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There are several ways to tackle this V1, so it should not be too much difficult to solve it.






PS code : 3x3::k:4864:3585:3585:3585:4868:2565:2565:2565:4872:2569:4864:4619:4619:4868:2062:2062:4872:1809:2569:2835:4864:4619:4868:2062:4872:3865:1809:3355:2835:2845:6430:6430:6430:3361:3865:3619:3355:3365:2845:6430:5928:6430:3361:3883:3619:3355:3365:5928:5928:3121:5928:5928:3883:3619:3894:3365:2360:4921:3121:4667:4924:3883:1854:3894:2360:4921:4921:3121:4667:4667:4924:1854:2360:2377:2377:2377:3121:5197:5197:5197:4924:

Solution :

SSscore : 1.30

On the other hand, the solving path is more narrow for this V2 : the solution is the same, the cage pattern slightly different.
Of course, T.E is not required to solve it despite of the score : you "only" have to find the good step . . .





PS code : 3x3::k:4864:3585:3585:3585:4868:2565:2565:2565:4872:2569:4864:4619:4619:4868:2062:2062:4872:1809:2569:2835:4864:4619:4868:2062:4872:3865:1809:1819:2835:2845:6430:6430:6430:3361:3865:2339:1819:3365:2845:6430:5928:6430:3361:3883:2339:5421:3365:5928:5928:3121:5928:5928:3883:3125:5421:3365:2360:4921:3121:4667:4924:3883:3125:5421:2360:4921:4921:3121:4667:4667:4924:3125:2360:2377:2377:2377:3121:5197:5197:5197:4924:

Solution :

SSscore : 2.33

Thanks manu for a fun puzzle. It was good to have an easier one although I can see that the V2 is going to be a lot harder; step 9 won't be as effective and step 14, which gave my first placements for this puzzle, won't be available.

I'll rate A156 at 1.0. I did use one killer triple but it was such an obvious one that I won't increase the rating because of it. I've since found that the killer triple can be easily avoided, see comment after step 5.

Here is my walkthrough.

Prelims

a) R23C1 = {19/28/37/46}, no 5
b) R23C9 = {16/25/34}, no 7,8,9
c) R34C2 = {29/38/47/56}, no 1
d) R34C8 = {69/78}
e) R45C3 = {29/38/47/56}, no1
f) R45C7 = {49/58/67}, no 1,2,3
g) R78C1 = {69/78}
h) R78C9 = {16/25/34}, no 7,8,9
i) 19(3) cage in N1 = {289/379/469/478/568}, no 1
j) R123C5 = {289/379/469/478/568}, no 1
k) R1C678 = {127/136/145/235}, no 8,9
l) 8(3) cage at R2C6 = {125/134}, CPE no 1 in R2C4
m) 19(3) cage in N3 = {289/379/469/478/568}, no 1
n) 9(3) cage in N7 = {126/135/234}, no 7,8,9
o) 19(3) cage at R7C4 = {289/379/469/478/568}, no 1
p) 19(3) cage in N9 = {289/379/469/478/568}, no 1
q) R9C234 = {126/135/234}, no 7,8,9
r) R9C678 = {389/479/569/578}, no 1,2
s) R6789C5 = {1236/1245}, no 7,8,9, 1,2 locked for C5

1. 45 rule on C1 2 innies R19C1 = 7 = {25/34}/[61], no 7,8,9, no 6 in R9C1

2. 45 rule on C9 2 innies R19C9 = 17 = {89}, locked for C9
2a. 7 in C9 locked in R456C9, locked for N6, clean-up: no 8 in R3C8, no 6 in R45C7

3. 45 rule on C5 2 innies R45C5 = 14 = {59/68}
3a. 7 in C5 locked in R123C5, locked for N2
3b. R123C5 = {379/478}, no 5,6

4. 45 rule on R1 3 innies R1C159 = 21 = {489/579/678}, no 2,3, clean-up: no 4,5 in R9C1 (step 1)
4a. R1C1 = {456} -> no 4 in R1C5

5. Killer triple 1,2,3 in R9C1 and R9C234, locked for R9
5a. R6789C5 = {1236/1245}
5b. 6 of {1236} must be in R9C5 -> no 6 in R678C5
[The killer triple can be avoided by
45 rule on R9 3 innies R9C159 = 16
Max R9C19 = 12 -> min R9C5 = 4 (as in Afmob’s step 1h)
7 in R9 locked in R9C678 = {479/578}, no 3,6]

