SudokuSolver Forum

Hello everyone, here's my latest contribution, my first attempt at an "X" puzzle.

On the "How to Make a Killer" thread, here, http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=175 it was suggested that the extra diagonal constraint made for easier composition. I didn't find that to be true in this case! It took me a long time to get the level "just right".

Also sending out a personal request to anyone who posts a WT or other comments -- please use hidden text for any and all remarks regarding "human" ratings. This is MY puzzle, and I feel I have the right to ask this of everyone.
BTW I have V2 about finished, and will gladly post it when A166 is spoken for.

Assassin 165



code:
3x3:d:k:2048:5889:5122:5122:5636:7173:7173:4871:4616:5889:2048:2048:5122:5636:7173:4616:4616:4871:5889:5395:2836:5122:5636:7173:1560:3097:4871:5889:5395:3357:2836:5636:1560:1057:3097:4871:1828:5395:1830:3357:5636:1057:2090:3097:4140:1828:5166:1830:3376:5937:2866:2090:4660:4140:5166:5166:3376:2361:5937:1595:2866:4660:4660:5166:2880:4417:2361:5937:1595:5445:3398:4660:2880:4417:4417:4417:5937:5445:5445:5445:3398:


SS score: 1.28

Thanks Ronnie! I trust it's not too indiscreet a subjective rating to say it well deserves a place in the Assassin schedule: seems impossible to me at first (as often happens), then one notices ...

cheers

_________________
Joe

Thanks Ronnie for giving us A165!

Like Joe said, it takes some time to find the crucial moves. But once you've found them, this Killer is much easier than SudokuSolver suggests (which uses several Killer triples).

A165 Walkthrough:
1. D\/
a) Innies+Outies D/: 3 = R2C7 - R5C5 -> R2C7 <> 1,2,3 and R5C5 <> 7,8,9
b) Innies+Outies D\: -2 = R2C3 - R5C5 -> R5C5 <> 1,2 and R2C3 <> 5
c) Innies+Outies D/: 3 = R2C7 - R5C5: R2C7 <> 4,5
d) 1 locked in 8(3) @ D\ for N1
e) 8(3): R1C1+R2C2 <> 2 since R2C3 <> 1,5
f) Innies+Outies D/: 3 = R2C7 - R5C5 <> 3

2. C789
a) 16(2) = {79} locked for C9+N6
b) 8(2) <> 1
c) 4(2) = {13} -> CPE: R4C456+R5C78 <> 1,3
d) Innies+Outies C89: 6 = R2C7 - R8C9 -> R2C7 = (789); R8C9 = (123)

3. R6789 !
a) Hidden Killer pair (13) in Outies R6789 for R5
b) ! Outies R6789 = 6{149/239/347} <> 5 because (79) only possible @ R5C9
-> 6 locked for R5
c) 8(2) = {26} locked for C7+N6

4. D\/
a) Innies+Outies D\: -2 = R2C3 - R5C5: R2C3 <> 4
b) 8(3): R1C1+R2C2 <> 3 since R2C3 = (23)
c) 2,3 locked in both 11(2) @ D\ = {2389} locked for D\
d) 13(2) @ D\ = {67} -> R9C9 = 6, R8C8 = 7

5. C456+D/
a) 6 locked in 28(4) @ C6 for N2 -> 28(4) = {5689}; CPE: R1C45 <> 5,8,9
b) Hidden Single: R9C6 = 7 @ C6, R2C7 = 7 @ N3
c) 18(3) <> 1,4
d) 1 locked in 6(2) @ D/ = {15} -> R3C7 = 1, R4C6 = 5
e) R5C5 = 4
f) 6(2) @ N8 = {24} locked for C6+N8
g) 11(2) @ R6C6 = {38} locked for D\
h) 13(2) @ R4C3 = [49/67]

6. R123
a) 8(3) = {125} -> R2C3 = 2; 5 locked for N1
b) R3C3 = 9, R4C4 = 2
c) 28(4) = {5689} -> R1C7 = 5; 8,9 locked for C6+N2
d) R1C1 = 1, R2C2 = 5
e) 23(4) = {3479} -> R4C1 = 9; 3,4,7 locked for N1

