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This one seems straightforward after recent Assassins but hopefully still passes the interesting test. I'll give it an Easy 1.25 rating. This cage pattern started out as an X, but this puzzle is not. I'm not planning a V2 - though started one with a couple of cages joined together. Someone else feel free!

Assassin 151
NOTE: r5c5 is intentionally blank.

SS(3.3.0)score = 1.36


Cheers
Ed

Thanks Ed for a straightforward Assassin. It was fun. It will be a good one for newbies to do once they have solved the puzzles recommended in my Advice "sticky".

Nice cage pattern! I like the way R5C5 was left blank to maintain the central symmetry.

This was the quickest I've solved an Assassin since the first dozen of Ruud's ones. After finding fairly early breakthroughs it flowed nicely. I'm sure there must be a lot of ways to solve this one; Afmob will probably find a more direct solution.

I'll rate A151 as Hard 1.0 because that's the rating that I give for easy killer triples; others would rate it Easy 1.25 because they never rate killer triples lower than that.

Here is my walkthrough. Looks like I was careless with my manual eliminations first time through. I've done minor editing, moving R78C4 to step 24.

Prelims

a) R78C1 = {16/25/34}, no 7,8,9
b) R1C456 = {127/136/145/235}, no 8,9
c) R234C5 = {489/579/678}, no 1,2,3
d) R5C678 = {128/137/146/236/245}, no 9
e) 23(3) cage at R6C2 = {689}, CPE no 6,8,9 in R45C2
f) R678C5 = {127/136/145/235}, no 8,9
g) 9(3) cage at R6C6 = {126/135/234}, no 7,8,9
h) 23(3) cage at R7C6 = {689}, CPE no 6,8,9 in R8C45

1. 45 rule on complete grid 1 innie R5C5 = 7

2. 45 rule on C5 2 remaining innies R19C5 = 7 = {16/25/34}, no 8,9

3. 8,9 in C5 locked in R234C5 = {489}, locked for C5, clean-up: no 3 in R19C5 (step 2)

4. 45 rule on R1234 2 innies R4C19 = 6 = {15/24}

5. 45 rule on R6789 2 innies R6C19 = 13 = {49/58/67}, no 1,2,3
5a. Killer triple 6,8,9 in R6C19 and R6C23, locked for R6

6. 45 rule on R5 2 remaining innies R5C19 = 9 = {18/36/45}, no 2,9
6a. 9 in R5 locked in R5C234 = {189/369/459}, no 2
6b. 1,3 of {189/369} must be in R5C2 -> no 1,3 in R5C34

7. 45 rule on R9 2 outies R78C9 = 8 = {17/26/35}
7a. 45 rule on R9 3 innies R9C789 = 19 = {289/379/469/478/568}, no 1

8. 45 rule on C1234 2 innies R19C4 = 6 = {15/24}

9. 45 rule on C6789 2 innies R19C6 = 9 = [18]/{27/36/45}, no 1,9 in R9C6

10. R9C456 = {147/156/246/345} (cannot be {138/237} because 3,7,8 only in R9C6), no 8, clean-up: no 1 in R1C6 (step 9)

11. 45 rule on N6 3 outies R37C8 + R5C6 = 7
11a. Min R37C8 = 3 -> max R5C6 = 4
11b. Max R37C8 = 6, no 6,7,8,9

12. 13(3) cage at R6C7 = {157/247}, no 3, 7 locked in R6C78, locked for R6 and N6, clean-up: no 6 in R6C19 (step 5)
12a. 6 in R6 locked in R6C23, locked for N4 and 23(3) cage at R6C2, clean-up: no 3 in R5C9 (step 6)
12b. 7 in R4 locked in R4C23, locked for 18(4) cage at R3C1

13. R456C1 = {139/148/238}, no 5, clean-up: no 1 in R4C9 (step 4), no 4 in R5C9 (step 6), no 8 in R6C9 (step 5)
13a. Killer pair 8,9 in R456C1 and R6C23, locked for N4

