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My original puzzle was designed around this idea. But.....couldn't solve it. So, had to keep chopping it down and kept getting lower and lower SSscores until finally found one I could solve! Sooo frustrating. Hope the result is not too easy.

I'll post an "old school" v2 of A110 (same solution: slightly different cage pattern) when I've had another crack myself first. So, a very big thankyou to Nasenbaer for volunteering for A111!!

Assassin 110X (note: a 35(7) cage runs down the D/)



Solution:
+-------+-------+-------+
| 6 4 9 | 7 1 8 | 2 5 3 |
| 2 8 1 | 5 9 3 | 6 7 4 |
| 5 3 7 | 4 2 6 | 8 1 9 |
+-------+-------+-------+
| 4 5 6 | 3 7 2 | 9 8 1 |
| 7 1 2 | 8 5 9 | 3 4 6 |
| 8 9 3 | 1 6 4 | 7 2 5 |
+-------+-------+-------+
| 3 2 4 | 9 8 5 | 1 6 7 |
| 1 6 5 | 2 3 7 | 4 9 8 |
| 9 7 8 | 6 4 1 | 5 3 2 |
+-------+-------+-------+


SS(v3.2.1) score = 0.79

Cheers
Ed

Thanks Ed for an Assassin with an interesting cage structure! Especially the large 35(7) is nice. I tried the same (providing larger cages) with A109.

I think my step 3a is too advanced for a 0.75 Killer and since SS also uses this move SudokuSolver's rating is a bit off, in my opinion.

A110X Walkthrough:

1. R789
a) 16(2) = {79} locked for R9+N7
b) 14(2) = {68} locked for R9
c) 8(2) = {35} locked for R9+N9
d) 13(2) <> 8

2. N1478
a) Outies N14 = 5(2) = [23/32/41]
b) Innies N1478 = 13(2) <> 1,2,3; R7C4 <> 4,6
c) 7(2) <> 3,4 because (34) is a Killer pair of Outies N14
d) Innies N147 = 17(3) = 8{36/45} because 8 locked there @ N7 -> 8 locked for C3
and R8C3 <> 6,8 because 3 only possible there

3. N5 !
a) ! Using Innies N1478: Innies+Outies R6789: 8 = R5C6 - R6C4 -> R5C6 = 9, R6C4 = 1
b) Innies = 8(3) <> 6,7,8
c) Using Innies N1478: Outies N5 = 14(2) = [59/68/86]

4. C1 !
a) 7(2): R8C1 <> 6
b) ! Innies = 17(3) = 9{17/25/36} because R8C1 = (125) -> R9C1 = 9; R5C1 = (367)
c) R9C2 = 7

5. N5
a) Outies = 14(2) = {68} locked for R3+35(7)
b) Innies N1478 = 13(2) = {49} -> R7C3 = 4, R7C4 = 9
c) Innies = 8(3) = {125} locked for N5+D/
d) R8C2 = 6 -> R8C1 = 1

6. N478+C1
a) 11(2) = {38} -> R7C1 = 3, R6C1 = 8
b) R7C2 = 2, R8C3 = 5, R9C3 = 8, R9C4 = 6
c) Innies C1 = R5C1 = 7
d) 10(3) = {127} -> R5C2 = 1, R5C3 = 2
e) 14(3) = {239} -> 3,9 locked for R6+N4
f) R4C3 = 6

7. N13
a) 13(2) = {49} -> R1C2 = 4, R1C3 = 9
b) R3C7 = 8
c) 11(2) = {47} -> R2C8 = 7, R2C9 = 4
d) R1C9 = 3 -> R1C8 = 5
e) 10(2) = {28} -> R1C7 = 2, R1C6 = 8
f) 18(3) = 9{18/27/45} <> 3 because R3C8 = (19)

8. Rest is singles without considering the diagonals.

Rating: 1.0.

Great. It would have been too notorious to have the first 0.75 rating Assassin since......