7. C123
a) 7(2) @ C1 = {25} since {34} blocked by R2C1 = (34) -> R5C1 = 2, R6C1 = 5
b) 11(2) @ N7 = {38} locked for N7+D/
c) Killer pair (46) locked in R4C3 + 7(2) for C3
d) Innie C12 = R9C2 = 2
e) 17(4) = {1259} since R89C3 = {15} -> R9C4 = 9; 1 locked for C3+N7
f) R7C3 = 7, R6C4 = 6

8. N6
a) Hidden Single: R5C8 = 5
b) R4C7 = 3
c) 12(3) = [34/61]5

9. Rest is singles.

Make that 3/3. Well disguised breakthough. Took lots of hunting and as Joe also said, probably a very narrow solution. So, I came to the same key spot (Afmob's step 3c) but from the opposite direction. It only takes 6 of my (optimised) steps to get there but that leaves out the 60 before finding it! Thanks for a really good challenge Ronnie.

Partial Walk-through for A165

Cheers
Ed

This is a kind of "one-trick'pony" killer, hard to begin...

I have cracked it using a small move by contradiction, different to Afmob's and Ed's WT.I know that some of you prefer avoiding
this kind of step ; in fact I feel that the idea I have used is more difficult to explain in a direct way.

Thanks Ronnie for this challenging Assassin.



FIRST STEPS FOR SOLVING A 165

Well, Ed asked for this V2, so here you go!

Once again, I'll ask all posters to please use hidden text when discussing human ratings. Thanks for your cooperation!

Assassin 165 V2



code:
3x3:d:k:2816:5633:5634:5634:11524:4613:4613:4103:4360:5633:2816:2816:5634:11524:4613:4360:4360:4103:5633:5395:2068:5634:11524:4613:1304:3865:4103:5633:5395:3613:2068:11524:1304:2337:3865:4103:2596:5395:2854:3613:11524:2337:2858:3865:2860:2596:2862:2854:3632:11524:3890:2858:6452:2860:2862:2862:3632:2105:11524:2363:3890:6452:6452:2862:4160:4160:2105:11524:2363:4165:4165:6452:4160:3145:3145:3145:11524:3405:3405:3405:4165:



SS Score: 1.73

Notes: this is a killer X, no repeats on the diagonals.
Enjoy!!

Ronnie

Thanks for V2, Ronnie! It was really fun to solve!

Like V1 SudokuSolver overrates this Killer, I wonder why it chooses Killer triples and Hidden Killer pairs before easy CPE like in my step 2b.

A165 V2 Walkthrough:

1. R789 !
a) Outies N7 = 8(2+1) <> 7,8,9; R6C2+R9C4 = (12) since R6C4 >= 5
b) 11(4) = {1235} -> 3,5 locked for N7; CPE: R89C2 <> 1,2
c) Innies R9 = 20(3) <> 1,2
d) 16(3) @ N7 = {169/178/268} <> 4 -> R8C3 = (12)
e) ! 16(3) @ N7 = 8{17/26} since {169} blocked by Killer pair (69) of 14(2)
-> 8 locked for N7+D/
f) 14(2) = [59] -> R6C4 = 5, R7C3 = 9
g) 12(3) = 4{17/26} -> 4 locked for R9; R9C3 <> 1,2 because R9C4 = (12)

2. C1234 !
a) 11(2) <> 2; R5C3 <> 6
b) R78C1 <> 1,2 since it sees all 1,2 of N4
c) 11(4) = {1235} -> 3,5 locked for C1+N7; 1,2 locked for C2
d) 21(3) = 9{48/57} since {678} blocked by R8C2 = (678) -> 9 locked for C2
e) 3 locked in 11(2) @ N4 = {38} locked for C3+N4
f) 10(2) <> 2,7
g) ! 21(3) = {579} locked for C2 since {489} blocked by Killer pair (49) of 10(2)
h) 4 locked in 22(4) @ C4 for N2+22(4) -> 22(4) = 4{189/279/369/378/567}
i) 8(2) @ N8 <> 3
j) Killer pair (12) locked in 8(2) @ N8 + R9C4 for C4+N8
k) 4 locked in R456C1 @ N4 for C1