6. 19(3) cage in N1 = {469/478/568} (cannot be {289/379} because R1C1 only contains 4,5,6), no 2,3

7. 8 in N3 locked in 19(3) cage = {289/478/568}, no 3

8. 45 rule on R123 2 outies R4C28 = 15 = [69/78/96], R4C2 = {679}, clean-up: R3C2 = {245}

9. 45 rule on N7 2 innies R7C2 + R8C3 = 1 outie R9C4 + 12
9a. Max R7C2 + R8C3 = 16 (cannot be {89} which clashes with R78C1) -> max R9C4 = 4
9b. Min R7C2 + R8C3 = 13, no 1,2,3

10. 45 rule on N9 3 outies R789C6 = 1 innie R7C8 + 19
10a. Max R789C6 = 24 -> max R7C8 = 5
10b. Min R789C6 = 20, no 1,2

11. 45 rule on N9 1 outie R9C6 = 2 innies R7C8 + R8C7 + 1
11a. Max R7C8 + R8C7 = 8, no 8,9

12. 7 in R9 locked in R9C678 = {479/578}, no 6

13. 45 rule on C89 2 outies R37C7 = 2 innies R19C8 + 6
13a. Max R37C7 = 16 (cannot be {89} which clashes with R45C7) -> max R19C8 = 10, no 7 in R1C8

14. 45 rule on N6 2 innies R4C8 + R6C7 = 1 outie R7C8 + 3, IOU no 3 in R6C7
14a. Max R7C8 = 5 -> max R4C8 + R6C7 = 8 -> R4C8 = 6, R3C8 = 9, R1C9 = 8, R9C9 = 9, R4C2 = 9 (step 8), R3C2 = 2, clean-up: no 1,8 in R2C1, no 5 in R2C9, no 8 in R3C1, no 2 in R4C3, no 2,5 in R5C3, no 5,8 in R5C5 (step 3), no 4 in R5C7, no 4 in R9C678 (step 12)
14b. 45 rule on N6 1 outie R7C8 = 1 remaining innie R6C7 + 3, no 4,5,8,9 in R6C7, no 1,2,3 in R7C8

15. Naked triple {578} in R9C678, locked for R9
15a. R9C234 = {126/234}, 2 locked for R9
15b. R6789C5 = {1236/1245}
15c. 4 of {1245} must be in R9C5 -> no 4 in R678C5

16. R9C6 = R7C8 + R8C7 + 1 (step 11)
16a. Min R7C8 + R8C7 = 5 -> no 5 in R9C6
16b. 5 in R9 locked in R9C78, locked for N9 -> R7C8 = 4, R6C7 = 1 (step 14b), clean-up: no 2,3 in R78C9
16c. 45 rule on N9 R9C6 = 1 remaining innie R8C7 + 5 -> no 6,7 in R8C7

17. Naked pair {16} in R78C9, locked for C9 and N9

18. R1C8 = 1 (hidden single in C8)

19. 1 in 8(3) cage at R2C6 locked in R23C6, locked for C6 and N2
19a. 1 in C5 locked in R78C5, locked for N8

20. R789C6 = R7C8 + 19 (step 10), R7C8 = 4 -> R789C6 = 23 = {689} -> R9C6 = 8, R78C6 = {69}, locked for C6 and N8, R8C7 = 3 (step 16c or from cage sum)
20a. Naked pair {57} in R9C78, locked for N9
[I missed an elimination. R78C6 = {69} makes R9C5 a naked single.]

21. R7C8 = 4 -> R56C8 = 11 = {38}, locked for C8 and N6, R8C8 = 2, R7C7 = 8, clean-up: no 5 in R45C7, no 7 in R8C1
21a. R45C7 = [49], R5C5 = 6, R4C5 = 8 (step 3), R9C5 = 4, clean-up: no 5 in R4C3, no 3,7 in R5C3, no 3 in R9C234 (step 15a)
21b. Naked triple {379} in R123C5, locked for C5 and N2, clean-up: no 4 in R23C6 (prelim l)
21c. Naked triple {257} in R456C9, locked for C9

22. R9C4 = 2, R9C23 = {16}, locked for N7, R9C1 = 3, clean-up: no 7 in R23C1, no 9 in R78C1
22a. R78C1 = [78], R7C23 = [52], R8C23 = [49], R7C45 = [31], R8C45 = [75], R78C6 = [96], R78C9 = [61], R6C5 = 2

