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I decided to make a messy Assassin since it's been a long time since Messy One #6. I hope you can see which cell belongs to which cage.

Assassin 155



3x3::k:3329:3329:3331:3331:5378:4613:4613:5127:5127:3329:5380:5378:5378:4613:7942:4613:5127:3080:5380:5380:5378:7942:7942:7942:7942:3080:3080:5380:7694:2827:2827:7689:7689:7689:7689:3080:7694:7694:4877:4877:2827:3084:3084:7689:3850:4111:7694:7694:4882:4877:3084:7689:3084:3850:4111:4111:4882:4882:4882:4883:4883:4883:2836:2576:2576:4881:4882:4629:4629:2070:2836:2836:2576:4881:4881:4629:2070:2070:4887:4887:4887:


SS Score: 1.08
Estimated rating: Hard 1.0

Thanks Afmob for another fun puzzle! Didn't get to look at it until today, and it took me a good 2 hours, maybe a little longer, to solve. I'm getting slow in my old age!

It seems I made tons of eliminations before finding the first placement, and even when I thought I had it cracked, many more moves were needed to finally get to "singles only".

I kept some rough & sloppy notes & will try to sort them out into a coherent WT, but I must take a break for now.

Thanks again!

My first solving path was using some contradictions between combos which was not satisfying, until I found step 2a of my WT ( two cloned cages).
This is a hard to solve puzzle that resists a lot, until the end ! Thanks Afmob.

ASSASSIN 155 WALKTHROUGH



Edit : Ed has pointed out some typos : thanks

Well I FINALLY finished my walk-through.

Maybe it took so long because I have so little experience in writing them for an audience other than myself. Please send your comments & corrections.

Thanks, Andrew, for providing a few corrections & clarifications, in blue:

I don't rate puzzles, but don't think I used anything harder than a hidden killer pair. However it took me MANY small steps to complete this puzzle. This could be the longest WT in history for a relatively easy puzzle! Haven't yet looked at manu's version, maybe he came up with something clever to shorten the path.

Walk-Through A155:

Beginning with Sumocue mark-ups.

1) 8(3) @ R8C7: 1 locked -> no 1 @ R8C456 (CPE)

2) R123 outies: R4C19 = 14(2) = [86/95]
2a) R4C9 = {56} -> no 5,6 elsewhere in 12(4) cage ->
1,2 locked in 12(4) cage for N3

3) 30(5) in N4 can’t have both (89), because R4C1 = {89} ->
Remaining combos for 30(5): 567{39/48} -> no 1,2 in 30(5) cage
3a) 567 locked in 30(5) for N4
3b) KP (89) in N4 @ R4C1 and 30(5) cage -> not elsewhere in N4
3c) R5C3 = {234}, so rest of 19(3) cage R5C4+R6C5 = {6789}

4) R789 outies: R6C14 = 4(2) = {13}, locked for R6
4a) 2 locked in N4 & C3 @ R45C3
4b) 1 locked in 12(4) cage @ R5C67, locked for R5. No 6 @R5C67
4c) 16(3) @ R6C1 must have one of (13), no combos have both ->
R7C12 = {456789}

5) IOD C12: R6C3 = R9C2, no 2,3 in R9C2
5a) 2 locked in 10(3) cage in N7 -> 10(3) = 2{17/35}, no 4,6

6) IOD for N7: R6C1 = R7C3 -> R7C3 = {13}
6a) 19(5) @ R6C4 has both 1&3 (@R6C4 & R7C3): 1,3 not elsewhere in cage 19(5)
6b) KP (13) for N7 @ R7C3 & 10(3) cage -> not elsewhere in N7
6c) 1 locked in N8 for R9, not elsewhere in R9

7) R89 outies: R7C459 = h10(3) cage (after removing 4(2) cage @ R6C4 + R7C3):
h10(3) = {127/145/235} (can’t be {136} since 1,3 are only in R7C9) ->
R7C45 = {2457}, R7C9 = {13}
7a) NP (13) @ R7C39, locked for R7
7b) 11(3) in N9 <> {245}, since it must have 1 or 3 -> no 5 in 11(3) cage