Glad you liked that cage. I'm hoping it will yield a v2 with some nice triple cross-over moves (udosuk's name: but there is probably a more technically correct term, something something fish)

Cheers
Ed

Hi folks,

I've just finished this one after more than 3 hours of chipping away at the candidates in 2 sessions , wondering how the puzzle could be so easy. After what was probably about 30 steps, including an implied cage blocker and a simple chain (!) I finally stumbled across Afmob's step 3a, which really killed the puzzle off. The rest then took less than 5 minutes. So Afmob's step 3a really seems to be the big chink in the armor for this puzzle: how long it takes to do the puzzle depends on how long it takes to see this move. Incidentally, this is one reason why I'm not so keen on rating puzzles depending on how long it takes to do them, since one person could see such a key move in a couple of minutes, and another after several hours.


Last but not least, many thanks for the puzzle, Ed!

_________________
Cheers,
Mike

Hope you kept your notes! This "old school" V2 has the same solution as the original, but takes out the "easy" opening (Afmob's step 3a). Finally worked out how to solve this next one nicely, so technically, it could be a 1.25 rating (no chains needed), but since it took me all week to find, I'll estimate it as 1.5.

Next time, I'll give myself 2 weeks to make the Assassin.

Assassin 110x V2


Solution: same as original

SS(v3.2.1) score = 1.31

Cheers
Ed

Hi folks,

Both of these puzzles (A110X and A110X V2) were good, but the "V2" would IMO have been an even better "V1" than the original. Thanks once again, Ed, for providing us with the opportunity for making some interesting moves!

I found it difficult to write a WT for the V2, because, as is common for Killer-X puzzles, there were often several ways to go, and, when the puzzle starts to crack, things happen so quickly, that one tends to fall over one's toes (so to speak) trying to keep up.

Afmob commented on my A109 WT that I did too much in the preliminaries. He has a point, because for puzzles with a "racing start", like with my A107 cage pattern, it's even possible to get placements (!) within the preliminaries if one starts considering cage-external effects such as locked candidates and conflicting combinations (not to mention the resulting clean-ups). Therefore, starting with this WT, I am only doing combinational reductions at the preliminaries stage, like most automated solvers do. Any locked candidates, conflicting combinations, naked subsets, and so on, arising from the preliminaries stage are handled as regular WT steps.

This WT does not go "by the book", so is sprinkled with moves that are too complex for a V1.25. One move (step 27b) is even bordering on T&E , but was easy to spot after step 26 and should provide an interesting alternative to going down the "beaten track", as it were. So I decided to keep it in.

Hopefully, at least one other WT will be posted with a more conventional approach (Afmob?, Andrew?, ...), which will probably show that the SScore is spot on in this case.

Edited to incorporate late feedback from Andrew. Thanks!

_________________
Cheers,
Mike

Ed was spot on with his description since the moves weren't too difficult (technical rating: 1.25, most difficult step: 4c) but it took me quite some time to find them. That's why I rate this Killer (hard) 1.25.
But I have to really wonder why it took me so long to find step 5c which was quite easy to see.

A110X V2 Walkthrough:

1. R789
a) 16(2) = {79} locked for R9+N7
b) 14(2) = {68} locked for R9
c) 8(2) = {35} locked for R9+N9
d) 13(2) <> 8
e) Outies N14 = 5(2) = {14/23}
f) 7(2) <> 3,4 because (34) is a Killer pair of Outies N14
g) Innies N147 = 17(3) = 8{36/45} -> 8 locked for C3

2. N5
a) Innies N5 = 8(3) = 1{25/34} -> 1 locked for N5+D/+35(7)
b) Innies N2369 = 14(2) = {59/68}
c) Using Innies N2369: Outies N5 = 13(2) = [49/67] because
(58) is a Killer pair of Innies N2369

3. R789+D/
a) Innies N147 = 17(3): R8C3 = (35) because it's only possible there
b) Hidden Single: R9C3 = 8 @ C3, R9C4 = 6
c) 18(4) = 35{19/28} because R8C3 = (35) and R9C56 = (124) blocks 4{158/239/257}; CPE: R8C6 <> 3,5
d) 17(4) = 4{139/157/238} because 4 locked there @ N8; R78C6 <> 1,2,4 because R9C56 = (124)
and R7C6 = (35) because it's only possible there
e) 4 locked in R9C56 @ N8 for R9
f) 4 locked in R7C123 @ N7 for R7
g) 5 locked in R8C123 @ N7 for R8
h) 7(2): R8C1 <> 6
i) 6 locked in R7C3+R8C2 @ N7 for D/
j) 22(4): R678C9 <> 1,2 because R9C9 = (12)