14. R5C234 (step 6a) = {459} (only remaining combination, cannot be {189/369} because R5C3 only contains 4,5) -> R5C4 = 9, R5C23 = {45}, locked for R5 and N4, clean-up: no 2 in R4C9 (step 4), no 9 in R6C9 (step 5)

15. Naked pair {45} in R46C9, locked for C9 and N6, R5C9 = 6 (cage sum), R5C1 = 3 (step 6), clean-up: no 4 in R78C1, no 2,3 in R78C9 (step 7)
15a. Killer pair 1,2 in R4C1 and R78C1, locked for C1
15b. Naked pair {17} in R78C9, locked for C9 and N9, clean-up: no 3 in R9C789 (step 7a)
15c. 3 in C9 locked in R123C9, locked for N3

16. R4C78 = {39} (hidden pair in N6), locked for R4, R3C8 = 1 (cage sum)
16a. Naked triple {127} in R4C123, locked for R4

17. 3 locked in R123C9 = {238/239} (R123C9 = {389} is more than 19), 2 locked for C9 and N3, R1C8 = {56} (cage sum)

18. 3 in N9 locked in R7C7 + R8C8, locked for 9(3) cage at R6C6
18a. 9(3) cage at R6C6 = {135/234}, no 6
18b. 1 of {135} must be in R6C6 -> no 5 in R6C6

19. 9 in N8 locked in R78C6, locked for C6 and 23(3) cage at R7C6
19a. 9 in N9 locked in R9C789, locked for R9
19b. R9C789 (step 7a) = {289/469}, no 5

20. R9C456 (step 10) = {147/156/345} (cannot be {246} which clashes with R9C789), no 2, clean-up: no 4 in R1C4 (step 8), no 5 in R1C5 (step 2), no 7 in R1C6 (step 9)
20a. 3,7 of {147/345} must be in R9C6 -> no 4 in R9C6, clean-up: no 5 in R1C6 (step 9)

21. R1C456 = {136/145/235}
21a. Killer pair 5,6 in R1C456 and R1C8, locked for R1
21b. 3,4 only in R1C6 -> R1C6 = {34}, clean-up: no 3,7 in R9C6 (step 9)
21c. R1C456 = [163/514/523], no 2 in R1C4, clean-up: no 4 in R9C4 (step 8)

22. Naked pair {15} in R19C4, locked for C4
22a. Naked triple {156} in R9C456, locked for R9 and N8, clean-up: no 4 in R9C78 (step 19b)
22b. Naked triple {289} in R9C789, locked for R9 and N9 -> R8C7 = 6, clean-up: no 1 in R7C1
22c. Naked triple {347} in R9C123, locked for N7

23. Naked pair {23} in R78C5, locked for C5 and N8, R6C5 = 5 (prelim f), R6C9 = 4, R4C9 = 5, R4C1 = 1 (step 4), R6C1 = 9 (step 5), clean-up: no 6 in R7C1
23a. Naked pair {25} in R78C1, locked for C1 and N7

24. R6C4 = 3 (hidden single in R6), R7C3 = 6 (hidden single in R7), R8C2 = 8 (cage sum), R6C23 = [68], R7C2 = 9, R78C6 = [89], R8C3 = 1, R78C9 = [17], R78C4 = [74]

25. Naked pair {12} in R56C6, locked for C6

26. 7 in C6 locked in R23C6, locked for 23(4) cage at R1C7
26a. 7 in N3 locked in 18(3) cage at R2C8 = {567} (only remaining combination) -> R4C6 = 6, R4C45 = [84], R9C456 = [165], R1C45 = [51], R1C6 = 4 (step 9), R1C8 = 6
26b. Naked pair {57} in R2C8 + R3C7, locked for N3

27. R23C6 = {37} = 10 -> R12C7 = 13 = [94], R4C78 = [39], R7C7 = 5, R78C8 = [43], R78C1 = [25], R78C5 = [32], R3C7 = 7, R2C8 = 5, R23C6 = [73], R6C6 = 1 (step 18a)

28. R23C4 = {26} = 8 -> R12C3 = 10 = [73]

and the rest is naked singles

Don't put so much pressure on me, Andrew!