8) IOD R89: R8C4 = R7C9 + 5 -> R8C4 = {68}

9) Hidden KP (89) for N7 @ R7C12 & 19(3) cage -> 16(3) @ R6C1 <> {367}
9a) KP (89) for R7: since R7C12 must have one of (89), 19(3) @ R7C678 can’t have
both -> 19(3) <> {289}, no 2 in 19(3) cage
NOTE: Andrew points out the uncertainty of calling this a KP versus HKP. I often
confuse them myself, when I realize there are only two places for them to go.
My use of conventions is still lacking in many such regards!
9b) 2 locked @ R7C45 for 19(5) cage & N8: 19(5) = 123 {58/67}, no 4
9c) 8(3) @ R8C7: R8C7 <> 5, since R9C56 can’t be {12}

10) IOD N9: R8C7 + 4 = R7C6 -> R7C6 = {5678}
10a) 9 locked in 18(3) cage in N8: 18(3) = 9{18/36/45}, no 7 in 18(3)
10b) 7 locked in N8 for R7, not elsewhere in R7
At this point, I should have realized 6 locked in 19(3) for R7, not elsewhere in R7,
which would lead to a faster placement: R6C1=3. Oh well.

11) Outies N9: R7C6 + R9C56 = 12(3) = {138/147/345}
(combo {156} blocked by KP (56) in 19(5) cage)
11a) No 5 @ R9C56, since R7C6 can’t be 3 or 4. No 6 @ R7C6.

12) 8(3) @ R8C7 = {134}: no 2 @ R8C7, no 3,4 @ R9C789 & R8C56 (CPE’s)
12a) Remaining combos for 19(3) in N9: 8{29/56}, 8 locked for N9 & R9, no 7
12b) Hidden triple (134) @ R9C456, locked for R9

13) 6 locked in N8 for R8, not elsewhere in R8
13a) 11(3) in N9 = {137} (last combo), locked for N9 & 7 is locked for R8
13b) FINALLY A PLACEMENT!! R8C7 = 4 (NS), R9C4 = 4 (HS)

14) R8C56 = {59}, since {68} blocked by R8C4. (59) locked for N8 & R8
14a) R8C34 = [86]
14b) R9C23 = {56} locked for R9 & N7
14c) R9C1 = 7 (HS), R8C12 = {12}, locked for R8 & N7
14d) R7C39 = [31], R6C14 = [31]
14e) R7C6 = 8 (HS), R7C78 = {56}

15) 30(5) in N4 = {45678} (last combo), locked for N4
15a) R4C1 = 9, R45C3 = [12], R7C12 = [49]
15b) R5C4 + R6C5 = {89}, locked for N5
15c) R4C4 + R5C5 = {37} (can’t be {46} since R4C4 contains no 4 or 6),
(37) locked for N5

16) 30(6) @ R4C5 = 2347{59/68}
16a) 3 & 7 locked in 30(6) in N6, not elsewhere in N6
16b) 15(2) in N6 = {69}, locked for N6 & C9
16c) NS: R4C9 = 5
16d) HS: R3C8 = 1, R23C9 = {24}, locked for N3 & C9

17) NS: R9C9 = 8
17a) 20(3) @ N3 must have 3 or 7: 20(3) = 8{39/57}, no 6. 8 locked for N3 & C8
17b) 6 locked in N3 for C7 -> R7C78 = [56]
17c) HP (58) @ R12C8 -> R1C9 = 7

18) R8C89 = [73]

19) 12(4) @ R5C6 = {1245}, no 6
19a) R6C7 <> 2, 5 locked in 12(4) cage for N5 & C6
19b) R8C56 = [59]

20) (Should have put this after step 17)
13(2) @ R1C3 = [49], since {58} blocked by R1C8

21) 13(3) @ N1 = 2{38/56} -> 2 locked for N1, no 1 in 13(3) cage
(Step re-written for greater clarity)
21a) KP’s (35) & (36) locked in 13(3) & 21(4) for N1 ->
R23C3 = {79}, (79) locked for N1, C3, & 21(4) cage
21b) 21(4) @ R1C5 = {2379} -> R1C5 + R2C4 = {23}, locked for N2

22) 18(4) @ R1C6 = {1368} -> no 4,7,9
22a) (36) locked @ R12C7 for C7 & 18(4) cage -> R3C7 = 9

And at last!! All singles from here.