23. R1C9 = 8 -> R2C8 + R3C7 = 11 = [56], R12C7 = [72], R1C6 = 2 (prelim k), R1C5 = 9, R1C1 = 4 (step 4), R23C6 = [15], R1C4 = 6, R1C23 = [35], R9C78 = [57], clean-up: no 6 in R2C1
23a. R23C1 = [91]

24. R45C1 = {25}, locked for C1, R6C1 = 6

27. R5C2 = 1 (hidden single in N4), R6C2 = 7 (cage sum), R9C23 = [61], R4C3 = 3, R5C3 = 8

and the rest is naked singles

I agree with Andrew, this Killer was lots of fun. There were a lot of IOD moves in my unoptimized walkthrough.

A156 Walkthrough:

1. C159
a) Innies C9 = 17(2) = {89} locked for C9
b) Innies C5 = 14(2) = {59/68}
c) 7 locked in 19(3) @ C5 for N2 -> 19(3) = 7{39/48}
d) 7 locked in 14(3) @ C9 for N6
e) Innies C1 = 7(2) <> 7,8,9
f) Innies R1 = 21(3) <> 2,3; R1C5 <> 4 since R1C1 = (456)
g) Innies C1 = 7(2): R9C1 = (123)
h) Innies R9 = 16(3): R9C5 <> 1,2,3 since R9C19 <= 12

2. N23 !
a) Outies N3 = 14(3+1) <> 9 -> R123C6 <= 8 <> 6 and must have 1 -> 1 locked for C6+N2
b) 6 locked in R123C4 @ N2 for C4
c) ! Outies N3 = 14(3+1): R4C8 = (68) -> R123C6 = 6/8 = 12{3/5} since {134} blocked by Killer pair (34) of 19(3) @ N2
-> 2 locked for C6+N2

3. N69
a) 7 locked in 20(3) @ R9 = 7{49/58}
b) Innies+Outies N9: 1 = R9C6 - (R7C8+R8C7) -> R7C8+R8C7 <> 8,9
c) Innies+Outies N6: -3 = R7C8 - (R4C8+R6C7): R6C7 <> 6,8,9 and R7C8 <> 1,2,3 since R4C8 >= 6
d) Innies+Outies N9: 1 = R9C6 - (R7C8+R8C7): R8C7 = (123) and R9C6 <> 4,5 since R7C8 >= 4
e) 18(3): R78C6 = (6789) because R8C7 <= 3

4. C6789 !
a) Innies C6789 = 15(3+1) <> 8,9 since R456C6 <> 1,2
b) 4 locked in R456C6 @ C6 for N5
c) ! Innies C6789 = 15(3+1) = {345}+3 / {346}+2 / {347}+1 (step 4a) -> R6C7 = (123) and 3 locked in R456C6 for C6+N5
d) Outies N3 = 14(3+1): R123C6 = {125} locked for C6+N2 -> R4C8 = 6
e) Cage sum: R3C8 = 9

5. R123+N9
a) Innie R123 = R3C2 = 2
b) Cage sum: R4C2 = 9
c) R1C9 = 8, R9C9 = 9
d) 20(3) = {578} -> 5 locked for R9+N9
e) Innies+Outies N9: 1 = R9C6 - (R7C8+R8C7): R7C8 <> 7 since R9C6 <= 8
f) R7C8 = 4
g) 7(2) @ N9 = {16} locked for C9+N9
h) Hidden Single: R5C7 = 9 @ N6 -> R4C7 = 4
i) 15(3) = {348} -> 3,8 locked for C8+N6
j) 19(3) @ N3 = {568} -> R2C8 = 5, R3C7 = 6

6. C456
a) Innies C5 = 14(2) = {68} -> R4C5 = 8, R5C5 = 6
b) 19(3) @ N2 = {379} locked for C5+N2
c) 18(3) @ N2 = {468} since R23C4 = (468) -> 6 locked for R2

7. C123
a) 11(2) = [38/74]
b) Hidden Single: R6C4 = 9 @ N5, R6C7 = 1 @ N6
c) 23(5) = {13469} since R6C6 = (347) -> 3,4 locked for R6

8. Rest is singles.

Rating: Hard 1.0. I used large Innies and Outies.

V2 needed the same breakthrough moves as V1 so this wt is not much different from the first one.