3. R789 !
a) 7 locked in R9C13 @ N7 for R9
b) Outies N9 = 24(2+1) -> R6C8+R9C6 = (789)
c) 13(3) = 3{19/28} since R9C6 = (89) -> 3 locked for R9+N9; R9C78 <> 8,9
d) Innies R9 = 20(3) = 5{69/78}: R9C1 <> 8 since 7 only possible there
e) Hidden Single: R8C2 = 8
f) 15(2): R6C6 <> 6
g) ! Outies N9 = 24(2+1) must have 7 since it cannot be {888} -> 7 locked for R6; CPE: R8C8 <> 7

4. C1234
a) Hidden Killer pair (34) in 11(3) + R1C2 for N1 since 11(3) cannot have both of them
-> R1C2 = (34), 11(3) <> 8
b) 8 locked in 22(4) @ C1 = 8{149/239/347} <> 6 since R1C2 = (34)
c) 14(2) = [59/68]
d) 22(4) @ C4 <> 1 because {1489} blocked by R5C4 = (89)
e) Innies+Outies N4: -3 = R3C2 - (R4C13+R6C2) -> R4C1 <> 7,9 since R4C3 >= 5
f) 22(4) @ C1: R23C1 <> 1,2 because R1C2+R4C1 = (1234)
g) Innies+Outies C12: 1 = R28C3 - R9C2: R9C1 = (46) -> R28C3 = 5/7(2) = [41/52/61] -> R2C3 = (456)
h) 11(3) must have one of (12) -> R1C1 = (12)
i) 1 locked in R1C1+R3C3 for D\

5. C789+D/ !
a) ! Innies+Outies D/: 7 = R2C7+R8C3 - R5C5: R5C5 = (234) and R2C7 = (789) since R8C3 <= 2 and R5C5 >= 2
b) Innies+Outies C89: 10 = R28C7 - R9C8: R8C7 <> 1,7,9 since R9C8 <= 3 and R2C7 >= 7
c) 16(3) = 2{59/68} -> 2 locked for R8+N9
d) R8C3 = 1 -> R9C1 = 7
e) 13(3) = {139} -> R9C6 = 9; 1 locked for R9+N9
f) 15(2) = {78} locked for D\; CPE: R6C7+R7C6 <> 7,8
g) 16(3) = {259} -> R9C9 = 5, R8C7 = 2, R8C8 = 9

6. C789+D\
a) 8(2) = {26} -> R4C4 = 6, R3C3 = 2
b) 11(3) = {146} -> R1C1 = 1, R2C2 = 4, R3C3 = 6
c) Innies+Outies C89: 8 = R2C7 - R9C8 -> R2C7 = 9, R9C8 = 1
d) 17(3) = {269} -> R2C8 = 2, R1C9 = 6
e) R5C5 = 3, R9C7 = 3
f) 11(2) @ C7 = [56/74]
g) Hidden Single: R5C6 = 1 @ R5 -> R4C7 = 8

7. Rest is singles.

You have made a really, really great puzzle with this V2 Ronnie !!; I have had much pleasure with it !

I guess my solving path is not the most simple, but I wanted to use some cloning cells.

Assassin A165 V2 Walkthrough

And now for the last of the three V1 Assassins in the A160 to A165 range that I got stuck on at the time.

I'm a bit surprised that nobody has mentioned the first key breakthrough step for A165, the CPE resulting from the 4(2) cage at R4C7 being a naked pair. That turned out to be the reason why I'd got stuck. Once I'd found the part of it that I'd missed before the rest of the puzzle was straightforward; I'd already found the 45 in step 14a but it wasn't much help without that CPE applying to R5C8. For that reason I felt that Afmob's step 2c was also worth a !


Here is my walkthrough for A165.