Thanks for this nice Killer, Ed! It was fun to solve and I didn't use any Killer pairs. I was tempted to also use the Killer triple Andrew found but after having a closer look at the grid I found that it wasn't needed.

A151 Walkthrough:

1. C456
a) Innie of grid = R5C5 = 7
b) 21(3) = {489} locked for C5
c) Innies C1234 = 6(2) = {15/24}
d) Innies C5 = 7(2) <> 3
e) 10(3) @ N2: R1C6 <> 2,6 since (37) only possible there
f) 12(3) @ R9 <> 8 since R9C45 <> 3,8
g) Innies C6789 = 9(2) <> 1,9; R9C6 <> 3,7
h) 12(3) @ R9 = 6{15/24} -> 6 locked for R9+N8
i) 23(3) = {689} -> R8C7 = 6; 8,9 locked for C6+N8

2. N69 !
a) ! Outies N6 = 7(2+1) <> 6,7,8,9; R5C6 <> 5
b) Innies+Outies N9: -3 = R6C6 - R7C8 -> R7C8 = (45), R6C6 = (12)
c) 9(3) = 3{15/24} -> 3 locked for N9
d) Outies R9 = 8(2) = {17} locked for C9+N9
e) Innies R9 = 19(3) = {289} locked for R9+N9

3. N78
a) 14(3) = {347} locked for R9+N7
b) 12(3) @ R9 = {156} locked for N8
c) 10(3) = {235} since R78C5 = (23) -> R6C5 = 5; 2,3 locked for C5+N8
d) 12(3) @ N7 = {147} because R78C4 = (47) -> R8C3 = 1; 4,7 locked for C4
e) 7(2) = {25} locked for C1+N7
f) 17(3) = 6{29/38} -> R6C4 = (23), R7C3 = 6
g) 23(3) @ N7 = {689} -> R6C2 = 6

4. R456
a) Innies R6789 = 13(2) = {49} locked for R6
b) R6C3 = 8, R7C2 = 9, R8C2 = 8 -> R6C4 = 3
c) Innies R1234 = 6(2) = [15/42]
d) 13(3) @ N4 = {139} -> R4C1 = 1, R6C1 = 9, R5C1 = 3
e) 18(3) @ R5 = {459} since R5C23 = (245) -> R5C4 = 9; 4,5 locked for R5+N4
f) 9 locked in 13(3) @ N6 = {139} -> R3C8 = 1

5. C456
a) Innies C1234 = 6(2) = {15} locked for C4
b) 10(3) = 1{36/45} -> 1 locked for R1+N2; R1C6 = (34)
c) Hidden Single: R2C2 = 1 @ N1
d) 18(3) @ N1 = {189} -> R3C3 = 9, R4C4 = 8
e) 18(4) = {2367} since R23C4 = (26) -> 3,7 locked for C3+N1; 2,6 locked for N2

6. R123
a) 18(4) @ R3C1 = {2457} -> R3C1 = 4, R4C3 = 2, R4C2 = 7, R3C2 = 5
b) R4C5 = 4, R4C6 = 6, R3C5 = 8, R2C5 = 9
c) 18(3) @ N3 = {567} because R3C7 <> 4,8 -> R3C7 = 7, R2C8 = 5
d) R4C9 = 5, R6C9 = 4 -> R5C9 = 6, R7C8 = 4, R8C8 = 3, R7C7 = 5 -> R6C6 = 1

7. Rest is singles.

Rating: Easy 1.0. I used IOD and hidden cages.

For me the biggest difficulty was remembering that it wasn't a diagonal. You get into an awful mess if you think it is.

cheers

_________________
Joe

I am not sure of the protocol for creating a version 2. So if I have committed procedural trangressions, please disregard the rest of this post .

JSudoku, Perfect Sudoku, SudokuSolver and I have together conspired to create the following. We decided to make it diagonal and symmetric. It measures 1.74 on the Richter scale. To help you get started I will tell you 1.2345679% of the solution. The centre cell is 9. Enjoy .

Assassin 151 v2

NOTE: r5c5 is intentionally blank. See hint above



SS(3.3.0)score = 1.74

Cheers - Frank

Thanks for making a harder version, this puzzle certainly needs one. Did you solve it yourself first? I'd rather solve puzzles that I know have been hand solved first.

