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Hi,

this is a classical assassin for this week. Everything should go easily. Enjoy !

ASSASSIN 164




3x3::k:4352:4097:4097:2819:2819:2819:4358:4358:3848:4352:4352:4097:3852:3853:3853:5135:4358:3848:3090:3090:3852:3852:3853:5135:5135:3609:3848:3090:5148:7453:5406:5406:4384:3609:3609:4643:5148:5148:7453:7453:5406:4384:4384:4643:4643:5148:3374:3374:7453:5406:5406:4384:4643:4661:4918:3374:2360:2360:3386:4923:4923:4661:4661:4918:2624:2360:3386:3386:4923:3397:4166:4166:4918:2624:2624:4683:4683:4683:3397:3397:4166:


Solution :


SSscore : 1.28

Thanks for A164, manu! I liked that this one offered lots of IOD moves. After going through JSudoku's and SudokuSolver's log I noticed that Hidden Killer pairs are the means to crack this Killer but the good thing is that there are several ways to do this, as you can see in my wt.

A164 Walkthrough:

1. R789
a) Innies+Outies N7: -7 = R7C4 - R7C2 -> R7C4 = (12), R7C2 = (89)
b) Innies+Outies N8: 5 = R7C7 - R7C4 -> R7C7 = (67)
c) Innies+Outies N9: 2 = R6C9 - R7C7 -> R6C9 = (89)
d) 19(3) @ R7C6: R78C6 <> 2,6,7 since R7C7 = (67)
e) 13(3) @ N9: R6C23 = (1234) since R7C2 = (89)

2. R123
a) Innies+Outies N3: 7 = R3C6 - R3C8 -> R3C6 = (89), R3C8 = (12)
b) Innies+Outies N2: -4 = R3C3 - R3C6 -> R3C3 = (45)
c) Innies+Outies N1: R4C1 = R3C3 = (45)

3. N245 !
a) Killer pair (89) locked in R3C6 + 19(3) for C6
b) Hidden Killer pair (89) in 29(4) for N5 since 21(5) can only have one of (89)
c) Hidden Killer pair (89) in 20(4) for N4 since R45C3 @ 29(4) can only have one of (89)
d) 6 locked in 20(4) @ N4 = {1469/1568/2369/2468} <> 7
e) 7 locked in 29(4) @ N4 for C3+29(4)
f) Hidden Killer pair (89) in 29(4) for N4 since 20(4) can only have one of (89)
-> Each of R45C3 and R56C4 must have one of (89)
g) Hidden Killer pair (89) in 21(5) for N5 because R56C4 can only have one of (89)
-> 21(5) = 12{369/378/468} <> 5 since 145{29/38} blocked by R56C3 = (589); 1,2 locked for N5
h) From step e): 5 locked in R56C4 for C4+N5+29(4)

4. C456
a) 1,2 locked in Innies C6789 = 13(4) = 12{37/46}
b) 5 locked in 19(3) @ C6 for N8 -> 19(3) = {568} -> R7C7 = 6; 8 locked for C6+N8
c) Innie N8 = R7C4 = 1
d) R3C6 = 9
e) Outie N2 = 5
f) 9(3) = {126} -> R7C3 = 2, R8C3 = 6
g) 13(3) = {247} locked for N8; 2 also locked for R8

5. C123
a) Innie N7 = R7C2 = 8
b) Outie N1 = R4C1 = 5
c) 19(3) = {379} locked for C1+N7
d) 12(3) = [16/43/61]5

6. C789
a) Innie N3 = R3C8 = 2
b) R7C6 = 5
c) 18(3) = {378} -> R6C9 = 8; 3,7 locked for R7+N9
d) 16(3) = {259} -> R9C9 = 2; 5,9 locked for R8+N9
e) 14(3) = {239} -> 3,9 locked for R4+N6
f) 18(4) = {1467} locked for N6
g) 15(3) = {456} locked for C9+N3 since 5{19/37} blocked by R7C9 = (37) and R8C9 = (59)
h) 20(3) = {389} -> 3,8 locked for C7+N3
i) R4C7 = 9, R4C8 = 3, R7C8 = 7
j) Hidden Single: R1C7 = 7 @ C7, R2C2 = 7 @ N1