Regards, Ronnie

The cage pattern was certainly a good Messy One but this Assassin was waaaay harder than any in the Messy One series, even though the SS score is fairly low.

IMHO that's quick for solving an Assassin. This one took me a lot longer; I got stuck and came back to it later. I did manage to solve A156, including writing my walkthrough as I went along, in that sort of time but the only other Assassins that I can remember solving in that time were Ruud's very early ones when I was writing walkthroughs but not posting them.

I get the impression that Afmob is a much quicker solver than I am. I don't know how long others take.

So did I; see step 14 of my first walkthrough.

It certainly does!

manu's step 2a is really neat! The immediate result in step 2b was obtained more directly by Ronnie's step 7 and my step 11. However its importance became obvious with manu's steps 2d and 2e. These led more quickly to the first placement and to a shorter WT.

Congratulations Ronnie on your first posted WT! An excellent effort!

After mentioning to Ed that I'd used difficult combination analysis (step 14) and an ALS block (step 16) he told me that I must have missed something easy. I therefore went back and eventually found what I'd missed. As a result I've decided to post both my walkthroughs for A155. For clarity I've posted them as separate messages and given them separate ratings.

I'll rate my first walkthrough at Hard 1.25 because of steps 14 and 16.

Here is my first walkthrough.

Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R56C9 = {69/78}
c) 20(3) cage in N3 = {389/479/569/578}, no 1,2
d) 11(3) cage at R4C3 = {128/137/146/236/245}, no 9
e) 19(3) cage at R5C3 = {289/379/469/478/568}, no 1
f) R7C678 = {289/379/469/478/568}, no 1
g) 10(3) cage in N7 = {127/136/145/235}, no 8,9
h) 19(3) cage in N7 = {289/379/469/478/568}, no 1
i) R9C789 = {289/379/469/478/568}, no 1
j) 11(3) cage in N9 = {128/137/146/236/245}, no 9
k) 8(3) cage at R8C7 = {125/134}, CPE no 1 in R8C456 (also R9C789 if I hadn’t done that 19(3) cage first)
l) 12(4) cage at R2C9 = {1236/1245}, no 7,8,9
m) 12(4) cage at R5C6 = {1236/1245}, no 7,8,9

1. 45 rule on R123 2 outies R4C19 = 14 = [95/86]
1a. 12(4) cage at R2C9 = {1236/1245}
1b. 1,2 locked in R2C9 + R3C89, locked for N3
1c. R4C9 = {56} -> no 5,6 in R2C9 + R3C89

2. 45 rule on R789 2 outies R6C14 = 4 = {13}, locked for R6
2a. 12(4) cage at R5C6 = {1236/1245}
2b. 1 locked in R5C67, locked for R5
2c. 1,3 of {1236} must be in R5C67 -> no 6 in R5C67
2d. Max R6C1 = 3 -> min R7C12 = 13, no 1,2,3

3. 45 rule on N7 1 outie R6C1 = 1 innie R7C3 -> R7C3 = {13}
[Alternatively 45 rule on N89 2 outies R6C4 + R7C4 = 4 = {13}]
3a. Naked pair {13} in R6C4 + R7C3, locked for 19(5) cage
3b. 1 in N8 locked in R9C456, locked for R9

4. 45 rule on N9 1 outie R7C6 = 1 innie R8C7 + 4, no 2,3,4 in R7C6

5. 45 rule on R89 1 innie R8C4 = 1 outie R7C9 + 5, no 5,6,7,8 in R7C9, no 2,4,5 in R8C4

6. 45 rule on N89 3 innies R7C45 + R8C4 = 15 = {249/258/267/456}
6a. 8,9 of {249/258} must be in R8C4 -> no 8,9 in R7C45
[Alternatively R7C45 + R8C4 = 15 from 19(5) cage with R6C4 + R7C3 = {13} = 4]

7. 45 rule on N4 4 innies R46C1 + R45C3 = 15 = {1239/1248} (only valid combinations because R4C1 must contain one of 8,9), no 5,6,7, 1,2 locked for N4
7a. 2 locked in R45C3, locked for C3, CPE no 2 in R5C5
7b. R4C1 = {89} -> no 8,9 in R45C3
7c. Max R5C3 = 4 -> min R5C4 + R6C5 = 15, no 2,3,4,5

