SudokuSolver Forum

(This week a little bit earlier than usual so you guys in Australia have something for breakfast)

I almost changed my plan for this weeks Assassin because of a new one that just popped up (rating: 1.5). It would be really great for a v2 but time is running short and I'm still working on a v1 so it will have to wait. But don't be disappointed, this newborn killer is already reciting Arnold Schwarzenegger: "I'll be back!"

But first you'll have to work on this one. Nothing fancy (except that it is a Killer X), just good old basic stuff.

Assassin 121
Attention: This is a Killer X (1-9 cannot repeat on the diagonals)




Rating SSolver(3.2.1): 1.20
My personal rating: 1.0


V2 is already waiting to be posted.

Have fun!

Cheers,
Nasenbaer

Thanks Nasenbaer for a fun puzzle! I look forward to V2.

I'll rate A121 at Hard 1.0 because I used a Hidden Killer Pair as well as fairly routine combination analysis.

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.

Probably not the most direct solving path. I was trying to get it finished before people in Europe. Thanks Nasenbaer for the feedback. Now I know some of the things that I missed, one of which would have made my walkthrough quite a lot shorter.

Prelims

a) R1C34 = {59/68}
b) R1C67 = {14/23}
c) R45C2 = {59/68}
d) R45C8 = {19/28/37/46}, no 5
e) R56C3 = {78} (cannot be {69} which clashes with R45C2), locked for C3 and N4, clean-up: no 6 in R1C4, no 6 in R45C2
f) R56C7 = {29/38/47/56}, no 1
g) R67C4 = {39/48/57}, no 1,2,6
h) R67C6 = {14/23}
i) 20(3) cage in N3 = {389/479/569/578}, no 1,2
j) 10(3) cage in N3 = {127/136/145/235}, no 8,9
k) 21(3) cage in N7 = {489/579/678}, no 1,2,3
l) 11(3) cage in N7 = {128/137/146/236/245}, no 9
m) R9C234 = {127/136/145/235}, no 8,9
n) 31(7) cage at R3C5 = {1234579/1234678}

1. Naked pair {59} in R45C2, locked for C2 and N4

2. 45 rule on R89 2 innies R8C37 = 16 = [97], clean-up: no 5 in R1C4, no 4 in R67C7
2a. R8C3 = 9 -> R7C23 = 12 = [75/84]
2b. R8C7 = 7 -> R7C78 = 10 = {19/28/46}, no 3,5
2c. 11(3) cage in N7 = {128/137/146/236} (cannot be {245} which clashes with R7C3), no 5

3. 45 rule on C1234 3 innies R258C4 = 8 = {125/134}, 1 locked for C4

4. 45 rule on C6789 3 innies R258C6 = 21 = {489/579/678}, no 1,2,3
4a. 5 of {579} must be in R8C6 -> no 5 in R25C6

5. 45 rule on C9 3 outies R168C8 = 21 = {489/579/678}, no 1,2,3
5a. 5 of {579} must be in R8C8 -> no 5 in R16C8

6. 45 rule on C89 4 innies R2379C8 = 14 = {1238/1256/1346/2345} (cannot be {1247} which clashes with R168C8), no 7,9, clean-up: no 1 in R7C7 (step 2b)

7. 45 rule on N1 3 innies R1C3 + R3C13 = 17 = {269/359/368/458/467} (cannot be {179/278} because R1C3 only contains 5,6), no 1
7a. 7,8,9 only in R3C1 -> R3C1 = {789}
7b. R1C3 = {56} -> no 5,6 in R3C3

8. 45 rule on N7 1 innie R7C1 = 1 outie R9C4 + 3, no 1,2,3,4 in R7C1, no 6,7 in R9C4

9. 45 rule on N47 2 outies R3C1 + R9C4 = 1 innie R4C3 + 10, max R3C1 + R9C4 = 14 -> max R4C3 = 4

10. 45 rule on N9 1 outie R9C6 = 1 innie R7C9 + 4, no 1,2,3,4 in R9C6, no 6,8,9 in R7C9