7. R123
a) Killer pair (46) locked in 12(3) + R3C9 for R3
b) 15(3) @ N2: R2C4 = (23)
c) 17(3) @ N1 = {278} since {467} blocked by Killer pair (46) of 12(3)
-> 2,8 locked for C1+N1
d) 11(3) <> 8 since {128} blocked by R1C1 = (28)
e) Hidden Single: R1C1 = 8 @ R1
f) R2C1 = 2, R2C4 = 3 -> R3C4 = 7

8. N56
a) Hidden Single: R8C5 = 7 @ N8, R6C6 = 7 @ R6
b) 17(4) = {2456} -> 4,6 locked for C4+N5
c) R2C6 = 1, R3C5 = 8 -> R2C5 = 6

9. Rest is singles.

Rating: Hard 1.0. I used some Hidden Killer pairs.

Thanks manu for a really challenging Assassin. This is a short way to get to the cracker (step 9a). I was stuck for quite a while and did all sorts of other contortions first so this is the optimised way.

Part WT for A164
[10 steps]Please let me know of any corrections or things that could be clearer.
Prelims
i. 11(3)n2: no 9
ii. 20(3)n3: no 1,2
iii. 29(4)n4 = {5789}
iv. 19(3)n7: no 1
v. 9(3)n7: no 7,8,9
vi. 19(3)n8: no 1
vii. 10(3)n7: no 8,9

1. "45" n3: 1 outie r3c6 - 7 = 1 innie r3c8
1a. r3c6 = (89)
1b. r3c8 = (12)

2. "45" n12: 1 outie r4c1 + 4 = r3c6
2a. r4c1 = (45)

3. "45" n7: 1 outie r7c4 + 7 = r7c2
3a. r7c4 = (12)
3b. r7c2 = (89)

4. r7c2 = (89) -> r6c23 = 4 or 5 (no 5..9)

5. 6 in n4 is only in 20(4) -> other 3 cells = 14 -> have at most one of 7/8/9
5a. hidden killer triple -> r45c3 must have two of 7/8/9 (no 5)

6. 5 must be in 29(4)n4 at r56c4: 5 locked for c4 & n5

7. "45" n8: 1 outie r7c7 - 5 = 1 innie r7c4
7a. r7c7 = (67)

8. r7c7 = (67) -> r78c6 = 12 or 13 -> no 2 or 6 in r78c6 (r78c6 can't be {66}; can't be {67} because of r7c7)

9. "45" c789: 5 outies r34578c6 = 32 (no 1)
9a. {26789} blocked since r78c6 must total 12 or 13 (step 8) which could only be {67} but no 6 is available
9b. h32(5) = {35789/45689}(no 2)
9c. 5, 8 and 9 locked for c6

10. 5 in c6 only in r78c6: 5 locked for n8 and 19(3) = {568} only
10a. r7c7 = 6
10b. r78c6 = {58}: both locked for c6 & n8

It's cracked.

Cheers
Ed

Thanks Afmob and Ed for yours nice wts, and Ronnie G for being volunteer for the next Assassin .... You can try now this V1.5, a bit more difficult. I should (may be) say "V1.5" since both solution and cage pattern have been slightly reworked , so this puzzle could be quite different from the previous V1.

ASSASSIN 164 V1.5




3x3::k:2816:2305:2305:5123:5123:5123:3078:3078:3592:2816:2816:4363:4363:3597:3597:2575:3078:3592:4626:4626:4363:4363:3597:2575:2575:4377:2842:4626:4892:3613:4638:4638:7456:4377:4377:2842:4892:4892:3613:3613:4638:7456:7456:4651:4651:3373:3118:3118:3613:4638:4638:7456:4651:1589:3373:3118:5432:5432:4410:4923:4923:1589:1589:1343:4160:5432:4410:4410:4923:4923:4934:4934:1343:4160:4160:4683:4683:4683:2126:2126:4934:




SSScore : 1.60

Thanks for a different version, manu!

To be honest, this one was easier than V1. SudokuSolver missed my step 3a and thereby made this Killer look harder than it really is.