4. R789 !
a) 3 locked in R8C345 @ R8 @ 18(4) -> R7C5 <> 3
b) Hidden Killer pair (12) in 18(4) for R8 since 7(2) can only have one of (12)
-> R7C5 <> 1,2
c) ! Innies+Outies R8: -7 = R7C5 - R8C69
- R7C5 <> 9 because (79) is a Killer pair of 13(2)
- R8C9 <> 7 (IOU @ N8)
- R8C9 <> 9 because R8C6 <> 3,6
- R8C6 <> 9, R8C9 <> 6 because (69) is a Killer pair of 13(2)
d) Innies+Outies R8: -7 = R7C5 - R8C69 -> R8C69 = 12/15(2) = 8{7/4} -> 8 locked for R8

5. C456+D/ !
a) Innies N2 = 17(3) <> 5 because 5{39/48} blocked by R7C6 = (35) and (58) is a Killer pair of 17(4)
b) 35(7) = 14569{28/37} because of Innies N5 and R7C3 = (46) -> 4,5 locked for D/
c) ! Killer pair (24) locked in R7C3+R8C2 + Innies N5 for D/
d) 7(2): R8C1 <> 2
e) 8(2) = [17/53]
f) 8 locked in R2C8+R3C7 @ D/ for N3
g) 11(2) = [74/83/92]

6. R123
a) Innies N2356 = 14(2) = [68/95]
b) Outies N69 = 10(2) <> 2,3,5,7 because R1C9 = (37)
c) Using Outies N69: Innies N3 = 16(3) <> 3 because R3C7 = (58) and R9C7 = (35) blocks {358}
and R2C7 <> 5 because R3C7 = (58)
-> Innies N3 = {178/259/268/457}
d) 10(2) <> 3,7 because R1C9 = (37); R1C6 <> 2
e) 9(2) @ N3 <> 4 and R2C6 <> 1,6
f) Killer pair (69) locked in R3C6 + Outies N69 for R3
g) Innies N3 = 16(3) <> 4 because (57) is a Killer pair of 8(2)
and R2C7 <> 1 because R1C7 <> 7,8
h) 9(2) <> 8
i) 10(2): R1C6 <> 6

7. R123+D/
a) 9 locked in R2C8+R9C1 @ D/ -> CPE: R2C1 <> 9
b) 9 locked in R1C123 @ N1 for R1
c) 10(2) <> 1
d) Innies N3 = 16(3) = {268} -> R3C7 = 8, {26} locked for C7+N3
e) 11(2) = {47} -> R2C8 = 7, R2C9 = 4
f) 9(2) @ N3 = {36} -> R2C6 = 3, R2C7 = 6
g) 10(2) = {28} -> R1C6 = 8, R1C7 = 2
h) R1C9 = 3 -> R1C8 = 5
i) 9(2) @ N1 = {18} -> R2C3 = 1, R2C2 = 8
j) 1 locked in R1C45 @ R1 @ 13(3) -> 13(3) = {157} -> R2C4 = 5, {17} locked for R1+N2

8. N17
a) 13(2) = {49} locked for R1+N1
b) R1C1 = 6, R2C1 = 2 -> R34C1 = 9(2) = [54] -> R3C1 = 5, R4C1 = 4
c) 35(7) = {124569} -> R7C4 = 9, R3C6 = 6, R7C3 = 4, {125} locked for N5+D/
d) R8C1 = 1, R7C1 = 3, R7C2 = 2
e) 21(5) = 123{69/78} -> R5C3 = 2, R5C2 = 1
f) 21(4) = {3567} -> 5,6 locked for R4+N4

9. Rest is singles

Rating: (Hard) 1.25. I used Killer pairs and Innies+Outies analysis.

Here is my 5-step walkthrough for V2. I haven't read the others' moves but I suspect the critical ones might be similar.


I like this puzzle because after the intense actions the mopping up is really short and sweet.