Prelims

a) 11(2) cage at R3C3 = {29/38/47/56}, no 1
b) 6(2) cage at R3C7 = {15/24}
c) 13(2) cage at R4C3 = {49/58/67}, no 1,2,3
d) 4(2) cage at R4C7 = {13}
e) R56C1 = {16/25/34}, no 7,8,9
f) R56C3 = {16/25/34}, no 7,8,9
g) R56C7 = {17/26/35}, no 4,8,9
h) R56C9 = {79}
h) 13(2) cage at R6C4 = {49/58/67}, no 1,2,3
i) 11(2) cage at R6C6 = {29/38/47/56}, no 1
j) R78C4 = {18/27/36/45}, no 9
k) R78C6 = {15/24}
l) 11(2) cage in N7 = {29/38/47/56}, no 1
m) 13(2) cage in N9 = {49/58/67}, no 1,2,3
n) 8(3) cage in N1 = {125/134}
o) R345C2 = {489/579/678}, no 1,2,3
p) 28(4) cage at R1C6 = {4789/5689}, no 1,2,3

1. Immediate follow-up steps
1a. 8(3) cage in N1 = {125/134}, 1 locked for N1
1b. Naked pair {13} in 4(2) cage at R4C7, CPE no 1,3 in R4C456 + R5C78 (see comment before step 14), clean-up: no 8 in R3C3, no 5 in R3C7, no 5,7 in R6C7
1c. Naked pair {79} in R56C9, locked for C9 and N6, clean-up: no 1 in R6C7, no 4,6 in R8C8
1d. 28(4) cage at R1C6 = {4789/5689}, CPE no 8,9 in R1C45
1e. R78C4 = {18/27/36} (cannot be {45} which clashes with R78C6, no 4,5
1f. 4,8 in N6 only in R456C8 + R4C9, CPE no 4,8 in R1C8

2. 45 rule on D\ 1 innie R5C5 = 1 outie R2C3 + 2, no 1,2,8,9 in R5C5
2a. 1 on D\ locked in R1C1 + R2C2, locked for N1, clean-up: no 3 in R5C5

3. 45 rule on D/ 1 outie R2C7 = 1 innie R5C5 + 3, R2C7 = {789}, no 7 in R5C5, clean-up: no 5 in R2C3 (step 2)

4. 8(3) cage in N1 = {125/134}
4a. 2 of {125} must be in R2C3 -> no 2 in R1C1 + R2C2

5. 45 rule on D\ 3 innies R1C1 + R2C2 + R5C5 = 10 = {136/145}
5a. 11(2) cage at R3C3 = {29/38/47} (cannot be {56} which clashes with R1C1 + R2C2 + R5C5), no 5,6
5b. 11(2) cage at R6C6 = {29/38/47} (cannot be {56} which clashes with R1C1 + R2C2 + R5C5), no 5,6
5c. Killer triple 2,3,4 in R1C1 + R2C2 + R5C5, 11(2) cage at R3C3 and 11(2) cage at R6C6, locked for D\, clean-up: no 9 in R8C8
5d. 6 on D\ locked in R5C5 + R9C9, CPE no 6 in R9C5
[I originally started step 5 with
2 on D\ locked in 11(2) cage at R3C3 or 11(2) cage at R6C6 -> one of these cages must be {29}, 9 locked for D\, clean-up: no 4 in R9C9
This uses locking cages which is a type of combined cage.]

6. 1 on D/ locked in R1C9 + R2C8 + R3C7, locked for N3

7. 45 rule on C12 1 outie R2C3 = 1 innie R9C2, R9C2 = {234}

8. 45 rule on C89 1 outie R2C7 = 1 innie R9C8 + 6, R9C8 = {123}

9. Killer triple 4,5,6 in 6(2) cage at R3C7, R5C5 and 13(2) cage at R6C4, locked for D/, clean-up: no 7 in 11(2) cage in N7

10. 45 rule on D/ 3 innies R1C9 + R2C8 + R5C5 = 15 = {159/168/249/267/348/357} (cannot be {258/456} which clash with 6(2) cage)
10a. 7,9 of {249/267} must be in R2C8 -> no 2 in R2C8

11. R345C8 = {138/147/156/246/345} (cannot be {129} which clashes with R456C7 ALS block, cannot be {237} which clashes with R56C7), no 9
11a. 8 of {138} must be in R5C8 -> no 8 in R34C8