A164 V1.5 Walkthrough:

1. N5
a) 9 locked in R45C6 @ N5 for C6+29(4)
b) 18(5) = 12{348/357/456} -> 1,2 locked for N5
c) Outies N5 = 16(2+2): R45C3 = 1{2/3} since R56C7 >= 12 -> 1 locked for C3+N4;
R56C7 <= 13 = 5{7/8} -> 5 locked for C7+N6+29(4)
d) 14(4) <> 7 since {1247} blocked by Killer pair (47) of 18(5)

2. R789
a) Innies R789 = 12(4) = 12{36/45} -> 1,2 locked for R7
b) Innies N8 = 10(3) <> 7,8,9 since (12) only possible @ R8C6 -> R8C6 = (12); R7C6 <> 6 because R7C4 >= 4

3. C789 !
a) ! Innies+Outies N36: 21 = R345C6 - R6C9 -> R3C6 <> 1,2,3,4
b) ! Innies+Outies N3: -9 = R3C6 - R3C89 -> R3C89 <> 9 (IOU @ R3)
c) ! 12(3) <> 8,9 since 1{29/38} blocked by Killer pairs (12,13) of 10(3)
d) 9 locked in 14(2) @ N3 = {59} locked for C9+N3
e) 10(3) <> 7 since {127} blocked by Killer pair (12) of 12(3)
f) Innies+Outies N36: 21 = R345C6 - R6C9: R6C9 <> 3 since R3C6 <= 6
g) 6(3) = {123} -> 3 locked for R7+N9

4. R789
a) 3 locked in Innies R789@ R7 = 12(4) = {1236} -> R7C1 = 6
b) Cage sum: R6C1 = 7
c) 8(2) <> 5
d) 5 locked in 19(3) @ N9 = {568} -> R8C8 = 5; 6,8 locked for C9+N9
e) 8(2) = {17} locked for R9+N9
f) 19(4) = {1459} -> R8C6 = 1, R7C6 = 5; 4,9 locked for C7
g) R7C4 = 4
h) 18(3) = {369} locked for R9+N8
i) 5(2) = {23} -> R9C1 = 2, R8C1 = 3

5. R123
a) 10(3) = {136} -> R3C6 = 6; 1,3 locked for C7+N3
b) 12(3) = {246} locked for N3; 4 also locked for C8
c) R3C9 = 7 -> R4C9 = 4
d) Outie N12 = R4C1 = 5
e) 18(3) = {459} -> 4,9 locked for R3+N1
f) 11(3) = {128} since R12C1 = (18) -> R2C2 = 2; 1,8 locked for C1+N1
g) 9(2) = {36} locked for R1+N1
h) R3C3 = 5, R2C3 = 7
i) 17(4) = {2357} -> R2C4 = 3, R3C4 = 2

6. N234
a) 19(3) = {469} locked for N4; 6 also locked for C2; 4 also locked for R5
b) R1C7 = 2, R1C8 = 4
c) 20(3) = {578} locked for R1+N2

7. Rest is singles.

Rating: 1.0 - Hard 1.0. I used IOU and IOD of large size.

I'll agree with that. I haven't yet finished A164 but managed to finish the "V1.5" is one evening, which had a 2 hour break to watch TV; that's faster than I manage to solve most Assassins.


Here is my walkthrough for A164 "V1.5". As soon as I started looking at Afmob's walkthrough I realised that I'd missed one of the prelims so I haven't looked at the rest of it. That sort of thing can happen when one does one's own prelims but, even so, I'm happy to continue solving using an Excel worksheet. I haven't time at the moment to re-work my walkthrough so I'm posting it as I did it; I'll be watching the Saturday and Sunday stages of the Tour de France and also the Hungarian GP before I have time to re-work it.

Edit. I've had another look at my walkthrough, see comment after Prelims. Then I went through Afmob's walkthrough, which has a very different solving path than mine.