_________________
ADYFNC HJPLI BVSM GgK Oa m

Thanks Ed. A110X was a fun puzzle. I enjoyed the 35(7) cage along and "hugging" the diagonal and it was also very helpful for the solution.

I reached the result of Afmob's step 3a fairly early but using a slightly different route.

After going through Afmob's one, I now realise that my walkthrough could have been quite a lot shorter if I'd obtained the result of step 8 before I did step 3; unfortunately I never thought of revisiting step 3 after doing step 8.

I'll also rate A110X at 1.0. I don't think I can rate it lower with the chain of 45s that I used in step 5.

Here is my walkthrough. I've given eliminations on the diagonals; it's so easy for those of us doing manual eliminations to overlook them.

Prelims

a) R1C23 = {49/58/67}, no 1,2,3
b) R1C67 = {19/28/37/46}, no 5
c) R1C89 = {17/26/35}, no 4,8,9
d) R2C23 = {18/27/36/45}, no 9
e) R2C67 = {18/27/36/45}, no 9
f) R2C89 = {29/38/47/56}, no 1
g) R67C1 = {29/38/47/56}, no 1
h) R8C12 = {16/25/34}, no 7,8,9
i) R8C78 = {49/58/67}, no 1,2,3
j) R9C34 = {59/68}
k) R9C78 = {17/26/35}, no 4,8,9
l) R9C12 = {79}, locked for R9 and N7, clean-up: no 2,4 in R6C1, no 5 in R9C34, no 1 in R9C78
m) R5C123 = {127/136/145/235}, no 8,9
n) 19(3) cage in N5 = {289/379/469/478/568}, no 1

1. Naked pair {68} in R9C34, locked for R9, clean-up: no 2 in R9C78
1a. Naked pair {35} in R9C78, locked for R9 and N9, clean-up: no 8 in R8C78

2. 45 rule on N5 3 innies R4C6 + R5C5 + R6C4 = 8 = {125/134}, 1 locked for N5, D/ and 35(7) cage, clean-up: no 7 in R1C8, no 6 in R8C1

3. 45 rule on C1 3 innies R589C1 = 17 = {179/269/359/467}
3a. 1,2 of {179/269} must be in R8C1 -> no 1,2 in R5C1
3b. 6 of {467} must be in R5C1 -> no 4 in R5C1

4. 45 rule on C123 3 innies R789C3 = 17 = {368/458}, no 1,2, 8 locked for C3 and N7, clean-up: no 5 in R1C2, no 1 in R2C2, no 3 in R6C1

5. 45 rule on N14 3 innies R6C123 = 20 = {389/479/569/578}, no 1,2
[I noticed while checking through this walkthrough that taken together with the 14(3) cage this gives R6C1 = R7C2 + 6, R6C1 = {789}, R7C2 = {123}. This is obtained from step 8 so I haven’t tried to rewrite my steps.]
5a. 45 rule on N9 3 outies R6C789 = 14
5b. 45 rule on R6 3 innies R6C456 = 11 = {128/137/146} (cannot be {236/245} because R6C56 must total at least 10 for the 19(3) cage), no 5,9 -> R6C4 = 1
[Alternatively can use R6C456 = 11 together with 19(3) to get R5C6 = R6C4 + 8 -> R5C6 = 9, R6C4 = 1.]
5c. R6C56 = {28/37/46} = 10 -> R5C6 = 9, clean-up: no 1 in R1C7
5d. 18(3) cage in N5 = {378/468/567}, no 2

6. 35(7) cage at R3C6 = {1235789/1245689/1345679}, CPE no 9 in R3C4

7. R5C123 = {127/136/145/235}
7a. 7 of {127} must be in R5C1 -> no 7 in R5C23

8. 45 rule on N14 2 outies R7C12 = 5 = [23/32/41], no 5,6, no 4 in R7C2, clean-up: no 5,6 in R6C1

9. Killer pair 3,4 in R7C12 and R78C3, locked for N7
[I could have got that elimination after step 4 from the clash with R78C3.]