12. 6(2) cage at R3C7 = {15/24}, 11(2) cage in N7 = {29/38} -> combined cage R3C7 + R4C6 + R8C2 + R9C1 = 17 = {1529/1538/2438}
12a. 13(2) cage at R6C4 = {49/67} (cannot be {58} which clashes with combined cage), no 5,8
12b. R1C9 + R2C8 + R5C5 (step 10) = {159/249/267/348} (cannot be {168/357} which clash with combined cage)
12c. 1 of {159} must be in R1C9 -> no 1 in R2C8

13. 5 on D/ only in R4C6 + R5C5, locked for N5, clean-up: no 8 in R4C3

[When I first did the CPE in step 1b, I only saw the more obvious R4C6 and R5C7 and overlooked that it also applied to R4C45 and R5C8. No 1,3 in R5C8 makes a big difference to the next step; without those eliminations this puzzle I think would be extremely difficult to solve.]
14. Hidden killer pair 1,3 in R5C13 and R5C6 for R5, R5C6 = {13} -> R5C13 must contain one of 1,3
14a. 45 rule on R6789 4 outies R5C1379 = 20 = {1469/2369} (cannot be {1379} because 7,9 only in R5C9, cannot be {2459/2567} which don’t contain 1 or 3, cannot be {3467} because the 7(2) cages in N4 cannot both be {34}), no 5 -> R5C9 = 9, R6C9 = 7, 6 locked in R5C137, locked for R5, clean-up: no 4 in R2C3 (step 2), no 9 in R2C7 (step 3), no 4,7 in R4C3, no 2 in R6C1, no 2 in R6C3, no 3 in R6C7, no 6 in R7C3, no 4 in R7C7

15. Naked pair {26} in R56C7, locked for C7 and N6, clean-up: no 4 in R4C6, no 9 in R6C6
15a. Killer pair 2,5 in R4C6 and R78C6, locked for C6, clean-up: no 9 in R7C7
15b. 5 in N6 only in R456C8 + R4C9, CPE no 5 in R1C8

16. 11(2) cage at R3C7 = {29} (hidden pair on D\), CPE no 2,9 in R3C4 + R4C3, clean-up: no 4 in R5C4

17. R345C8 (step 11) = {138/147/156/345} (cannot be {246} because 2,6 only in R3C8), no 2

18. R1C1 + R2C2 + R5C5 (step 5) = {145} (only remaining combination), locked for D\, clean-up: no 7 in R7C7, no 8 in 13(2) cage in N9
18a. R8C8 = 7, R9C9 = 6, clean-up: no 2 in R7C4

19. R6C4 = 6, R7C3 = 7 (hidden pair on D/), R56C7 = [62], clean-up: no 1 in R56C1, no 1 in R56C3, no 3 in R7C4, no 2,3 in R8C4
19a. R5C6 = 1 (hidden single in R5) R4C7 = 3, R7C7 = 8, R6C6 = 3, R78C4 = [18], R2C7 = 7, R5C5 = 4 (step 3), placed for both diagonals, R2C3 = 2 (step 2), R3C3 = 9, R4C4 = 2, R3C7 = 1, R4C6 = 5, R5C3 = 3, R6C3 = 4, R56C1 = [25], R1C1 = 1, R2C2 = 5, R4C3 = 6, R5C4 = 7, R1C3 = 8, R5C2 = 8, R5C8 = 5, clean-up: no 9 in R8C2, no 3 in R9C1

20. Naked pair {79} in R4C12, locked for R4 and N4 -> R4C5 = 8, R6C2 = 1, R6C5 = 9, R6C8 = 8

21. R2C7 = 7 -> R1C9 + R2C8 = 11 -> R1C9 = 2, R2C8 = 9, both placed for D/, R8C2 = 3, R9C1 = 8

22. Naked pair {24} in R78C6, locked for C6 and N8

23. R1C6 = 9 (hidden single in R1), R9C6 = 7
23a. Naked triple {356} in R789C5, locked for C5 and N8 -> R123C5 = [712], R9C4 = 9

24. R1C6 = 9, R23C6 = {68} = 14 -> R1C7 = 5 (cage sum), R89C7 = [94], R9C2 = 2

25. R9C6 = 7, R89C7 = [94] = 13 -> R9C8 = 1 (cage sum), R4C8 = 4, R3C8 = 3 (step 17), R1C8 = 6, R1C2 = 4

26. R5C2 = 8 -> R34C2 = 13 = [67]

and the rest is naked singles.