A156 V2 Walkthrough:

1. C159
a) Innies C9 = 17(2) = {89} locked for C9
b) Innies C5 = 14(2) = {59/68}
c) 7 locked in 19(3) @ C5 for N2 -> 19(3) = 7{39/48}
d) Innies C1 = 7(2) <> 7,8,9
e) Innies R1 = 21(3) <> 2,3; R1C5 <> 4 since R1C1 = (456)
f) Innies C1 = 7(2): R9C1 = (123)
g) Innies R9 = 16(3): R9C5 <> 1,2,3 since R9C19 <= 12

2. C6789 !
a) Outies N3 = 14(3+1) <> 9 -> R123C6 <= 8 <> 6 and must have 1 -> 1 locked for C6+N2
b) 6 locked in R123C4 @ N2 for C4
c) ! Outies N3 = 14(3+1): R4C8 = (678) -> R123C6 = 6/7/8 = 12{3/4/5} since {134} blocked by Killer pair (34) of 19(3) @ N2
-> 2 locked for C6+N2
d) Innies C6789 = 15(3+1) <> 8,9 since R456C6 <> 1,2; R6C7 = (123) since R456C6 >= 12
e) 8,9 locked in R789C6 @ C6 for N8
f) ! Innies C6789 = 15(3+1): R456C6 <= 14 must have 3 since R456C7 <> 1,2 -> 3 locked for C6+N5

3. C456 !
a) 19(3) @ N7 must have one of (89) -> R8C3 = (89)
b) 19(3) @ N7 = 7{39/48} since R78C6 <> 8,9 -> 7 locked for C4+N5
c) ! 7 locked in Innies C6789 @ C6 = 15(3+1) = {347}+1 -> R6C7 = 1; 4 locked for C6+N5
d) 6 locked in R456C5 @ N5 for C5
e) 12(4) = {1245} locked for C5 since R9C5 = (45); 1,4 also locked for N8
f) 19(3) @ N8 = {379} -> R8C3 = 9; 3 locked for C4
g) 19(3) @ N2 = {379} locked for N2+C5

4. R1234
a) Outies N3 = 14(3+1): R4C8 = 6 since R123C6 = {125} locked for C6+N2
b) Cage sum: R3C8 = 9
c) Innie R123 = R3C2 = 2
d) Cage sum: R4C2 = 9
e) R4C5 = 8, R5C5 = 6
f) 11(2) = [38/47/74]
g) R1C9 = 8, R9C9 = 9
h) 7(2) = {25} locked for C1+N4 since (34) is a Killer pair of 11(2)

5. R6789
a) 20(3) = {578} -> R9C6 = 8; 5,7 locked for R9+N9
b) 21(3) = {678} locked for C1
c) R8C6 = 6, R7C6 = 9 -> R8C7 = 3

6. C123
a) 10(2) = {19} -> R3C1 = 1, R2C1 = 9
b) R1C1 = 4, R9C1 = 3, R9C4 = 2
c) 19(3) @ N1 = {478} -> 7,8 locked for N1
d) Hidden Single: R7C3 = 2 @ N7 -> R8C2 = 4
e) 13(3) @ C2 = {157} -> R6C2 = 7, R5C2 = 1, R7C2 = 5
f) 11(2) = {38} -> R4C3 = 3, R5C3 = 8

7. Rest is singles.

Rating: Hard 1.0. I used large Innies and Outies.

It is. At least one of my key steps was also used by Afmob but our walkthroughs were still sufficiently different for me to post my one.

I'll rate A156 V2 at Easy 1.25 because I used 4(3+1) innies and because it needed more work than A156 before the first placement.

Here is my walkthrough.

Prelims

a) R23C1 = {19/28/37/46}, no 5
b) R23C9 = {16/25/34}, no 7,8,9
c) R34C2 = {29/38/47/56}, no 1
d) R34C8 = {69/78}
e) R45C1 = {16/25/34}, no 7,8,9
f) R45C3 = {29/38/47/56}, no1
g) R45C7 = {49/58/67}, no 1,2,3
h) R45C9 = {18/27/36/45}, no 9
i) 19(3) cage in N1 = {289/379/469/478/568}, no 1
j) R123C5 = {289/379/469/478/568}, no 1
k) R1C678 = {127/136/145/235}, no 8,9
l) 8(3) cage at R2C6 = {125/134}, CPE no 1 in R2C4
m) 19(3) cage in N3 = {289/379/469/478/568}, no 1
n) R678C1 = {489/579/678}, no 1,2,3
o) 9(3) cage in N7 = {126/135/234}, no 7,8,9
p) 19(3) cage at R7C4 = {289/379/469/478/568}, no 1
q) 19(3) cage in N9 = {289/379/469/478/568}, no 1
r) R9C234 = {126/135/234}, no 7,8,9
s) R9C678 = {389/479/569/578}, no 1,2
t) R6789C5 = {1236/1245}, no 7,8,9, 1,2 locked for C5