10. 45 rule on R12 2 outies R34C1 = 1 innie R2C5
10a. Min R34C1 = 3 -> min R2C5 = 3
10b. Max R2C5 = 9 -> max R34C1 = 9, no 9

11. 45 rule on N78 4 innies R7C1234 = 18, R7C12 = 5 (step 8) -> R7C34 = 13 = [49/58/67/85], no 3 in R7C3, no 2,3,4,6 in R7C4
11a. R7C34 = 13, R4C6 + R5C5 + R6C4 = 8 (step 2) -> R3C67 = 14 (cage sum) = [59/68/86], R3C6 = {568}, R3C7 = {689}

12. 35(7) cage at R3C6 = {1245689/1345679} (cannot be {1235789} which clashes with R4C6 + R5C5), 4 locked in R4C6 + R5C5 + R7C3, locked for D/, clean-up: no 7 in R2C9
12a. {1245689} must be {68}{25}1[49], {1345679} must be [59]{34}1[67] -> R7C34 = [49/67], no 5,8
12b. CPE no 6 in R3C3

13. R789C3 (step 4) = {368/458}
13a. 3 of {368} must be in R8C3 -> no 8 in R8C3
13b. R9C3 = 8 (hidden single in C3), R9C4 = 6
13c. R7C3 = {46} -> no 4,6 in R8C3
13d. 4 in N7 locked in R7C13, locked for R7

14. 45 rule on N69 2 outies R3C89 = 10 = {19/28/37/46}, no 5

15. 17(4) cage in N8 = {1457/2348} (cannot be {1358/2357} because R9C56 must contain two of 1,2,4), 4 locked in R9C56 (because they only contain 1,2,4), locked for R9 and N8
15a. R9C56 = {124} -> no 1,2 in R78C6
15b. R78C6 = {38/57}

16. Min R7C78 = {16} (cannot be {12} which clashes with R9C9) = 7 -> max R6C78 = 9, no 8,9 in R6C78
16a. Max R6C78 = 9 -> min R6C9 = 5 (step 5a)

17. R6789C9 = {1489/1579/1678/2479/2569/2578} (cannot be {4567} which doesn’t contain 1,2)
17a. R9C9 = {12} -> no 1,2 in R78C9

18. Hidden killer pair 1,2 in R7C78 and R9C9 for N9 -> R7C78 must contain 1 or 2
18a. Killer pair 1,2 in R7C12 and R7C78, locked for R7

19. R6C789 = 14 (step 5a)
19a. R7C78 must contain 1 or 2 (step 18) -> R6C78 cannot be {23} because cannot form 16(4) cage including all of 1,2,3 -> no 9 in R6C9 (cage sum)

20. 9 in R6 locked in R6C123, locked for N4

21. 5 in N7 locked in R8C123, locked for R8, clean-up: no 7 in R7C6 (step 15b)
21a. 18(4) cage at R8C3 = {1359/2358} (cannot be {1278} because R8C3 only contains 3,5), no 7
21b. 1 of {1359} must be in R8C5 -> no 9 in R8C5

22. 45 rule on N2 3 innies R123C6 = 17 = {278/368/458/467}, no 1, clean-up: no 9 in R1C7, no 8 in R2C7

23. R9C6 = 1 (hidden single in C6), R9C9 = 2, locked for D\, R9C5 = 4, clean-up: no 6 in R1C8, no 7 in R2C3, no 9 in R2C8, no 3,5 in R4C6 (step 2), no 3,8 in R78C6 (step 15b)
23a. R78C6 = [57], R7C4 = 9, R7C3 = 4 (step 12a), R4C6 = 2, R5C5 = 5 (step 2), 2,5 locked for D/, 5 locked for D\, R8C2 = 6, R8C1 = 1, 6 locked for D/, R3C7 = 8, R3C6 = 6, clean-up: no 9 in R1C2, no 7 in R1C3, no 3,4 in R1C7, no 2,3 in R1C8, no 3 in R2C3, no 2,3,4,7 in R2C7, no 3 in R2C8, no 3,5,6,9 in R2C9, no 7 in R6C1, no 3,8 in R6C5, no 8 in R6C6 (both step 5b)
23b. R2C89 = [74], 7 locked for D/, R1C9 = 3, R1C8 = 5, R9C1 = 9, R9C2 = 7, R9C78 = [53] , R6C1 = 8, R7C1 = 3, R7C2 = 2, R7C5 = 8, R8C3 = 5, clean-up: no 8 in R1C2, no 6 in R1C3, no 2 in R2C3
23c. R1C23 = [49], R1C6 = 8, R1C7 = 2, R2C6 = 3, R2C7 = 6, R2C23 = [81], 8 locked for D\, R2C5 = 9, R1C45 = [71], R1C1 = 6, locked for D\, R5C1 = 7, R6C6 = 4, R4C4 = 3 , 3,4 locked for D\, R3C3 = 7, locked for D\