I wish I could say something witty to match your wonderful way with words Frank...you add some much needed humour to this forum!

Thanks
Ed

Thanks for giving us a V2, Frank!

I usually try to avoid contradiction chains but I found it easier to express my hardest step (6b) this way than by explaining it via a forcing chain.

A151 V2 Walkthrough:

1. D\/
a) Innie of grid = R5C5 = 9
b) Innies D/ = 15(2) = {78} locked for D/; CPE: R1C1+R9C9 <> 7,8
c) Innies D\ = 10(2) = {46} locked for D\
d) 14(3) = 5{18/27} -> 5 locked for D\
e) 15(4) = 1{248/257/347} <> 6,9 since R1C9 = (78); 1 locked for N3; R1C8+R23C9 <> 7,8

2. C456
a) Innies C5 = 3(2) = {12} locked for C5
b) Innies C1234 = 9(2) <> 1; R9C4 <> 2
c) Innies C6789 = 7(2) <> 7

3. R456
a) Innies R1234 = 6(2) = {15/24}
b) Innies R6789 = 12(2) = [39/48/57]
c) 9(3) = 3{15/24} since R6C1 = (345) -> 3 locked for C1+N4

4. C789
a) Outies C9 = 12(2) = [39/48/57]
b) 15(4) = 1{248/257/347} -> 1 locked for C9
c) 17(3) <> 7 because 7{46/28} blocked by R1C9 = (78) and R9C9 = (46)

5. R456
a) Innies R6789 = 12(2) <> 5
b) Innies R5 = 8(2) <> 1,4,8; R5C9 <> 2
c) Innies R1234 = 6(2): R4C1 <> 5

6. R456+D\ !
a) 17(3) @ N6 <> {368} since R4C9 = (245)
b) ! 17(3) @ N6 <> 8 since it sees all 4 of D\ because 17(3) = {458} -> R9C9 <> 4 and R6C9 = 8 -> R6C1 = 4 (Innie R6) -> R1C1 <> 4
c) Innies R6 = 12(2) = [39] -> R6C1 = 3, R6C9 = 9
d) 17(3) @ N6 = [26/53]9
e) Innies R1234 = 6(2): R4C1 <> 2
f) 12(3) @ D\ = 3{18/27} -> 3 locked for N9
g) 9 locked in 21(3) @ N4 for 21(3); 21(3) <> 6

7. R1234 !
a) 12(3): R4C6 <> 3,6 because 1 only possible there and (24,45) are Killer pairs of 15(4)
b) ! Hidden Killer pair (36) in R4C5 + 13(3) for R4 since R4C78 = {36} blocked by R5C9 = (36)
-> R4C5 = (36) and 13(3) = {139/238/256/346} <> 7
c) 18(3): R23C5 <> 3,6 since R4C5 = (36)
d) ! 3 in R23 must be in 21(4) + N3 -> CPE: R1C38 <> 3 (Grouped/Caged X-Wing?)

8. C6789
a) Outies C9 = 12(2) <> 9
b) 25(4) = {4678} locked for N9; 4,6 also locked for C9
c) R5C9 = 3 -> R4C9 = 5
d) 13(3) <> 9 because R4C78 <> 3,9
e) Hidden Single: R7C8 = 9 @ C8, R4C5 = 3 @ R4
f) 12(3) @ N6 = {129} -> 1,2 locked for R6+N6
g) 23(4) = 59{18/27} because R89C7 = (125) -> R8C6 = 9; R7C6 = (78); 5 locked for C7
h) Naked pair (78) locked in R67C6 for C6
i) 28(4) = {5689} since R23C6 = (456) -> R23C6 = {56} locked for C6+N2; R12C7 = {89} locked for C7+N3
j) 16(3) = 8{17/26} -> R5C8 = 8
k) 13(3) = {346} since R4C78 = (46) -> R3C8 = 3; 4,6 locked for R4+N6

9. R1234
a) 9(3) @ N2 = {234} -> R1C5 = 2; 3,4 locked for R1+N2
b) R1C1 = 6, R9C9 = 4
c) Naked pair (78) locked in R23C5 for C5+N2
d) Hidden Single: R2C3 = 3 @ N1
e) 21(4) = {1389} since R23C4 = (19) -> R1C3 = 8; 1 locked for C4
f) 23(4) = {1679} locked for N1
g) Innie R1234 = R4C1 = 1
h) Cage sum: R5C1 = 5

10. Rest is singles.

Rating: Hard 1.5. I used a small contradiction chain and an interesting CPE move.