8. 11(3) cage at R4C3 = {128/137/146/236/245}
8a. 8 of {128} must be in R5C5 -> no 8 in R4C4

9. 45 rule on N1 3 innies R123C3 = 1 outie R4C1 + 11
9a. R4C1 = {89} -> R123C3 = 19,20, no 1

10. 45 rule on C12 1 outie R6C3 = 1 innie R9C2, no 2,3 in R9C2
10a. 2 in N7 locked in 10(3) cage = {127/235}, no 4,6
10b. Killer pair 1,3 in R7C3 and 10(3) cage, locked for N7

11. 45 rule on N7 3 innies R7C123 = 16
11a. 45 rule on R7 remaining innies R7C459 = 10 = {127/145/235} (cannot be {136} which clashes with R7C3), no 6
11b. 1,3 only in R7C9 -> R7C9 = {13}, clean-up: no 7,9 in R8C4 (step 5)
11c. Naked pair {13} in R7C39, locked for R7
[At this stage I ought to have listed the combinations for R7C123 or for the 19(3) cage in N7. See alternative walkthrough in my next message.]

12. 11(3) cage in N9 = {128/137/146/236} (cannot be {245} because R7C9 only contains 1,3), no 5

13. R7C45 + R8C4 (step 6) = {258/267/456}
13a. 45 rule on N9 3 outies R7C6 + R9C56 = 12 = {129/138/147/345} (cannot be {156/246} which clash with R7C45 + R8C4, cannot be {237} which clashes with combinations of 8(3) cage at R8C7), no 6, clean-up: no 2 in R8C7 (step 4)

14. 45 rule on N9 3 innies R7C78 + R8C7 = 15 = {249/258/456} (cannot be {159/357} because R7C678 cannot be 5{59}/7{57}, cannot be {168/267/348} which clash with 11(3) cage), no 1,3,7, clean-up: no 5,7 in R7C6 (step 4)

15. 8(3) cage at R8C7 = {125/134}
15a. 1 locked in R9C56, locked for R9
15b. R8C7 = {45} -> no 4,5 in R9C56

16. 18(3) cage in N8 = {279/378/459} (cannot be {369} which clashes with R7C6 + R8C4 (ALS block), cannot be {468/567} which clash with R7C45 + R8C4), no 6

17. R8C4 = 6 (hidden single in N8), R7C9 = 1 (step 5), R7C3 = 3, R6C4 = 1, R6C1 = 3, clean-up: no 7 in R1C3, no 5 in 10(3) cage in N7 (step 10a)
17a. R7C9 = 1 -> R8C89 (step 12) = {28/37}, no 4
17b. Killer pair 2,7 in R8C12 and R8C89, locked for R8
17c. Naked triple {127} in 10(3) cage, locked for N7, clean-up: no 7 in R6C3 (step 10)
17d. 18(3) cage in N8 (step 16) = {378/459} (cannot be {279} because 2,7 only in R9C4), no 2
17e. 7 of {378} must be in R9C4 -> no 3 in R9C4

18. R3C8 = 1 (hidden single in C8)
18a. R234C9 = {236/245}, 2 locked for C9, clean-up: no 8 in R8C8 (step 17a)

19. R6C1 = 3 -> R46C1 + R45C3 (step 7) = {1239} (only remaining combination) -> R4C1 = 9, R45C3 = [12], R4C9 = 5 (step 1), clean-up: no 3 in R23C9 (step 18a), no 9 in R9C2 (step 10)
19a. Naked pair {24} in R23C9, locked for C9 and N3

20. R5C3 = 2 -> R5C4 + R6C5 = 17 = {89}, locked for N5

21. R5C7 = 1 (hidden single in R5)
21a. 12(4) cage at R5C6 = {1236/1245}, 2 locked in R6C68, locked for R6

22. R4C3 = 1 -> R4C4 + R5C5 = 10 = [37/46/73], no 2 in R4C4, no 4,5 in R5C5

23. 30(6) cage at R4C5 = {234678} (only remaining combination), no 9, 8 locked in R4C78 + R5C8 + R6C7, locked for N6, clean-up: no 7 in R56C9