After eventually finishing A165, I had a go at the V2 and was pleasantly surprised by it. Thanks Ronnie for a nice variant.

Even ignoring the problem I had with the V1, I feel that V2 is a bit easier; I've said a bit more about that in the rating comment, for those who want to read it.


Here is my walkthrough for A165 V2.

Prelims

a) 8(2) cage at R3C3 = {17/26/35}, no 4,8,9
b) 5(2) cage at R3C7 = {14/23}
c) 14(2) cage at R4C3 = {59/68}
d) 9(2) cage at R4C7 = {18/27/36/45}, no 9
e) R56C1 = {19/28/37/46}, no 5
f) R56C3 = {29/38/47/56}, no 1
g) R56C7 = {29/38/47/56}, no 1
h) R56C9 = {29/38/47/56}, no 1
i) 14(2) cage at R6C4 = {59/68}
j) 15(2) cage at R6C6 = {69/78}
k) R78C4 = {17/26/35}, no 4,8,9
l) R78C6 = {18/27/36/45}, no 9
m) 11(3) cage in N1 = {128/137/146/236/245}, no 9
n) 21(3) cage at R3C2 = {489/579/678}, no 1,2,3
o) 11(4) cage at R6C2 = {1235}, CPE no 1,2,3,5 in R89C2

1. 45 rule on R9 3 innies R9C159 = 20 = {389/479/569/578}, no 1,2

2. 45 rule on N7 1 innie R7C3 = 2 outies R6C2 + R9C4 + 6
2a. Min R6C2 + R9C4 = 2 -> min R7C3 = 8, clean-up: no 8,9 in R6C4
2b. Max R6C2 + R9C4 = 3 -> R6C2 + R9C4 = {11/12}
2c. 3,5 of 11(4) cage at R6C2 only in R7C12 + R8C1, locked for N7

3. 16(3) cage in N7 = {169/178/268}, no 4
3a. 1,2 only in R8C3 -> R8C3 = {12}
3b. 16(3) cage in N7 = {178/268} (cannot be {169} which clashes on D/ with 14(2) cage at R6C4), no 9, 8 locked in R8C2 + R9C1, locked for N7 and D/
3c. Naked quad {1235} in R7C12 + R8C13, locked for N7
3d. 4 in N7 only in R9C23, locked for R9
3e. 4 in C4 only in R123C4, locked for N2 and 22(4) cage at R1C3, no 4 in R1C3

4. R7C3 = 9, R6C4 = 5, both placed for D/, clean-up: no 3 in R3C3, no 4 in R4C7, no 2,6 in R5C3, no 6 in R5C7, no 6 in R5C9, no 2 in R6C3, no 6 in R6C6, no 3 in R78C4
4a. Killer pair 1,2 in R78C4 and R9C4, locked for C4 and N8, clean-up: no 6,7 in R3C3, no 7,8 in R78C6

5. 45 rule on D/ 2 outies R2C7 + R8C3 = 1 innie R5C5 + 7
5a. Max R2C7 + R8C3 = 11 -> max R5C5 = 4
5b. Min R2C7 + R8C3 = 8 -> min R2C7 = 6

6. 21(3) cage at R3C2 = {489/579} (cannot be {678} which clashes with R8C2), no 6, 9 locked for C2

7. 1,2 in N4 only in R456C1 + R6C2, CPE no 1,2 in R78C1
7a. Naked pair {35} in R78C1, locked for C1 and N7, clean-up: no 7 in R56C1
7b. Naked pair {12} in R67C2, locked for C2

8. 3 in N4 only in R56C3 = {38}, locked for C3 and N4, clean-up: no 2 in R56C1, no 6 in R5C4
8a. 21(3) cage at R3C2 (step 6) = {489/579}
8b. 8 of {489} only in R3C2 -> no 4 in R3C2

9. 45 rule on N9 3(2+1) outies R6C68 + R9C6 = 24
9a. Max R6C68 = 17 -> min R9C6 = 7
9b. Max R69C6 = 17 -> min R6C8 = 7