11. 45 rule on R12 2 outies R3C28 = 9 = [36/45/63/72/81], no 1,2 in R3C2, no 4 in R3C8

12. 10(3) cage in N3 = {136/145/235}
12a. Hidden killer pair 1,2 in 10(3) cage and R1C7 + R3C79 for N3 -> R1C7 + R3C79 must contain one of 1,2
12b. 45 rule on N3 3 innies R1C7 + R3C79 = 15 = {168/249/258/267} (cannot be {159} which clashes with 10(3) cage, cannot be {348/357/456} which don’t contain 1 or 2), no 3, clean-up: no 2 in R1C6
12c. 1 of {168} must be in R1C7 -> no 1 in R3C79
12d. 20(3) cage in N3 = {389/479/578} (cannot be {569} which clashes with 10(3) cage), no 6

13. 45 rule on C123 4 outies R1349C4 = 25 = {2689/3679/4678} (cannot be {3589/4579} which clash with R258C4), no 5, clean-up: no 8 in R7C1 (step 8)
13a. R9C4 = {234} -> no 2,3,4 in R34C4

14. 6 in C4 locked in R34C4, locked in 18(4) cage at R3C3 = {1269/1368/1467/2367}
14a. 1 of {1467} must be in R4C3 -> no 4 in R4C3

15. R9C234 = {127/136/145/235}
15a. 4 of {145} must be in R9C4 -> no 4 in R9C23

16. 45 rule on C789 4 outies R1349C6 = {1459/1468/1567/2359/2368} (cannot be {1279/1369/1378/2458/2467/3457} which clash with R67C6)
16a. 3 of {2359/2368} must be in R1C6 -> no 3 in R34C6

17. 45 rule on N69 2 outies R3C9 + R9C6 = 1 innie R4C7 + 11, max R3C9 + R9C6 = 18 -> no 8,9 in R4C7
[Nasenbaer pointed out that I missed Min R4C7 = 1 -> min R3C9 + R9C6 = 12, no 2 in R3C9.]

18. 15(3) cage at R6C1 = {267/456} (cannot be {357} because 5,7 only in R7C1), no 1,3
18a. 5,7 only in R7C1 -> R7C1 = {57}
[Here I missed clean-up: no 3 in R9C4 (step 8) which proves to be an important elimination.]
18b. 6 locked in R6C12, locked for R6 and N4, clean-up: no 5 in R5C7
[Nasenbaer pointed out that I missed R7C23 (step 2a) = [84] (cannot be [75] which clashes with R7C1. Oops! I must have been getting tired. That would have made the later stages much quicker because it leads directly to R7C78 = [91] …]

19. 45 rule on N4 2 outies R37C1 = 1 innie R4C3 + 13
19a. R4C3 = {123} -> R37C1 = 14,15,16 = [95/87/97], no 7 in R3C1

20. R345C1 = {149/239} (cannot be {248} which clashes with 15(3) cage at R6C1) -> R3C1 = 9
20a. Killer pair 2,4 in R45C1 and R6C12, locked for N4

21. R1C3 + R3C13 (step 7) = {269/359}, no 4

22. R3C1 + R9C4 = R4C3 + 10 (step 9), R3C1 = 9 -> R9C4 = R4C3 + 1, no 3 in R9C4

23. R9C234 = {127/145/235} (cannot be {136} because R9C4 only contains 2,4), no 6
23a. R9C4 = {24} -> no 2,4 in R9C23

24. 2,6 in N7 locked in 11(3) cage = {236}, locked for N7
24a. 1 in N7 locked in R9C23, locked for R9

25. R7C2 = 8 (hidden single in N7), R7C3 = 4 (step 2a), locked for D/, clean-up: no 8 in R6C4, no 1 in R6C6, no 2,6 in R7C78 (step 2b), no 8 in R9C6 (step 10)
25a. R7C78 = [91], 9 locked for D\, clean-up: no 9 in R45C8, no 2 in R56C7, no 3 in R6C4, no 4 in R6C6, no 5 in R9C6 (step 10)
25b. Naked pair {23} in R3C3 and R6C6, locked for D\
25c. Naked pair {23} in R67C6, locked for C6, clean-up: no 2 in R1C7
25d. Naked pair {14} in R1C67, locked for R1