Prelims

a) R1C23 = {18/27/36/45}, no 9
b) R12C9 = {59/68}
c) R34C9 = {29/38/47/56} (cannot be {56} which clashes with R12C9), no 1,5,6
d) R67C1 = {49/58/67}, no 1,2,3
e) R89C1 = {14/23}
f) R9C78 = {17/26/35}, no 4,8,9
g) 11(3) cage in N1 = {128/137/146/236/245}, no 9
h) R1C456 = {389/479/569/578}, no 1,2
i) 10(3) cage at R2C7 = {127/136/145/235}, no 8,9
j) 19(3) cage in N4 = {289/379/469/478/568}, no 1
k) 6(3) cage at R6C9 = {123}, CPE no 1,2,3 in R89C9
l) 21(3) cage at R7C3 = {489/579/678}, no 1,2,3
m) 19(3) cage in N9 = {289/379/469/478/568}, no 1
n) 14(4) cage at R4C3 = {1238/1247/1256/1346/2345}, no 9
o) 29(4) cage at R4C6 = {5789}
[I missed 18(5) cage in N5 = {12348/12357/12456}, no 9, 1,2 locked for N5. However apart for locking 9 in R45C6 it doesn’t seem to make much difference to my walkthrough so I haven’t re-worked it.]

1. Killer triple 1,2,3 in R7C89 and R9C78, locked for N9

2. 45 rule on N89 1 innie R7C4 = 1 outie R6C9 + 3 -> R7C4 = {456}
2a. 21(3) cage at R7C3 = {489/579/678}
2b. R7C4 = {456} -> no 4,5,6 in R78C3

3. 45 rule on N12 1 innie R3C6 = 1 outie R4C1 + 1, no 1 in R3C6, no 7,8,9 in R4C1

4. 45 rule on N36 3 outies R345C6 = 1 innie R6C9 + 21
4a. R6C9 = {123} -> R345C6 = 22,23,24 = {589/679/689/789} -> R3C6 = {567}, R45C6 = {79/89}, no 5, 9 locked for C6, N5 and 29(4) cage at R4C6, clean-up: no 1,2,3 in R4C1 (step 3)
4b. 5 in 29(4) cage at R4C6 locked in R56C7, locked for C7 and N6, clean-up: no 3 in R9C8

5. 10(3) cage at R2C7 = {127/136/145/235}
5a. R3C6 = {567} -> no 6,7 in R23C7

6. 45 rule on N8 3 innies R7C4 + R78C6 = 10 = {136/145/235} (cannot be {127} because R7C6 only contains 4,5,6), no 7,8
6a. 6 of {136} must be in R7C4 -> no 6 in R78C6

7. 45 rule on R123 2 innies R3C89 = 1 outie R4C1 + 10
7a. Min R4C1 = 4 -> min R3C89 = 14, no 1,2,3,4 in R3C89, clean-up: no 7,8,9 in R4C9

8. 45 rule on N2 3 innies R23C4 + R3C6 = 11 = {137/146/236/245} (cannot be {128} because R3C6 only contains 5,6,7), no 8,9
8a. R3C6 = {567} -> no 5,6,7 in R23C4

9. 45 rule on N2 2 outies R23C3 = 1 innie R3C6 + 6
9a. Min R3C6 = 5 -> min R23C3 = 11, no 1 in R23C3

10. 45 rule on N9 2 innies R78C7 = 1 outie R6C9 + 12
10a. R6C9 = {123} -> R78C7 = 13,14,15 = {49/68/69} (cannot be {67} which clashes with 19(3) cage, cannot be {78} which clashes with R56C7, ALS block), no 7

11. 19(3) cage in N9 = {478/568} (cannot be {469} which clashes with R78C7), no 9, 8 locked for N9
11a. 9 in N9 locked in R78C7, locked for C7

12. 9 locked in R78C7 for 19(4) cage at R7C7 = 9{136/145} (cannot be 9{235} because R78C7 only contain 4,6,9), no 2, 1 locked in R78C6, locked for C6 and N8
12a. 4 of 9{145} must be in R78C7 -> no 4 in R78C6

13. R7C4 + R78C6 (step 6) = {136/145}
13a. 4,6 only in R7C4 -> R7C4 = {46}, clean-up: no 2 in R6C9 (step 2)
13b. 21(3) cage at R7C3 = {489/678} (only remaining combinations), 8 locked in R78C3, locked for C3 and N7, clean-up: no 1 in R1C2, no 5 in R6C1

14. 2 in 6(3) cage at R6C9 locked in R6C89, locked for R6 and N9, clean-up: no 6 in R9C78

15. 45 rule on R789 2 innies R7C12 = 1 outie R6C9 + 6
15a. Max R6C9 = 3 -> max R7C12 = 9, no 7,9 in R7C1, no 6,7,9 in R7C2, clean-up: no 4,6 in R6C1

16. R7C35 = {78} (hidden pair in R7), R7C7 = 9 (hidden single in R7)

17. 45 rule on N7 2 innies R7C12 = 1 outie R7C4 + 3, IOU no 3 in R7C2

18. 45 rule on N3 2 innie R3C89 = 1 outie R3C6 + 9, IOU no 9 in R3C89, clean-up: no 2 in R4C9
[Steps 17 and 18 are better than steps 7 and 15 because they give the same results plus IOUs. However I didn’t spot the IOU steps until now.]