Returning briefly to A151; I've only recently noticed that Frank's V2 was posted so haven't tried it yet.

Nice walkthrough! It's not often we get one without any killer pairs, etc. and still only using simple combo work.

You probably weren't surprised that I used that killer triple. It was so obvious and consistent with the SS score and Ed's rating that I didn't think twice about looking for something simpler.

I guess that's one difference between our solving approaches. You, Ed, Mike and udosuk (there may be others) like to optimise WTs. I've never been interested in doing that. If I can find a solving path at the expected level of difficulty, or occasionally better, I'm happy with that; I've usually spent quite a long time solving the puzzle.


Although I thought that at the time, I've now realised it would be better for me with a single cell cage at R5C5. When I set up a killer on my Excel worksheet the first check I do is that the cage totals sum to 405, which obviously can't be done when there are blank cell(s). It's only after that check that I set up the cage patterns by colouring the cells.

Thanks for this V2 !

The main difficulty was working both on cage combinations and Innies for the four 3-cages at the puzzle border.
The killer pair found at step 5g then enables to crack this puzzle.


Walkthrough A151 V2

A151 V2 was then next one of my backlog of unfinished puzzles that I went back to.

In Afmob's walkthrough steps 6b and 7d were neat while in manu's walkthrough the key step 3f was similar to my final breakthrough; I liked the way manu expressed it that the 3-cell cages in C1 and C9 cannot both contain 4.

Even though my solving path is similar to manu's, I decided to post my walkthrough because of the interesting step 31.


Here is my walkthrough for A151 V2. At the time this puzzle was originally active I'd got as far as step 24. When I resumed I did a bit of nibbling and then made real progress from step 28 onward.

Prelims

a) R1C456 = {126/135/234}, no 7,8,9
b) 21(3) cage at R3C2 = {489/579/678}, no 1,2,3
c) R456C1 = {126/135/234}, no 7,8,9
d) 9(3) cage at R6C4 = {126/135/234}, no 7,8,9
e) R9C456 = {127/136/145/235}, no 8,9
f) 28(4) cage at R1C7 = {4789/5689}, no 1,2,3

1. 45 rule on complete grid 1 innie R5C5 = 9, placed for D/ and D\

2. 45 rule on R1234 2 innies R4C19 = 6 = {15/24}

3. 45 rule on R5 2 remaining innies R5C19 = 8 = [17]/{26/35}, no 4,8, no 1 in R5C9

4. 45 rule on R6789 2 innies R6C19 = 12 = [39/48/57]

5. R456C1 = {135/234} (cannot be {126} because R6C1 only contains 3,4,5}, no 6, 3 locked in R56C1, locked for C1 and N4, clean-up: no 2 in R5C9 (step 3)

6. 45 rule on C1 2 outies R19C2 = 10 = {19/28/37/46}, no 5

7. 45 rule on C9 2 outies R19C8 = 12 = {39/48/57}, no 1,2,6

8. 45 rule on C1234 2 innies R19C4 = 9 = [27]/{36/45}, no 1, no 2 in R9C4

9. 45 rule on C5 2 remaining innies R19C5 = 3 = {12}, locked for C5

10. 45 rule on C6789 2 innies R19C6 = 7 = {16/25/34}, no 7

11. 45 rule on D/ 2 remaining innies R1C9 + R9C1 = 15 = {78}, locked for D/, CPE no 7,8 in R1C1 + R9C9