and the rest is naked singles without using diagonals

I see that Ed's V2 also removes my early breakthrough by removing 3 innies for N14 (step 5).

Continuing working through my backlog, the next variant I tried was A110X V2 which was another one which I found that I hadn't started.

Thanks Ed for another interesting and challenging variant. You have a knack for making good variants by just combining two cages, in this case the 10(3) cage at R5C1 and the 11(2) cage at R6C1.

It might have helped if I'd looked to see how I'd solved the original but I didn't need to; I solved this as a new puzzle.

When I went through the walkthroughs posted by Afmob, Mike and udosuk I found that they had all used critical moves based on the innie-outie difference for R8. I therefore found that, even though there were already 3 posted walkthroughs, mine was significantly different because I'd used a different innie-outie difference and related combination analysis. Edit. Then when I had to re-work my later steps, see below, I found that I needed to use the innie-outie difference for R8 so it appears to be the critical step for this puzzle.


Here is my walkthrough for A110X V2. Thanks Afmob for pointing out that my original step 16 was flawed. I've re-worked from after step 15 and also made a few minor changes to earlier steps. Then thanks again to Afmob for finding that my new step 21 was flawed. I've found an alternative way to do that step.

Prelims

a) R1C23 = {49/58/67}, no 1,2,3
b) R1C67 = {19/28/37/46}, no 5
c) R1C89 = {17/26/35}, no 4,8,9
d) R2C23 = {18/27/36/45}, no 9
e) R2C67 = {18/27/36/45}, no 9
f) R2C89 = {29/38/47/56}, no 1
g) R8C12 = {16/25/34}, no 7,8,9
h) R8C78 = {49/58/67}, no 1,2,3
i) R9C12 = {79}
j)R9C34 = {59/68}
k) R9C78 = {17/26/35}, no 4,8,9
l) 19(3) cage in N5 = {289/379/469/478/568}, no 1

Steps resulting from Prelims
1a. Naked pair {79} in R9C12, locked for R9 and N7, clean-up: no 5 in R9C34, no 1 in R9C78
1b. Naked pair {68} in R9C34, locked for R9, clean-up: no 2 in R9C78
1c. Naked pair {35} in R9C78, locked for R9 and N9, clean-up: no 8 in R8C78

2. 45 rule on N14 2 outies R7C12 = 5 = {14/23}
2a. R8C12 = {16/25} (cannot be {34} which clashes with R7C12), no 3,4
2b. Killer pair 1,2 in R7C12 and R8C12, locked for N7
2c. 8 in N7 only in R789C3, locked for C3, clean-up: no 5 in R1C2, no 1 in R2C2

3. 45 rule on N69 2 outies R3C89 = 10 = {19/28/37/46}, no 5

4. 45 rule on N5 3 innies R4C6 + R5C5 + R6C4 = 8 = {125/134}, 1 locked for N5, D/ and 35(7) cage at R3C6, clean-up: no 7 in R1C8, no 6 in R8C1
4a. 45 rule on N2369 2 innies R3C67 = 14 = {59/68}
4b. 45 rule on N1478 2 innies R7C34 = 13 = [49/67] (cannot be {58} which clashes with R3C67), no 1,2,3,5,8, no 4,6 in R7C4
4c. 35(7) cage at R3C6 = {125}{68}[49]/{134}{59}[67](combining combinations in steps 4, 4a and 4b)
4d. 4 only in R4C6 + R5C5 + R6C4 + R7C3, locked for D/, clean-up: no 7 in R2C9
4e. 9 only in R3C67 + R7C4, CPE no 9 in R3C4
4f. 5 in R7 only in R7C56, locked for N8
4g. 8 on D/ only in R2C8 + R3C7, locked for N3, clean-up: no 2 in R1C6, no 1 in R2C6, no 3 in R2C8, no 2 in R3C89 (step 3)