24. Naked pair {69} in R56C9, locked for C9 and N6

25. 6 of 30(6) cage at R4C5 (step 23) locked in R4C56, locked for R4 and N5, clean-up: no 4 in R4C4 (step 22)
25a. Naked pair {37} in R4C4 + R5C5, locked for N5
25b. 5 in N5 locked in R56C6, locked for C6

26. R6C1 = 3 -> R7C12 = 13 = [49/58/85], no 6 in R7C1, no 4,6 in R7C2
26a. 6 in N7 locked in R9C23, locked for R9

27. R7C678 = {469/568} (cannot be {289} which clashes with R7C12), no 2
27a. Killer pair 8,9 in R7C12 and R7C6, locked for R7

28. R7C45 = {27}(hidden pair in R7), locked for N8, clean-up: no 3,8 in 18(3) cage (step 17d)

29. R7C6 = 8 (hidden single in N8), R8C7 = 4 (step 4), R8C56 = [59], R9C4 = 4, R8C3 = 8, clean-up: no 9 in R1C3, no 5 in R1C4, no 4 in R6C3 (step 10), no 5 in R7C12 (step 26), no 2 in R8C8 (step 17a)
29a. R7C12 = [49]

30. Naked pair {37} in R8C89, locked for R8 and N9 -> R9C9 = 8, clean-up: no 5 in R9C78 (prelim i)
30a. R9C1 = 7 (hidden single in R9)

31. X-Wing for 7 in R4C4 + R5C5 and R7C45, no other 7 in C45, clean-up: no 6 in R1C3

32. R23C3 = {79} (hidden pair in C3), locked for N1 and 21(4) cage at R1C5
32a. R23C4 = {79} = 16 -> R1C5 + R2C4 = 5 = {23} (cannot be {14} because 1,4 only in R1C5), locked for N2
[Naked pair {56} in R69C3, locked for C3 -> R1C3 = 4, R1C4 = 9 …, as in step 28 of my second walkthrough, followed by naked pair {79} in R23C4 … is more direct.]

33. R3C4 = 5 (hidden single in C4)
33a. 31(5) cage at R2C6 = {35689/45679}, no 1
33b. 9 locked in R3C57, locked for R3 -> R23C3 = [97]

34. 20(3) cage in N3 = {389/578} (cannot be {569} because R1C9 only contains 3,7), no 6, 8 locked in R12C8, locked for C8 and N3
34a. R1C9 = {37} -> no 3,7 in R12C8

35. R7C8 = 6 (hidden single in C8), R7C7 = 5

36. 5 in N3 locked in 20(3) cage (step 34) = {578} -> R1C9 = 7, R12C8 = {58}, R8C89 = [73]
36a. Naked triple {369} in R123C7, locked for C7 -> R9C78 = [29]

37. 45 rule on N23 1 remaining innie R1C4 = 9, R1C3 = 4, R5C4 = 8, R6C5 = 9, R56C9 = [96], R6C3 = 5, R5C1 = 6, R9C23 = [56]
37a. R2C6 = 7 (hidden single in R2)
37b. R3C7 = 9 (hidden single in R3), clean-up: no 8 in R3C5 (step 33a)
37c. R5C6 = 5 (hidden single in R5)

38. Naked pair {46} in R3C56, locked for R3 and N2

39. 5 in N1 locked in R12C1 -> 13(3) cage = {256} (only remaining combination) -> R1C2 = 6, R12C1 = {25}, locked for C1 and N1

and the rest is naked singles

As I said above, I went back to find what I'd missed first time through.

And this one is even longer!

The solving path this time is fairly similar to the way Ronnie solved it but I've decided to post this anyway.

I'll rate my second walkthrough at (Very) Hard 1.0; that's also my rating for A155.

Here is my second walkthrough. The first 11 steps are the same as before; I've repeated them for clarity and in case anyone goes directly to my easier solving path.

Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R56C9 = {69/78}
c) 20(3) cage in N3 = {389/479/569/578}, no 1,2
d) 11(3) cage at R4C3 = {128/137/146/236/245}, no 9
e) 19(3) cage at R5C3 = {289/379/469/478/568}, no 1
f) R7C678 = {289/379/469/478/568}, no 1
g) 10(3) cage in N7 = {127/136/145/235}, no 8,9
h) 19(3) cage in N7 = {289/379/469/478/568}, no 1
i) R9C789 = {289/379/469/478/568}, no 1
j) 11(3) cage in N9 = {128/137/146/236/245}, no 9
k) 8(3) cage at R8C7 = {125/134}, CPE no 1 in R8C456 (also R9C789 if I hadn’t done that 19(3) cage first)
l) 12(4) cage at R2C9 = {1236/1245}, no 7,8,9
m) 12(4) cage at R5C6 = {1236/1245}, no 7,8,9

1. 45 rule on R123 2 outies R4C19 = 14 = [95/86]
1a. 12(4) cage at R2C9 = {1236/1245}
1b. 1,2 locked in R2C9 + R3C89, locked for N3
1c. R4C9 = {56} -> no 5,6 in R2C9 + R3C89

2. 45 rule on R789 2 outies R6C14 = 4 = {13}, locked for R6
2a. 12(4) cage at R5C6 = {1236/1245}
2b. 1 locked in R5C67, locked for R5
2c. 1,3 of {1236} must be in R5C67 -> no 6 in R5C67
2d. Max R6C1 = 3 -> min R7C12 = 13, no 1,2,3

3. 45 rule on N7 1 outie R6C1 = 1 innie R7C3 -> R7C3 = {13}
[Alternatively 45 rule on N89 2 outies R6C4 + R7C4 = 4 = {13}]
3a. Naked pair {13} in R6C4 + R7C3, locked for 19(5) cage
3b. 1 in N8 locked in R9C456, locked for R9

4. 45 rule on N9 1 outie R7C6 = 1 innie R8C7 + 4, no 2,3,4 in R7C6

5. 45 rule on R89 1 innie R8C4 = 1 outie R7C9 + 5, no 5,6,7,8 in R7C9, no 2,4,5 in R8C4

6. 45 rule on N89 3 innies R7C45 + R8C4 = 15 = {249/258/267/456}
6a. 8,9 of {249/258} must be in R8C4 -> no 8,9 in R7C45
[Alternatively R7C45 + R8C4 = 15 from 19(5) cage with R6C4 + R7C3 = {13} = 4]

7. 45 rule on N4 4 innies R46C1 + R45C3 = 15 = {1239/1248} (only valid combinations because R4C1 must contain one of 8,9), no 5,6,7, 1,2 locked for N4
7a. 2 locked in R45C3, locked for C3, CPE no 2 in R5C5
7b. R4C1 = {89} -> no 8,9 in R45C3
7c. Max R5C3 = 4 -> min R5C4 + R6C5 = 15, no 2,3,4,5

8. 11(3) cage at R4C3 = {128/137/146/236/245}
8a. 8 of {128} must be in R5C5 -> no 8 in R4C4

9. 45 rule on N1 3 innies R123C3 = 1 outie R4C1 + 11
9a. R4C1 = {89} -> R123C3 = 19,20, no 1

10. 45 rule on C12 1 outie R6C3 = 1 innie R9C2, no 2,3 in R9C2
10a. 2 in N7 locked in 10(3) cage = {127/235}, no 4,6
10b. Killer pair 1,3 in R7C3 and 10(3) cage, locked for N7

11. 45 rule on N7 3 innies R7C123 = 16
11a. 45 rule on R7 remaining innies R7C459 = 10 = {127/145/235} (cannot be {136} which clashes with R7C3), no 6
11b. 1,3 only in R7C9 -> R7C9 = {13}, clean-up: no 7,9 in R8C4 (step 5)
11c. Naked pair {13} in R7C39, locked for R7

And now the step that I missed first time.

12. R7C123 = {169/178/349/358} (cannot be {367} which clashes with 19(3) cage)
[Alternatively hidden killer pair 8,9 in R7C12 and 19(3) cage for N7, 19(3) only contains one of 8,9 -> R7C12 must contain one of 8,9]
12a. R7C678 = {469/478/568} (cannot be {289} which clashes with R7C12), no 2
12b. 2 in R7 locked in R7C45, locked for N8
12c. R7C45 + R8C4 (step 6) = {258/267}, no 4

13. 8(3) cage at R8C7 = {125/134}
13a. 2 of {125} must be in R8C7 -> no 5 in R8C7, clean-up: no 9 in R7C6 (step 4)

