27(5) cage at R1C6 must contain two even numbers (cannot be {24678} because 6,8 only in R4C7)
23a. R123C6 cannot contain both of 2,4 which would clash with R123C5, R3C7 is odd -> R4C7 must be even -> R4C7 = {2468}

24. 16(3) cage at R5C2 = {169/178/259/349/358/367/457} (cannot be {268} because no 2,6,8 in R7C3)
24a. 1,3 of {169/367} must be in R6C2 -> no 6 in R6C2
24b. 1,3 of {178/358} must be in R6C2 -> no 8 in R6C2

25. R1C123 = {169/178/268}
25a. 45 rule on R1 3 innies R1C456 = 15 = {159/249/258/357/456} (cannot be {168/267} which clash with R1C123, cannot be {348} which clashes with R123C5, ALS block even with overlap at R1C5)
25b. R1C789 = {149/239/248/356} (cannot be {158/347} which clash with 10(3) cage in N3, cannot be {167} which clashes with R1C123, cannot be {257} which clashes with R1C456), no 7
25c. Hidden killer pair 3,4 in R1C456 and R1C789 for R1, R1C789 contains one of 3,4 -> R1C456 must contain one of 3,4
25d. R1C456 = {249/357/456} (cannot be {159/258} which don’t contain 3 or 4), no 1,8
25e. 3 of {357} must be in R1C5 -> no 3 in R1C46
25f. 9 of {249} must be in R1C4 -> no 9 in R1C6

[At this stage I had a long look at the interactions between the 22(4) cage at R5C1, 21(4) cage at R7C1 and 16(3) cage at R5C2 (and also the equivalent cages in N69), each of which “see” most, but not all, of the cells of the adjacent cage but I couldn’t find any way to use them. Then I found the contradiction move in my next step, which cracked this puzzle.]

26. R127C3 = R4C2 + 18 (step 7)
26a. R4C2 cannot be 5, here’s how
R4C2 = 5 => R127C3 = 23 = {689} => R12C3 = {68} => 20(3) cage in N3 = {569/578} => R23C2 = {57/59} which clash with R4C2
26b. -> R4C2 = 3, R4C5 = 1, R4C9 = 5, R3C7 = 9 (step 2a), placed for D/, R4C8 = 9 (step 3), R5C4 = 3, R6C3 = 1, clean-up: no 7 in R5C6
26c. 3 in C5 only in R123C5, locked for N2

27. R4C2 = 3 -> 15(3) cage at R4C2 (step 19) = {348} (only remaining combination) -> R5C3 = 4, R6C4 = 8, R4C6 = 6, R4C4 = 4 (step 14), placed for D\, R7C4 = 2, R7C6 = 8, clean-up: no 7 in R89C5

28. Naked pair {69} in R89C5, locked for C5 and N8
28a. Naked pair {57} in R56C5, locked for C5 and N5 -> R5C6 = 9, R6C7 = 3, R6C6 = 2, placed for D\, R7C5 = 4, R5C7 = 6 (step 22)

29. Naked pair {47} in R6C89, locked for R6 and N6 -> R6C5 = 5, R5C5 = 7, placed for both diagonals, R6C2 = 9, R6C1 = 6, R7C3 = 5, placed for D/, R5C2 = 2 (cage sum), R3C3 = 3, placed for D\, R4C1 = 7 (step 1a), R4C37 = [82], R5C1 = 5, R7C7 = 1, placed for D\, R7C2 = 7, R8C2 = 4 (cage sum), placed for D/

31. 6 in R7 only in R7C89, locked for N9
31a. Naked pair {89} in R1C1 + R9C9, locked for D\ -> R8C8 = 5, placed for D\, R2C2 = 6
31b. R23C1 = {24} (hidden pair in N1), locked for C1
31c. R1C2 = 1 (hidden single in N1), R9C2 = 8, R9C9 = 9, placed for D\, R1C1 = 8, R1C3 = 7 (cage sum), R2C3 = 9, R3C2 = 5

32. R89C5 = [96], R89C3 = [62]
32a. R89C3 = [62] = 8 -> R89C4 = 12 = [75], R23C4 = [16], R1C4 = 9

33. Naked pair {23} in R1C9 + R2C8, locked for N3 + D/ -> R9C1 = 1

34. R89C6 = [13] = 4 -> R89C7 = 12 = [84]

and the rest is naked singles, without using the diagonals.