10. 13(3) cage at R9C6 = {139/157/238} (cannot be {256} because R9C6 only contains 7,8,9), no 6
10a. R9C6 = {789} -> no 7,8,9 in R9C78
10b. R9C159 (step 1) = {389/569/578}
10c. 6 of {569} must be in R9C1 -> no 6 in R9C59
10d. 6 in R9 only in R9C123, locked for N7
10e. Killer pair 7,8 in 21(3) cage at R3C2 and R8C2, locked for C2

11. 45 rule on D\ 2 outies R2C3 + R8C7 = 1 innie R5C5 + 5
11a. Max R5C5 = 4 -> max R2C3 + R8C7 = 9, no 9 in R8C7

12. 22(4) cage at R1C3 must contain 4 = {2479/3469/3478} (cannot be {1489} which clashes with R5C4, cannot be {4567} which clashes with R78C4), no 1,5
12a. 6 of {3469} must be in R1C3 -> no 6 in R123C4

13. 45 rule on C12 2 outies R28C3 = 1 innie R9C2 + 1
13a. Min R9C2 = 4 -> min R28C3 = 5, no 1,2 in R2C3
13b. Max R9C2 = 6 -> max R28C3 = 7, no 7 in R2C3

14. 11(3) cage in N1 = {146/236/245} (cannot be {128/137} because 1,2,7 only in R1C1), no 7,8
14a. 1,2 only in R1C1 -> R1C1 = {12}
14b. 3 of {236} must be in R2C2 -> no 6 in R2C2

15. Hidden killer pair 1,2 in R13C3 and R8C3 for C3 -> R13C3 must contain one of 1,2
15a. Killer pair 1,2 in R1C1 and R13C3, locked for N1

16. 1 in N1 only in R1C1 + R3C3, locked for D\
16a. R2C7 + R8C3 = R5C5 + 7 (step 5)
16b. Min R5C5 = 2 -> min R2C7 + R8C3 = 9, no 6 in R2C7
16c. R2C3 + R8C7 = R5C5 + 5 (step 11)
16d. Max R5C5 = 4 -> max R2C3 + R8C7 = 9, min R2C3 = 4 -> max R8C7 = 5

17. 16(3) cage in N9 = {169/178/259/349/367/457} (cannot be {268} which clashes on D\ with 15(2) cage at R6C6, cannot be {358} which clashes with 13(3) cage at R9C6)
17a. Killer pair 7,9 in 15(2) cage at R6C6 and R8C8 + R9C9, locked for D\, clean-up: no 1 in R3C3

18. R1C1 = 1 (hidden single in N1), clean-up: no 9 in R56C1
18a. 11(3) cage in N1 (step 14) = {146} (only remaining combination) -> R2C3 = 6, R2C2 = 4, placed for D\, R4C3 = 5, R5C4 = 9, R45C2 = [97], R3C2 = 5 (step 8a),
R3C3 = 2, R4C4 = 6, both placed for D\, R5C5 = 3, placed for both diagonals, R8C23 = [81], R9C2 = 6, R9C1 = 7, placed for D/, clean-up: no 2 in R4C6, no 2,3 in R4C7, no 4 in R5C6, no 2,4,8 in R6C7, no 2,4,8 in R6C9, no 2,7 in R7C4, no 2 in R8C4

19. R78C4 = [17], R9C4 = 2
19a. R4C1 = 2 (hidden single in C1)

20. Naked pair {14} in 5(2) cage at R3C7, locked for D/ -> R2C8 = 2, R1C9 = 6, R2C7 = 9 (cage sum), clean-up: no 2 in R5C7, no 5 in R5C9

21. R8C7 = 2 (hidden single in C7), R8C8 + R9C9 = 14 = {59}, locked for N9

22. Naked pair {13} in R9C78, locked for N9, R9C6 = 9 (step 10), R8C9 = 4, R9C9 = 5, R8C8 = 9, clean-up: no 7 in R6C9

23. 3 in N8 only in R78C6 = {36}, locked for C6 and N8 -> R8C5 = 5

and the rest is naked singles.