5. 45 rule on C123 3 innies R789C3 = 17 = {368/458}
5a. 3,5 only in R8C3 -> R8C3 = {35}
5b. R9C3 = 8 (hidden single in C3), R9C4 = 6
5c. 4 in N7 only in R7C123, locked for R7
5d. 6 in N7 only in R7C3 + R8C2, locked for D/, clean-up: no 2 in R1C8, no 5 in R2C9, no 8 in R3C6 (step 4a)
5e. 6 in 35(7) cage at R3C6 only in R3C6 + R7C3, CPE no 6 in R3C3

6. 45 rule on N9 2 innies R7C78 = 1 outie R6C9 + 2
6a. Min R7C78 = {16} = 7 (cannot be {12} which clashes with R7C12) -> min R6C9 = 5
6b. Max R7C78 = 11 -> R7C78 must contain one of 1,2
6c. Killer pair 1,2 in R7C12 and R7C78, locked for R7

7. 45 rule on C1 2 innies R89C1 = 2 outies R5C23 + 7
7a. Max R89C1 = 14 -> max R5C23 = 7, no 7,8,9

8. 45 rule on C789 3 innies R123C7 = 16 = {169/178/259/268/457} (cannot be {349} which clashes with R3C89, cannot be {358} which clashes with R9C7, cannot be {367} because no 3,6,7 in R3C7), no 3, clean-up: no 7 in R1C6, no 6 in R2C6

9. 17(4) cage in N8 = {1259/1349/1457/2348} (cannot be {1358/2357} because R9C56 must contain two of 1,2,4)
9a. 17(4) cage only contains two of 1,2,4 -> no 1,2,4 in R8C6
9b. 5 of {1457} must be in R7C6 -> no 7 in R7C6

10. Hidden killer pair 3,5 in R78C6 and R7C5 + R8C45 for N8, R78C6 contains one of 3,5 -> R7C5 + R8C45 must contain one of 3,5 -> 18(4) cage at R7C5 must contain both of 3,5 = {1359/2358}, no 4,7, CPE no 3 in R8C6
10a. 3 in R8 only in R8C345, locked for 18(4) cage, no 3 in R7C5
10b. Hidden killer pair 3,5 in R7C5 + R8C45 and R7C6 for N8, R7C5 + R8C45 contains one of 3,5 -> R7C6 = {35}

11. 4 in N8 only in R9C56, locked for R9
11a. Killer pair 1,2 in R7C78 and R9C9, locked for N9

12. 45 rule on N8 4 remaining innies R78C45 = 22 = {1579/2389/2578}
12a. 5 of {1579/2578} must be in R7C5, 9 of {2389} must be in R7C4 -> no 9 in R7C5

13. 45 rule on R89 2 outies R7C56 = 2 innies R89C9 + 3
13a. R7C56 = [53/85] = 8,13 -> R89C9 = 5,10 = [41/82/91], no 6,7 in R8C9

14. 5,8 in R7 only in R7C56789
14a. 45 rule on R7 5 remaining innies R7C56789 = 27 = {15678/23589}, R7C56 = [53/85] -> R7C789 = {167/289} = 14,19
14b. R7C78 = {16/17/28/29} = 7,8,10,11 -> R6C9 (step 6) = {5689}, no 7

15. 22(4) cage at R6C9 = {1489/1678/2578} (cannot be {4567} which doesn’t contain one of 1,2, cannot be {1579/2479/2569} which clash with R8C78), 8 locked for C9
15a. 1,4 of {1489} must be in R89C9 -> no 9 in R8C9
15b. 7 of {1678} must be in R7C9 -> no 6 in R7C9