19. R7C12 = R7C4 + 3 (step 17), R7C4 = {46} -> R7C12 = 7,9 = {16/45} (only remaining combinations)
19a. R89C9 = {23} (cannot be {14} which clashes with R7C12), locked for C9 and N9

20. 17(3) cage in N8 = {278/368/458} (cannot be {269/359} because R7C5 only contains 7,8, cannot be {467} which clashes with R7C4), no 9, 8 locked for N8
20a. 9 in N8 locked in R9C456, locked for R9

21. R9C9 = 8 (hidden single in R9), R3C9 = 7, R4C9 = 4, clean-up: no 6 in R12C9
21a. Naked pair {59} in R12C9, locked for C9 and N3 -> R8C9 = 6, R8C8 = 5 (step 11), R8C7 = 4, clean-up: no 3 in R9C7
[At this stage I noticed R3C6 = {56}, R4C1 = {56}, R3C6 = R4C1 + 1 (step 3)… However the placements for R3C6 and R4C1 came slightly more easily in step 22.]

22. 19(4) cage at R7C7 (step 12) = 9{145} (only remaining combination) -> R78C6 = [51], R3C6 = 6, R3C8 = 8, R4C1 = 5 (step 3), clean-up: no 8 in R6C1
22a. R3C6 = 6 -> R23C7 = 4 = {13}, locked for C7 and N3 -> R9C78 = [71]
22b. Naked pair {23} in R7C89, locked for 6(3) cage at R6C9 -> R6C9 = 1

23. Naked pair {46} in R7C14, locked for R7 -> R7C2 = 1, R7C1 = 6 (step 19), R6C1 = 7, R7C4 = 4
23a. 21(3) cage at R7C3 (step 13b) = {489} (only remaining combination) -> R78C3 = [89], R8C2 = 7, R7C5 = 7, clean-up: no 2 in R1C3
23b. 17(3) cage in N8 (step 20) = {278} (only remaining combination) -> R8C45 = {28}, locked for R8 and N8 -> R89C1 = [32], R9C6 = 3

24. R3C8 = 8 -> R4C78 = 9 = [27/63]
24a. Killer pair 2,3 in R4C78 and R5C9, locked for N6

25. Naked pair {58} in R56C7, locked for 29(4) cage at R4C6 -> R45C6 = {79}, locked for C6 and N5

26. 45 rule on N5 2 remaining innies R56C4 = 11 = {38/56}, no 1,2
26a. 45 rule on N5 2 remaining outies R45C3 = 3 = {12}, locked for C3 and N4, clean-up: no 8 in R1C2

27. R4C1 = 5 -> R3C12 = 13 = {49} (only remaining combination), locked for R3 and N1, clean-up: no 5 in R1C23
27a. Naked pair {18} in R12C1, locked for C1 and N1, R2C2 = 2 (cage sum), clean-up: no 7 in R1C3
27b. Naked pair {36} in R1C23, locked for R1 and N1

28. R7C2 = 1 -> R6C23 = 11 = [83], clean-up: no 3,8 in R5C4 (step 26)

29. R23C3 = [75] = 12 -> R23C4 = 5 = [32]

30. R1C78 = [24], R12C6 = [84], R12C1 = [18]
30a. 45 rule on R1 1 remaining innie R1C9 = 9

and the rest is naked singles.

Thanks manu! You are right, it should go easily but I got stuck; with hindsight I don't know why I found it hard to spot the steps I found after I came back to A164 this week.


While working on this puzzle I spotted several hidden killer pairs but didn't use any of them.

Here is my walkthrough for A164. I've given comments about where I got stuck and about simplifications that I made after I got started again. Thanks Afmob for suggesting a couple of detail changes (step 15 moved to become step 13c and the end of step 31 corrected).