1. 45 rule on C1 2 innies R19C1 = 7 = {25/34}/[61], no 7,8,9, no 6 in R9C1

2. 45 rule on C9 2 innies R19C9 = 17 = {89}, locked for C9, clean-up: no 1 in R45C9

3. 45 rule on C5 2 innies R45C5 = 14 = {59/68}
3a. 7 in C5 locked in R123C5, locked for N2
3b. R123C5 = {379/478}, no 5,6

4. 45 rule on R1 3 innies R1C159 = 21 = {489/579/678}, no 2,3, clean-up: no 4,5 in R9C1 (step 1)
4a. R1C1 = {456} -> no 4 in R1C5
4b. Killer triple 4,5,6 in R1C1, R45C1 and R678C1, locked for C1

5. Killer triple 1,2,3 in R9C1 and R9C234, locked for R9
5a. R6789C5 = {1236/1245}
5b. 6 of {1236} must be in R9C5 -> no 6 in R678C5

6. 19(3) cage in N1 = {469/478/568} (cannot be {289/379} because R1C1 only contains 4,5,6), no 2,3

7. 45 rule on R123 2 outies R4C28 = 15 = {69/78}, clean-up: no 6,7,8,9 in R3C2

8. 45 rule on R6789 3 outies R5C258 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R5C5), no 7,8,9, clean-up: no 5,6 in R4C5 (step 3)
8a. R5C5 = {56} -> no 5,6 in R5C28
8b. Killer pair 8,9 in R4C28 and R4C5, locked for R4, clean-up: no 2,3 in R5C3, no 4,5 in R5C7
8c. Max R5C8 = 4 -> min R67C8 = 11, no 1

9. 45 rule on N69 3 outies R789C6 = 2 innies R4C8 + R6C7 + 16
9a. Min R4C8 + R6C7 = 7 -> min R789C6 = 23 -> R789C6 = {689/789}, 8,9 locked for C6 and N8
9b. Max R789C6 = 24 -> max R4C8 + R6C7 = 8, no 8,9 in R4C8, R6C7 = {12}, clean-up: no 6,7 in R3C8, no 6,7 in R4C2 (step 7), no 4,5 in R3C2
9c. R45C7 = [49/58] (cannot be {67} which clashes with R4C8
9d. R45C9 = {27/36} (cannot be {45} which clashes with R4C7)
9e. Killer pair 6,7 in R4C8 and R45C9, locked for N6

10. R5C7 + R6C8 = {89} (hidden pair in N6)
10a. Naked pair {89} in R36C8, locked for C8
10b. Naked pair {89} in R1C9 and R3C8, locked for N3
10c. 19(3) cage in N3 = {379/469/478/568} (cannot be {289} which clashes with R3C8), no 2
10d. Min R56C8 = 9 -> max R7C8 = 6

11. 45 rule on N3 1 innie R3C8 = 3 outies R123C6 + 1
11a. R3C8 = {89} -> R123C6 = 7,8 = {124/125} (cannot be {134} which clashes with R123C5) , no 3,6, 1,2 locked for C6 and N2
11b. 6 in N2 locked in R123C4, locked for C4
11c. 3 in C6 locked in R456C6, locked for N5

12. Max R78C4 = {57} = 12 -> min R8C3 = 8 (19(3) cage cannot be {577})
[Afmob used 19(3) cage at R7C4 must contain one of 8,9 -> R8C3 = {89}, a more direct way to look at this step.]