26. R7C5 = 6 (hidden single in R7), clean-up: no 5,9 in 31(7) cage at R3C5 (prelim n), no 2 in R7C9 (step 10)
26a. R7C6 = 2 (hidden single in R7), R6C6 = 3, R3C3 = 2 (hidden single on D\), clean-up: no 8 in R5C7
[I should also have given R9C4 = 4 here (I must have been careless with candidate eliminations) but since it’s done in step 27 it’s not worth changing.]
26b. R3C5 = 3 (hidden single in 31(7) cage)

27. 18(4) cage at R3C3 (step 14) = {2367} (only remaining combination, cannot be {1368} because 1,3 only in R4C3) -> R4C3 = 3, R34C4 = {67}, locked for C4, R9C4 = 4 (step 22), clean-up: no 2 in R45C1 (step 20), no 7 in R5C8, no 5 in R67C4
27a. R67C4 = [93], 9 locked for D/, R1C4 = 8, R1C3 = 6, R7C9 = 5, R9C6 = 9 (step 10), R7C1 = 7, R9C23 = [15], R1C1 = 5, R2C3 = 1
27a. Naked pair {14} in R45C1, locked for C1 and N4
27b. Naked pair {26} in R6C12, locked for R6

28. 10(3) cage in N3 (step 12) = {235} (only remaining combination) -> R3C8 = 5, R2C78 = {23}, locked for R2 and N3, R1C89 = [97], 7 locked for D/, R1C25 = [32]

29. Naked triple {236} in R2C8 + R8C2 + R9C1, locked for D/, R3C7 = 8, locked for D/, R5C5 = 1, R4C6 = 5
29a. 6 on D/ locked in R8C2 + R9C1, locked for N7
29b. R23C9 = [46], R2C2 = 7, locked for D\, R4C4 = 6, locked for D\
29c. R6C7 = 5, R5C7 = 6

and the rest is naked singles

Thanks Nasenbaer for this fun killer!

A121 Walkthrough:

1. C123 !
a) 15(2) = {78} locked for C3+N4 since (69) is a Killer pair of 14(2)
b) 14(2) @ N4 = {59} locked for C2+N4
c) 21(3) = 9{48/57} because (78) only possible @ R7C2 -> 9 locked for C3+N7; R7C2 = (78)
d) 14(2) @ N1 = [59/68]
e) Innies N1 = 17(3) = {269/359/368/458/467} <> 1 because R1C3 = (56); R3C1 = (789), R3C3 = (234)
f) 15(3) must have one of (578) -> R7C1 = (578)
g) Innies+Outies N7: -3 = R9C4 - R7C1 -> R9C4 = (245)
h) 10(3) <> 6 because R9C4 = (245)
i) 6 locked in 11(3) @ N7 = 6{14/23}
j) ! Innies+Outies C12: -8 = R2C3 - R79C2: R9C2 <> 7 and R2C3 <> 5,6 because
R2C3 <> 7, R7C2 = (78) and R9C2 = (1234)

2. R789
a) Hidden pair (78) locked in R7C12 @ N7 for R7 -> R7C1 <> 5
b) Innies R89 = 16(2) = {79} -> R8C3 = 9, R8C7 = 7
c) Innies+Outies N7: -3 = R9C4 - R7C1 -> R9C4 <> 2
d) 5 locked in R79C3 @ N7 for C3
e) R1C3 = 6 -> R1C4 = 8
f) 12(2) = [39/75/93]

3. C456
a) Innies C1234 = 8(3) = 1{25/34} -> 1 locked for C4
b) Killer pair (45) locked in Innies C1234 + R9C4 for C4
c) 12(2) = {39} locked for C4
d) Innies C1234 = 8(3) = {125} locked for C4
e) R9C4 = 4
f) 10(3) = {145} -> R9C2 = 1, R9C3 = 5
g) R7C3 = 4 -> R7C2 = 8
h) R7C1 = 7 -> R6C12 = 8(2) = {26} locked for R6+N4