12. 45 rule on D\ 2 remaining innies R1C1 + R9C9 = 10 = {46}, locked for D\

13. R1C9 = {78} -> 15(4) cage in N3 = {1248/1257/1347} (other combinations don’t contain 7 or 8), no 6,9, 1 locked in R23C9, locked for C9 and N3, clean-up: no 5 in R4C1 (step 2), no 3 in R9C8 (step 7)
13a. R1C9 = {78} -> no 7,8 in R1C8 + R23C9, clean-up: no 4,5 in R9C8 (step 7)
13b 5 of {1257} must be in R1C8 -> no 5 in R23C9

14. R456C9 = {269/359/458} (cannot be {278} which clashes with R1C9, cannot be {368} because R4C9 only contains 2,4,5, cannot be {467} which clashes with R9C9), no 7, clean-up: no 1 in R5C1 (step 3), no 5 in R6C1 (step 4)

15. 12(3) cage at R6C6 = {138/237}, no 5, 3 locked for D\

16. R5C234 = {138/147/246} (cannot be {156/237} which clash with R5C19, cannot be {345} because 3 only in R5C4 and R5C23 = {45} clashes with R456C1), no 5
16a. 3 of {138} must be in R5C4 -> no 8 in R5C4

17. 45 rule on N4 4 innies R46C23 = 1 outie R5C4 + 24
17a. Max R46C23 = 30 -> max R5C4 = 6
17b. Min R46C23 = 25 (when R5C4 = 1) but cannot be {1789} which clashes with R5C234 = {47}1 -> no 1 in R6C23

18. Interactions between R1C456 and R9C456 using steps 8,9,10
18a. R1C456 cannot be [315/513] because R9C456 cannot be [622/424] -> R1C456 = {126/234}, no 5, 2 locked for R1 and N2, clean-up: no 8 in R9C2 (step 6), no 4 in R9C4 (step 8), no 2 in R9C6 (step 10)
18b. Killer pair 4,6 in R1C1 and R1C46, locked for R1, clean-up: no 4,6 in R9C2 (step 6), no 8 in R9C8 (step 7)
[Step 18a can be expressed more logically as
R19C4 = 9, R19C6 = 7 -> R1C4 cannot be 2 more than R1C6 -> R1C456 cannot be [513]
R19C5 = 3, R19C6 = 7 -> R1C6 cannot be 4 more than R1C5 -> R1C456 cannot be [315]
-> R1C456 cannot be [315/513] -> R1C456 = {126/234} …]

19. 15(4) cage in N3 (step 13) = {1257/1347} (cannot be {1248} because R1C8 only contains 3,5), no 8 -> R1C9 = 7, placed for D/ -> R9C1 = 8, clean-up: no 3 in R9C2 (step 6)
19a. R1C8 = {35} -> no 3 in R23C9

20. R9C456 = {136/145/235} (cannot be {127} which clashes with R9C28, ALS block), no 7, clean-up: no 2 in R1C4 (step 8)
20a. R1C456 (step 18a) = {126/234}
20b. 6 of {126} must be in R1C4 -> no 6 in R1C6, clean-up: no 1 in R9C6 (step 10)

21. 25(4) cage in N9 = {2689/3679/4678} (cannot be {3589} because R9C8 only contains 4,6, cannot be {4579} because 5,9 in R78C9 clashes with R456C9), no 5, 6 only in R789C9, locked for C9 and N9, clean-up: no 2 in R4C9 (step 14), no 4 in R4C1 (step 2), no 2 in R5C1 (step 3)
21a. 5 in C9 only in R45C9, locked for N6

22. Naked pair {35} in R5C19, locked for R5
22a. R5C234 (step 16) = {147/246}, no 8, 4 locked for R5

23. 23(4) cage in N1 = {1679/2489/2678/3479/3569} (cannot be {1589/2579/3578} because R1C1 only contains 4,6, cannot be {4568} which clashes with R456C1)
23a. R1C1 = {46} -> no 4,6 in R23C1

24. 45 rule on N3 3 innies R12C7 + R3C8 = 1 outie R4C6 + 18
24a. Max R12C7 + R3C8 = 23 -> max R4C6 = 5