14. 9 in N8 locked in 18(3) cage = {189/369/459}, no 7
14a. 1 of {189} must be in R9C4 -> no 8 in R9C4
14b. 7 in N8 locked in R7C456, locked for R7

15. 45 rule on N9 3 outies R7C6 + R9C56 = 12 = {138/147/345} (cannot be {156} which clashes with R7C45 + R8C4), no 6, clean-up: no 2 in R8C7 (step 4), no 5 in R9C56 (step 13)

16. Naked triple {134} in 8(3) cage at R1C7, CPE no 3,4 in R8C56 and R9C789
16a. R9C456 = {134} (hidden triple in N8), locked for R9, clean-up: no 4 in R6C3 (step 10)
[Alternatively 1,3,4 of 18(3) cage (step 14) only in R9C4 -> R9C4 = {134}
Naked triple {134} in R9C456, locked for R9, clean-up: no 4 in R6C3 (step 10)]

17. 45 rule on R9, 1 outie R8C3 = 1 remaining innie R9C1 + 1, no 4,5,7,9 in R8C3, no 2 in R9C1

18. 2 in R9 locked in R9C789, locked for N9
18a. R9C789 = {289}, locked for R9 and N9, clean-up: no 8,9 in R6C3 (step 10)

19. R7C678 = {478/568} -> R7C6 = 8, R8C4 = 6, R8C3 = 8, R8C7 = 4 (step 4), clean-up: no 7 in R1C3, no 5 in R1C4
19a. Naked pair {59} in R8C56, locked for R8 and N8, R9C4 = 4 (step 14), clean-up: no 9 in R1C3
19b. Naked triple {567} in R9C123, locked for N7

20. R7C12 = {49}, R7C3 = 3 (step 12), R6C14 = [31], R7C9 = 1
20a. R8C12 = {12} -> R9C1 = 7 (step 10a), clean-up: no 7 in R6C3 (step 10)

21. R46C1 + R45C3 (step 7) = {1239} (only remaining combination) -> R4C1 = 9, R45C3 = [12], R4C9 = 5 (step 1), R7C12 = [49]

22. R5C3 = 2 -> R5C4 + R6C5 = 17 = {89}, locked for N5

23. R4C3 = 1 -> R4C4 + R5C5 = 10 = {37} (only remaining combination), locked for N5

24. 5 in N5 locked in R56C6, locked for C6 -> R8C56 = [59]
24a. 5 locked in R56C6 -> 12(4) cage at R5C6 = {1245}, no 3,6, R5C7 = 1, 2 locked in R6C68, locked for R6

25. 30(6) cage at R4C5 = {234678} (only remaining combination), no 9, 8 locked in R4C78 + R5C8 + R6C7, locked for N6, clean-up: no 7 in R56C9

26. Naked pair {69} in R56C9, locked for C9 and N6
26a. 6 in N5 locked in R4C56, locked for R4

27. R4C1 = 5 -> 12(4) cage at R2C9 = {1245}, R2C8 = 1, R23C9 = {24}, locked for C9 and N3 -> R9C9 = 8

28. Naked pair {56} in R69C3, locked for C3 -> R1C3 = 4, R1C4 = 9, R5C4 = 8, R6C5 = 9, R56C9 = [96], R6C3 = 5, R5C1 = 6, R9C23 = [56]
28a. R5C6 = 5 (hidden single in R5)

29. Naked pair {79} in R23C9, locked for N1 and 21(4) cage at R1C5
29a. R23C9 = {79} = 16 -> R1C5 + R2C4 = 5 = {23}, locked for N2

30. R3C4 = 5 (hidden single in C4)
30a. 31(5) cage at R2C6 = {35689/45679}, no 1, R3C7 = 9, R23C3 = [97], R9C78 = [29]
30b. 31(5) cage at R2C6 = {45679} (only remaining combination) -> R2C6 = 7, R3C56 = {46}, locked for R3 and N2, R1C6 = 1, R2C5 = 8, R23C9 = [42], R9C56 = [13], R3C12 = [83], R2C2 = 1 (cage sum), R7C12 = [12]
30c. R1C2 = 6 (hidden single in N1)

31. R1C6 + R2C5 = [18] = 9 -> R12C7 = 9 = [36]

and the rest is naked singles