4. R123
a) 18(4) @ N1 = {2367} -> R4C3 = 3, R3C3 = 2
b) 12(3) = {147} -> R2C3 = 1, {47} locked for N1
c) 16(3) = {358} -> R1C2 = 3, R1C1 = 5, R2C1 = 8
d) 5(2) = {14} locked for R1
e) 20(3) = {479} because R1C89 = (79) -> R2C9 = 4, {79} locked for R1+N3
f) R1C7 = 1, R1C6 = 4, R2C2 = 7

5. N569
a) 17(3) @ R7C7 = {179} -> R7C7 = 9, R7C8 = 1
b) 5(2) = {23} -> R6C6 = 3, R7C6 = 2
c) R6C4 = 9, R4C4 = 6
d) R9C9 = 8, R8C8 = 4 -> R8C9 = 3
e) 17(3) @ R9 = {269} -> R9C6 = 9, {26} locked for R9+N9
f) R9C1 = 3
g) 14(3) = {158} -> R7C9 = 5, R6C8 = 8, R6C9 = 1
h) 10(2) = {37} -> R4C8 = 7, R5C8 = 3
i) R3C9 = 6, R3C8 = 5, R3C7 = 8, R2C8 = 2,

6. Rest is singles without considering diagonals.

Rating: 1.0.

Wonderful! Two different walkthroughs in such a short time! Bravo! And we can always rely on Afmob to produce a brilliant move (step 1j) that shortens the solving path.

This version has the same solution but a slightly altered cage pattern which removes the easy start from v1. It's only slightly harder than v1. Maybe I should have called it v1.5. Oh well.

Assassin 121 v2
Attention: This is a Killer X (1-9 cannot repeat on the diagonals)





Rating SSolver(3.2.1): 1.31
My personal rating: 1.25

(I would have liked to join the cages 15(2) @ r5c3 and 12(2) @ r6c4 because of the symmetry but that would produce a rating of 2.64 with extended T&E)

Have fun!

Cheers,
Nasenbaer

Like Nasenbaer said A121 V2 is more a V1.5 than a V2 but fun nonetheless. Thanks Nasenbaer!

I checked SudokuSolver's and JSudoku's solving path and it seems quite narrow though my Killer quint could have been replaced by some easier moves but since I like such moves I didn't change my walkthrough.

A121 V2 Walkthrough:

1. R123
a) Innies R12 = 13(4) = 1{237/246/345} <> 8,9; 1 locked for R2
b) Outies R12 = 9(2): R3C2 <> 1,9
c) Innies+Outies N1: 6 = R13C4 - R3C1 -> R1C4 <> 6 (IOU @ R3)

2. R789
a) Innies R89 = 16(2) = {79} locked for R8
b) Innies+Outies N7: -3 = R9C4 - R7C1 -> R9C4 <> 7 and R7C1 <> 1,2,3
c) Innies+Outies N9: 4 = R9C6 - R7C9 -> R9C6 = (56789) and R7C9 = (12345)

3. C1234 !
a) Innies C1234 = 8(3) = 1{25/34} -> 1 locked for C4
b) Killer pair (79) locked in 15(2) + R8C3 for C3
c) 14(2) = [59/68]
d) 9(2): R3C3 <> 8 and R3C4 <> 2
e) Innies N1 = 17(3) = {269/359/368/458/467} <> 1 because R1C3 = (56); R3C1 = (789), R3C3 = (234)
f) 9(2): R3C4 = (567)
g) Outies C1 = 11(3) <> 9
h) 9 locked in R123C1 @ N1 for C1
i) 9 locked in 21(3) @ N7 = 9{48/57}
j) Innies+Outies N7: -3 = R9C4 - R7C1 -> R9C4 <> 6 and R7C1 <> 4
k) ! Killer quint (12345) locked in R2589 + 12(2) for C4