25. 12(3) cage at R2C8 = {156/246/345}
25a. 3 of {345} must be in R2C8 + R3C7 (R2C8 + R3C7 cannot be {45} which clashes with 15(4) cage in N3), no 3 in R4C6

26. 12(3) cage at R6C6 (step 15) = {138/237}
26a. 1 of {138} must be in R7C7 + R8C8 (R7C7 + R8C8 cannot be {38} which clashes with 25(4) cage), no 1 in R6C6

27. 15(3) cage at R6C5 = {348/357/456}
27a. 7,8 of {348/357} must be in R78C5 (R78C5 cannot be {34/35} which clash with R9C456), no 7,8 in R6C5

28. 23(4) cage in N7 = {1589/2489/2678} (cannot be {4568} because R9C2 only contains 1,2,7,9)
28a. Killer triple 4,5,6 in R1C1, R56C1 and R78C1, locked for C1

29. R9C456 (step 20) = {136/145/235}
29a. R9C456 cannot be [514], here’s how
R9C456 = [514] => R1C4 = 4 (step 8), R9C9 = 6 => R1C1 = 4 clashes with R1C4
29b. -> R9C456 = {136/235}, no 4, 3 locked for R9 and N8, clean-up: no 3 in R1C6 (step 10)

30. R1C456 (step 18a) = {126/234}
30a. 3,6 only in R1C4 -> R1C4 = {36}, clean-up: no 5 in R9C4 (step 8)
30b. Naked pair {36} in R19C4, locked for C4

31. 6 in R1 only in R1C14, 6 in C4 only in R19C4, 6 on D\ only in R1C1 + R9C9 -> R9C49 must contain 6, locked for R9, clean-up: no 1 in R1C6 (step 10)
[I guess this is a sort of X-Wing using the diagonal, possibly XY-Wing, XYZ-Wing or some strangely named Fish.]
31a. 1 in N2 only in R1C5 + R23C4, CPE no 1 in R1C3
[This CPE has been there since step 9 but I’ve only just spotted it.]

32. 15(3) cage at R6C5 (step 27) = {348/357/456}
32a. 3 of {348} must be in R6C5, 4 of {456} must be in R78C5 (R78C5 cannot be {56} which clashes with R9C456), no 4 in R6C5

[Steps 29 and 31 gave me the idea how to continue.]
33. R456C1 (step 5) = {135/234}, R456C9 (step 14) = {359/458}
33a. R456C1 cannot be {234} and R456C9 cannot be {458}, here’s how
R456C1 = [234] => R456C9 = [458] (steps 2,3,4) => R1C1 = 6, R9C9 = 6 clash on D\
33b. -> R456C1 = [153], R456C9 = [539]

34. R4C5 = 3 (hidden single in R4), R23C5 = 15 = {78}, locked for C5 and N2

35. R9C6 = 3 (hidden single in C6), R9C4 = 6, R9C5 = 1 (step 29b) R1C4 = 3, R1C5 = 2, R1C6 = 4, R1C1 = 6, R9C9 = 4, R1C8 = 5, R9C8 = 7 (step 7)

36. R4C6 = 2, placed for D/, R2C8 + R3C7 = 10 = {46}, locked for N3 and D/

37. Naked pair {78} in R4C4 + R6C6, locked for N5 and D\

38. Naked pair {45} in R78C5, locked for C5 and N8 -> R6C5 = 6, R5C6 = 1, R5C4 = 4, R6C4 = 5, placed for D/

39. Naked pair {19} in R23C4, locked for C4, N2 and 21(4) cage at R1C3, no 1,9 in R12C3
39a. R23C4 = {19} = 10 -> R12C3 = 11 = [83], R7C3 = 1, R8C2 = 3, R12C7 = [98], R23C5 = [78], R1C2 = 1, R9C2 = 9 (step 6)

40. Naked pair {12} in R23C9, locked for C9 and N3 -> R3C8 = 3

41. Naked pair {25} in R2C2 + R3C3, locked for N1 and D\, R4C4 = 7 (cage sum)

42. Naked pair {28} in R78C4, locked for N8 and 22(4) cage at R7C4 -> R9C3 = 5

and the rest is naked singles.