Prelims

a) R1C456 = {128/137/146/236/245}, no 9
b) 20(3) cage at R2C7 = {389/479/569/578}, no 1,2
c) R789C1 = {289/379/469/478/568}, no 1
d) 9(3) cage at R7C3 = {126/135/234}, no 7,8,9
e) 10(3) cage in N7 = {127/136/145/235}, no 8,9
f) 19(3) cage at R7C6 = {289/379/469/478/568}, no 1
g) 29(4) cage at R4C3 = {5789}

1. 45 rule on N3 1 outie R3C6 = 1 innie R3C8 + 7, R3C6 = {89}, R3C8 = {12}
1a. Max R3C8 = 2 -> min R4C78 = 12, no 1,2 in R4C78

2. 45 rule on N2 1 innie R3C6 = 1 outie R3C3 + 4, R3C3 = {45}

3. 45 rule on N1 1 outie R4C1 = 1 innie R3C3, R4C1 = {45}

4. 45 rule on N7 1 innie R7C2 = 1 outie R7C4 + 7, R7C2 = {89}, R7C4 = {12}
4a. R789C1 = {379/469/478/568} (cannot be {289} which clashes with R7C2), no 2
4b. Min R7C2 = 8 -> max R6C23 = 5, no 5,6,7,8,9 in R6C23

5. 45 rule on N8 1 outie R7C7 = 1 innie R7C4 + 5, R7C7 = {67}
5a. 19(3) cage at R7C6 = {379/469/478/568} (cannot be {289} because R7C7 only contains 6,7), no 2
5b. R7C7 = {67} -> no 6,7 in R78C6
5c. Killer pair 8,9 in R3C6 and R78C6, locked for C6

6. 45 rule on N8 3 innies R7C4 + R78C6 = 14 = {149/158/239/248}
6a. R9C456 = {279/369/378/468/567} (cannot be {189/459} which clash with R7C4 + R78C6), no 1

7. 45 rule on N9 1 outie R6C9 = 1 innie R7C7 + 2, R6C9 = {89}

8. 45 rule on N4 3 innies R4C1 + R45C3 = 1 outie R7C2 + 12
8a. R7C2 = {89} -> R4C1 + R45C3 = 20,21 = {479/489/578/579}
8b. R4C1 = {45} -> no 5 in R45C3
8c. 5 in 29(4) cage at R4C3 locked in R56C4, locked for C4 and N5

9. 45 rule on N6 3 innies R56C7 + R6C9 = 1 outie R3C8 + 13
9a. Max R3C8 = 2 -> max R56C7 + R6C9 = 15, min R6C9 = 8 -> max R56C7 = 7, no 7,8,9 in R56C7

10. 45 rule on N2 3 innies R23C4 + R3C6 = 19 = {289/379/469/478/568}, no 1

11. 21(5) cage in N5 = {12369/12378/12468/13467}, 1 locked for N5

12. 45 rule on N1 3 innies R3C123 = 12 = {147/156/246/345} (cannot be {129/138/237} because R3C3 only contains 4,5), no 8,9 in R3C12

[When I first reached this stage my next step was
45 rule on N9 3 innies R7C789 = 16 = {178/367/457} (cannot be {169/268} which clash with R7C24 = [81/92], cannot be {259/349/358} because R7C7 only contains 6,7), no 2, 7 locked for R7 and N9.
However I felt that I wanted to find an easier way. Then I got stuck for a while.]

13. 45 rule on N5 4 innies R56C4 + R45C6 = 24
13a. R56C4 = {57/58/59} = 12,13,14 -> R45C6 = 10,11,12 = {37/46/47} (cannot total 12), no 2
13b. R45C6 = 10,11 -> R56C4 = 13,14 = {58/59}, no 7
13c. 7 in 29(4) cage at R4C3 locked in R45C3, locked for C3 and N4
[My first step here, when I looked at this Assassin again, was combination analysis for 17(4) cage at R4C6, looking at the available combination pairs for R45C6 and R56C7. Then I realised that it was simpler to use innies for N5 first.]