4. C123 !
a) 9(2) <> 4
b) Innies N1 = 17(3) <> 7
c) Outies N4 = 22(2+1): R7C1 <> 8 because R3C1 = (89) and R4C4 >= 6
d) Innies+Outies N7: -3 = R9C4 - R7C1 -> R9C4 <> 5
e) 10(3): R9C23 <> 4 since R9C4 <> 1,5
f) ! Innies N7 = 13(3) = 5{17/26} -> 5 locked for N7
g) 21(3) = {489} -> R8C3 = 9; {48} locked for R7+N7
h) 15(2) = {78} locked for C3+N4
i) R7C3 = 4, R7C2 = 8, R8C7 = 7

5. N89
a) 17(3) @ R7C7 = {179} -> 1,7 locked for R7+N9
b) Innies+Outies N9: 4 = R9C6 - R7C9 -> R9C6 <> 5,8
c) 12(2): R6C4 <> 3,8
d) 1,8 locked in 21(4) @ N8 = 18{39/57}

6. C1234
a) Killer pair (35) locked in Innies C1234 + 12(2) for C4
b) 10(3) = 1{27/45} -> 1 locked for R9+N7
c) 11(3) = {236} locked for N7
d) 12(3) = 4{17/26/35} because {156/237} blocked by R1C3 = (56) and R3C3 = (23)
-> 4 locked for C2+N1
e) 14(3) <> 3,6 because R3C1 = (89) and {239} blocked by R89C1 = (236)
f) 15(3) = 7{26/35} since {456} blocked by Killer pair (45) of 14(3) -> R7C1 = 7
g) 10(3) = {145} -> R9C4 = 4; 5 locked for R9
h) Innies C1234 = {125} locked for C4
i) R7C4 = 3 -> R6C4 = 9
j) R1C4 = 8 -> R1C3 = 6
k) 21(4) = {1578} -> R9C5 = 7; 5,8 locked for R8+N8

7. C6789
a) 15(3) = {348} -> R9C9 = 8; {34} locked for R8+N9
b) 17(3) @ R9 = {269} -> R9C6 = 9; 2,6 locked for R9+N9
c) R9C1 = 3, R7C9 = 5, R1C9 = 7
d) Outies C9 = 21(3) = {489} -> R8C8 = 4, R6C8 = 8, R1C8 = 9
e) Cage sums: R2C9 = 4, R6C9 = 1
f) Innies C6789 = 21(3) = {678} -> R8C6 = 8, {67} locked for C6
g) 16(4) = {2356} -> R7C6 = 2; 6 locked for C7+N6
h) 17(3) @ N3 = {269} -> R3C9 = 6; {29} locked for N6
i) 10(3) = {235} locked for N3
j) R1C7 = 1, R3C7 = 8 -> R3C6 = 1, R4C6 = 5, R2C8 = 2

8. Rest is singles.

Rating: 1.25. I used a Killer quint.

Thanks Nasenbaer. Another enjoyable variant. As you said the cage changes took away the early entry but I still had a naked pair in step 1 and a killer pair in step 2.

My impression after going through Afmob's walkthrough and mine is that it can't be too narrow although we both used the critical area in C4 but even then used different ways. I'll assume the comment meant that Afmob's solving path was very similar to that used by Sudoku Solver and JSudoku. Mine looks very different.

I'll also rate A121 V2 at 1.25. It wasn't much harder than A121.

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.

At the end I've also given some other moves that I was looking at before I found a more powerful step 18. From step 22a onward there may have been a more direct path; I was concentrating on finding hidden singles on the diagonals so that when I reached naked singles there were no more eliminations on the diagonals.