13. R789C6 = {689/789}
13a. Min R78C6 = {68} = 14 -> max R8C7 = 4

14. R678C9 = {147/156/345} (cannot be {237/246} which clash with R45C9), no 2

15. R567C2 = {148/157/247/256/346} (cannot be {139/238} which clash with R34C2), no 9

16. R567C8 = {159/249/258/348} (cannot be {168/267} which clash with R34C8, cannot be {357/456} because R6C8 only contains 8,9), no 6

17. 3 in C6 locked in R456C6
17a. 45 rule on C6789 4(3+1) innies R456C6 + R6C7 = 15 = {347}1/{346}2 (cannot be {356}2 which clashes with R4C5), no 5, 4 locked in R456C6, locked for C6 and N5

18. Naked triple {125} in R123C6, locked for N2
18a. R123C6 = 8 -> R3C8 = 9 (step 11), R4C8 = 6, R4C2 = 9 (step 7), R3C2 = 2, R1C9 = 8, R9C9 = 9, R4C5 = 8, R5C5 = 6 (step 3), R6C8 = 8, R5C7 = 9, R4C7 = 4, clean-up: no 1,8 in R2C1, no 4 in R23C5 (step 3b), no 3 in R2C7 (prelim l), no 5 in R2C9, no 8 in R3C1, no 1 in R4C1, no 2,5 in R4C3, no 3 in R45C9, no 1,3 in R5C1, no 5,7 in R5C3
18b. Naked triple {379} in R123C5, locked for C5 and N2

19. Naked triple {347} in R456C6, locked for C6 and N5, R6C7 = 1 (step 17a)

20. Naked pair {27} in R45C9, locked for C9 and N6 -> R5C8 = 3, R7C8 = 4 (step 16), R6C9 = 5, R6C45 = [92], R5C2 = 1 (step 8; also hidden single in N4), R45C4 = [15], clean-up: no 2 in R4C1

21. Naked pair {37} in R4C36, locked for R4 -> R4C1 = 5, R5C1 = 2, R45C9 = [27], R5C6 = 4, R5C3 = 8, R5C3 = 3, R4C6 = 7, R6C6 = 3, R8C3 = 9, clean-up: no 4 in R68C1 (prelim n)

22. Naked pair {57} in R29C8, locked for C8 -> R8C8 = 2, R1C8 = 1, R8C7 = 3, R7C7 = 8 (prelim q), clean-up: no 6 in R23C9

23. R1C9 = 8 -> R2C8 + R3C7 = 11 = [56], R12C7 = [72], R123C6 = [215], R1C5 = 9, R9C78 = [57], R9C6 = 8 (prelim s), R78C6 = [96], R9C5 = 4, R8C4 = 7, clean-up: no 3 in R9C234 (prelim r)
23a. R9C234 = [612], R1C9 = 3, clean-up: no 7 in R23C1
23b. R23C1 = [91]

and the rest is naked singles

I found the V1 harder than Afmob and Andrew did but managed to get it down to 8 steps before it's cracked. A really good puzzle with such different solutions possible. Thanks Manu!

Partial Walkthrough for Assassin 156

From the legal candidates mark-up. (feeling lazy with only a partial WT - see Andrew's WT for the list)

1. "45" c9: 2 innies r19c9 = 17 = {89}
1a. both locked for c9

2. 7 in c9 only in n6 -> 7 locked for n6
2a. no 8 in r3c8
2b. no 6 in 13(2)n6

3. 14(3)n6 = 7{16/25/34}: has one of 1,2,3
3a. 15(3)n6 has at most one of 1,2,3 since {23...} will not reach the cage sum
3b. hidden killer triple 1,2,3 in n6 -> r6c7 = (123)
3c. and 15(3)n6 {456} blocked
3d. and no 1,2,3 in r7c8 (step 3a)

4. 15(3)n6 = {159/249/258/348/357}(no 6) ({168/267} blocked by [6/8,6/7..] in 15(2)n3)

5. 7 in r9 only in 20(3) = 7{49/58} (no 3,6)

6. "45" n9: 1 outie r9c6 - 1 = 2 innies r7c8 + r8c7
6a. min 2 innies = [41] = 5 -> min. r9c6 = 6
6b. max. 2 innies = 8 (no 8,9)
6c. min. r7c8 = 4 -> max. r8c7 = 3 (can't have [44])

7. 7(2)n9 = {16/25/34}: has one of 1/2/3 and r8c7 = (123)
7a. hidden killer triple 1,2,3 in n9 -> 19(3) must have one of 1/2/3
7b. 19(3) = {289/379} (no 4,5,6)
7c. 9 locked for n9

8. 6 in n9 only in 7(2) = {16}, both locked for n9 & c9

9. r4c8 = 6 (hsingle n6)

Puzzle is cracked.

Cheers
Ed