14. 17(4) cage at R4C6 = {1367/1457/2357/2456}
14a. R45C6 must contain 3 or 4 (step 13a) -> no 3,4 in R56C7
14b. R56C7 = {15/16/25}

15. Moved to become step 13c.

16. 1,2 in C6 locked in R1269C6
16a. 45 rule on C6789 4 innies R1269C6 = 13 = {1237/1246}, no 5
16b. Killer pair 3,4 in R1269C6 and R45C6, locked for C6
[Using the killer pair wasn’t needed but since I spotted it I included it.]

17. 5 in C6 locked in R78C6, locked for N8
17a. 19(3) cage at R7C6 = {568} (only remaining combination) -> R7C7 = 6, R78C6 = {58}, locked for C6 and N8 -> R7C4 = 1 (step 5), R7C2 = 8 (step 4), R78C6 = [58], R6C9 = 8 (step 7), R3C6 = 9, R3C8 = 2 (step 1), R3C3 = 5 (step 2), R4C1 = 5 (step 3)
17b. R56C7 (step 14b) = {15/25}, 5 locked for C7 and N6

18. R6C9 = 8 -> R7C89 = 10 = {37} (only remaining combination), locked for R7 and N9
18a. R7C4 = 1 -> R78C3 = 8 = [26]

19. 13(3) cage in N8 = {247} (only remaining combination) -> R7C5 = 4, R8C45 = {27}, locked for R8 and N8, R7C1 = 9
19a. R89C1 = 10 = [37]
19b. Naked triple {369} in R9C456, locked for R9

20. 8 in N9 locked in 13(3) cage = {148} (only remaining combination), locked for N9
20a. R9C9 = 2, then R9C2 = 5 (hidden singles in R9)

21. R56C7 = {25} (hidden pair in C7)
21a. 45 rule on N5 2 innies R56C4 = 2 outies R56C7 + 7
21b. R56C7 = 7 -> R56C4 = 14 = {59}, locked for C4, N5 and 29(4) cage at R4C3
21c. Naked pair {78} in R45C3, locked for C3 and N4
21d. R9C5 = 9 (hidden single in R9)
[Ed pointed out that 45 rule on N56 2 remaining innies R56C4 = 14 = {59} … is an alternative to steps 21a and 21b.]

22. 9 in C3 locked in R12C3, locked for N1
22a. 16(3) cage in N1 = {169/349} (only remaining combinations), no 2,7

23. R4C1 = 5 -> R3C12 = 7 = [16/43/61], no 4,7 in R3C2

24. 17(3) cage in N1 = {278} (hidden triple in N1) -> R2C2 = 7, R12C1 = {28}, locked for C1
[Alternatively R2C2 = 7 (hidden single in C2), R12C1 = {28} (hidden pair in N1), locked for C1]

25. R3C8 = 2 -> R4C78 = 12 = {39} (only remaining combination), locked for R4 and N6

26. R5C2 = 9 (hidden single in C2), R56C4 = [59], R56C7 = [25]
26a. 20(4) cage in N4 = {1469} (only remaining combination), locked for N4 -> R6C23 = [23]

27. R123C9 = {456} (only remaining combination, cannot be {159} which clashes with R8C9, cannot be {357} which clashes with R7C9), locked for C9 and N3 -> R8C89 = [59]
27a. Naked pair {17} in R45C9, locked for C9 and N6 -> R7C89 = [73]
27b. Naked pair {46} in R56C8, locked for C8

28. 1 in N3 locked in 17(3) cage = {179} (only remaining combination) -> R1C7 = 7, R12C8 = {19}, locked for C8 and N3 -> R4C78 = [93], R9C8 = 8

29. 7 in R6 locked in R6C56, locked for N5, clean-up: no 3 in R5C6 (step 13a)
29a. Naked pair {46} in R45C6, locked for C6 and N5 -> R9C46 = [63]
29b. Naked pair {12} in R12C6, locked for C6 and N2 -> R6C56 = [17]
29c. Naked pair {28} in R4C45, locked for R4 and N6 -> R45C3 = [78], R45C9 = [17], R5C5 = 3

30. R3C3 = 5 -> R23C4 = 10 = [37]

31. R1C2 = 3 (hidden single in R1), R12C3 = {49} (step 22a), locked for C3 and N1, R8C45 = [27], R4C45 = [82], R1C4 = 4, R1C38 = [91]
31a. R1C4 = 4 -> R1C56 = 7 = [52]

and the rest is naked singles.