Prelims

a) R1C34 = {59/68}
b) R1C67 = {14/23}
c) R3C34 = {18/27/36/45}, no 9
d) R3C67 = {18/27/36/45}, no 9
e) R56C3 = {69/78}
f) R67C4 = {39/48/57}, no 1,2,6
g) 20(3) cage in N3 = {389/479/569/578}, no 1,2
h) 10(3) cage in N3 = {127/136/145/235}, no 8,9
i) 21(3) cage in N7 = {489/579/678}, no 1,2,3
j) 11(3) cage in N7 = {128/137/146/236/245}, no 9
k) R9C234 = {127/136/145/235}, no 8,9
l) 31(7) cage at R3C5 = {1234579/1234678}

1. 45 rule on R89 2 innies R8C37 = 16 = {79}, locked for R8

2. Killer pair 7,9 in R56C3 and R8C3, locked for C3, clean-up: no 5 in R1C4, no 2 in R3C4
2a. 21(3) cage in N7 = {489/579/678}
2b. 5 of {579} must be in R7C3 -> no 5 in R7C2

3. 45 rule on R12 2 outies R3C28 = 9 = {27/36/45}/[81], no 1,9 in R3C2

4. 45 rule on C1234 3 innies R258C4 = 8 = {125/134}, 1 locked for C4, clean-up: no 8 in R3C3

5. 45 rule on C6789 3 innies R258C6 = 21 = {489/579/678}
5a. 5 of {579} must be in R8C6 -> no 5 in R25C6

6. 45 rule on C9 3 outies R168C8 = 21 = {489/579/678}
6a. 5 of {579} must be in R8C8 -> no 5 in R16C8

7. 45 rule on C1 3 outies R168C2 = 11 = {128/137/146/236/245}, no 9

8. 45 rule on N7 1 innie R7C1 = 1 outie R9C4 + 3, no 1,2,3,4 in R7C1, no 7 in R9C4

9. 45 rule on N47 3 outies R3C1 + R49C4 = 19
9a. Max R9C4 = 6 -> min R3C1 + R4C4 = 13, no 1,2,3

10. 45 rule on N9 1 outie R9C6 = 1 innie R7C9 + 4, no 6,7,8,9 in R7C9, no 1,2,3,4 in R9C6

11. 45 rule on N4 3 outies R37C1 + R4C4 = 22, max R37C1 = 17 -> min R4C4 = 5

12. 6 in C4 locked in R1349C4
12a. 45 rule on C123 4 outies R1349C4 = 25 = {2689/3679/4678}, no 5, clean-up no 4 in R3C3, no 8 in R7C1 (step 8)

13. R9C234 = {127/136/145/235}
13a. 4 of {145} must be in R9C4 -> no 4 in R9C23

14. 45 rule on N7 3 innies R7C1 + R9C23 = 13 = {139/157/256}
14a. 6 of {256} must be in R7C1 (R9C23 cannot be {26} because R9C234 cannot be {26}2), no 6 in R9C23

15. 21(3) cage in N7 = {489/678} (cannot be {579} which clashes with R7C1 + R9C23), no 5, 8 locked in R7C23, locked for R7 and N7, clean-up: no 4 in R6C4
15a. R8C3 = {79} -> no 7,9 in R7C2
15b. 4 of {489} must be in R7C3 (R78C3 cannot be {89} which clashes with R56C3), no 4 in R7C2
15c. 6 of {678} must be in R7C2 (R78C3 cannot be {67} which clashes with R56C3), no 6 in R7C3
15d. -> 21(3) cage = [849/687]
15e. Killer pair 8,9 in R56C3 and R78C3, locked for C3, clean-up: no 6 in R1C4

16. 17(3) cage in N9 = {179/269/359} (cannot be {467} which clashes with R7C23), no 4, 9 locked for N9
16a. 9 in R9 locked in R9C56, locked for N8, clean-up: no 3 in R6C4

17. 45 rule on N1 3 innies R1C3 + R3C13 = 17 = {269/359/368} (cannot be {179/278} because R1C3 only contains 5,6, cannot be {458/467} because 4,7,8 only in R3C1), no 1,4,7, clean-up: no 8 in R3C4
17a. 8,9 only in R3C1 -> R3C1 = {89}
17b. 2,3 only in R3C3 -> R3C3 = {23}, clean-up: no 3,4 in R3C4

This was where I had my interesting original step 18, see comment at the end.