Re-worked from here
16. R7C789 = {167/289} (step 14a)
16a. 22(4) cage at R6C9 = {1489/2578} (cannot be {1678} which clashes with R7C789, CCC), no 6
16b. R6C9 = {589} -> R7C78 (step 6) = 7,10,11 = {16/28/29} (step 14b), no 7

[Looks like I need to use the same step as the other walkthroughs used although it’s simpler here after my earlier work.]
17. 45 rule on R8 2 innies R8C69 = 1 outie R7C5 + 7
17a. R7C5 = {58} -> R8C69 = 12,15 = [84/78], no 9, 8 locked for R8

18. 4 in N8 only in 17(4) cage (step 9) = {1457/2348} -> R78C6 = [38/57]
18a. 45 rule on N2 3 innies R123C6 = 17 = {179/269/368/467} (cannot be {278} because no 2,7,8 in R3C6, cannot be {359} which clashes with R7C6, cannot be {458} which clashes with R78C6), no 5, clean-up: no 4 in R2C7, no 9 in R3C7

19. 35(7) cage at R3C6 (step 4c) = {125}[68][49]/{134}[95][67], 5 locked for D/, clean-up: no 3 in R1C8, no 6 in R2C9, no 2 in R8C1
19a. Killer pair 2,6 in 35(7) cage at R3C6 and R8C2, locked for D/, clean-up: no 6 in R1C8, no 9 in R2C9
19b. R3C89 (step 3) = {19/46} (cannot be {37} which clashes with R1C9), no 3,7
19c. Killer pair 6,9 in R3C6 and R3C89, locked for R3
19d. 3 in N3 only in R12C9, locked for C9
19e. 5 in C9 only in R456C9, locked for N6

20. R1C67 = {19/46}/[82] (cannot be [37] which clashes with R1C9), no 3,7
20a. R123C7 (step 8) = {178/259/268} (cannot be {169} because R3C7 only contains 5,8, cannot be {457} which clashes with R1C89), no 4, clean-up: no 6 in R1C6
20b. R3C7 = {58} -> no 5 in R2C7, clean-up: no 4 in R2C6
20c. 7 of {178} must be in R2C7 -> no 1 in R2C7, clean-up: no 8 in R2C6

[Then I had to do further re-work, in this case only step 21, because my original step 21 was flawed.]
21. R2C67 = [27/36/72], R2C89 = [74/83/92] -> combined cage R2C6789 = [2783/3674/3692/7283]
21a. R123C7 (step 20a) = {259/268} (cannot be {178} = [178] which clashes with R2C6789 = [2783], CCC), no 1,7, 2 locked for C7 and N3, clean-up: no 9 in R1C6, no 2 in R2C6, no 9 in R2C8
[Having found that, I saw that Afmob used the simpler
9 on D/ only in R2C8 + R9C1, CPE no 9 in R2C1
9 in N1 only in R1C123, locked for R1 ...]

22. R9C1 = 9 (hidden single in D/), R9C2 = 7, clean-up: no 6 in R1C3, no 2 in R2C3

23. 9 in N1 only in R1C23 = {49}, locked for R1 and N1, clean-up: no 1 in R1C6, no 6 in R1C7, no 5 in R2C23
23a. R1C67 = [82], R2C7 = 6, R2C6 = 3, R2C9 = 4, R2C8 = 7, R1C9 = 3, placed for D/, R1C8 = 5, R3C7 = 8, R3C6 = 6 (step 4a), R78C6 = [57], R7C34 = [49], R1C23 = [49], R7C5 = 8, R7C9 = 7, R8C9 = 8, R7C7 = 1, R9C9 = 2, both placed for D\, R6C9 = 5 (step 16a), R7C8 = 6, R9C78 = [53], R2C23 = [81]

24. Naked pair {23} in R7C12, locked for N7 -> R8C3 = 5, R8C12 = [16]

25. R5C5 = 5, naked pair {12} in R4C6 + R6C4, locked for N5

26. Naked pair {17} in R1C45, locked for R1 and N2, R2C4 = 5 (cage sum)

27. Naked triple {169} in R345C9, locked for 23(5) cage at R3C9
27a. R345C9 = {169} = 16 -> R5C78 = 7 = [34], R56C6 = [94], R6C5 = 6 (cage sum)

and the rest is naked singles.