18. R1349C4 (step 12a) = {2689/3679/4678}
18a. 2,3,4 only in R9C4 -> R9C4 = {234}, clean-up: no 9 in R7C1 (step 8)

19. R8C3 = 9 (hidden single in N7), R8C7 = 7, R7C23 = [84] (step 15d), 4 locked for D/, clean-up: no 2,5 in R3C6, no 1 in R3C8 (step 3), no 6 in R56C3, no 8 in R6C4, no 8 in R9C6 (step 10)
19a. Naked pair {78} in R56C3, locked for N4
19b. R8C7 = 7 -> R7C78 = {19} (step 16), locked for R7 and N9, clean-up: no 5 in R9C6 (step 10)

20. R1349C4 (step 12a) = {2689/4678} (cannot be {3679} which clashes with R56C4), no 3, clean-up: no 6 in R7C1 (step 8)
[Alternatively Killer pair 3,5 in R258C4 and R67C4, locked for C4 gives the same eliminations.]
20a. 6 in R7 locked in R7C56, locked for N8, clean-up: no 2 in R7C9 (step 10)

21. R7C56 = {26} (hidden pair in R7), locked for N8 -> R9C4 = 4, R7C1 = 7 (step 8), clean-up: no 9 in R14C4 (step 20), no 3 in R258C4 (step 4), no 5 in R6C4, no 2,3 in R9C23 (step 13)
21a. R1C4 = 8, R1C3 = 6, clean-up: no 1 in R3C7
21b. R67C4 = [93] (hidden pair in C4), 9 locked for D/, R7C9 = 5, R9C6 = 9 (step 10), clean-up: no 4,5 in R258C6 (step 5)
21c. R8C6 = 8, R9C5 = 7 (hidden single in N8)
21d. Naked pair {15} in R9C23, locked for N7

22. Naked pair {67} in R25C6, locked for C6 -> R7C56 = [62], R5C6 = 7, R2C6 = 6, R4C4 = 6, locked for D\, R3C4 = 7, R3C3 = 2, locked for D\, R3C1 = 9 (step 17), R56C3 = [87], clean-up: no 3 in R1C7, no 3 in R3C7, no 5 in 31(7) cage at R3C5 (prelim l)
[While checking through this walkthrough, I realised that I could have started this step with R5C6 = 7 (hidden single in 31(7) cage at R3C5).]
22a. R2C2 = 7, R7C7 = 9, R9C9 = 8 (hidden singles in D\), R7C8 = 1, R8C8 = 4, locked for D\, R8C9 = 3 (cage sum), R1C89 = [97], R2C9 = 4, clean-up: no 1 in R1C6
22b. R3C7 = 8 (hidden single in D/), R3C6 = 1, R3C9 = 6
[It would have been more fun to use 1 on D/ locked in R4C6 + R5C5, locked for N5 first but the hidden single on D/ is more logical.]
22c. Naked pair {34} in R1C6 + R3C5, locked for N2
22d. R2C5 = 9 (hidden single in N2)

23. R5C5 = 1 (hidden single on D/), locked for D\, R5C4 = 2, R2C4 = 5, R8C45 = [15], R1C5 = 2, R1C7 = 1, R1C6 = 4, R3C5 = 3, R3C28 = [45]

24. R9C1 = 3 (hidden single in R9), locked for D/ -> R2C78 = [32], 2 locked for D/

25. R7C9 = 5 -> R6C89 = 9 = [81]
25a. R3C1 = 9 -> R45C1 = 5 = [14]

and the rest is naked singles

My original step 18 was

18. 8 in R7 locked in R7C23 = [84/68] (step 15d)
18a. 45 rule on R89 4 outies R7C2378 = 22 = {1489/1678/3478/3568} (cannot be {2389/2578} which don’t contain 4 or 6), no 2
18b. R7C2378 must contain 2 odd numbers -> R7C78 = {13579}

I'd also got the following in my notes for possible later use

15(3) cage in N9 must have at least one odd number
45 rule on N9 3 innies R7C9 + R9C78 = 13 must have at least one odd number
Hidden killer quint for odd numbers in N9, 17(3) cage in N9 contains three odd numbers -> 15(3) cage in N9 and R7C9 + R9C78 must each contain only one odd number

A pity that I wasn't able to use these steps.