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This puzzle has lots of small cages. Gives a very different feel to A190. Poor old JSudoku (JS) has a terrible time with this puzzle. It's become one of the criteria to help me find an Assassin - it must be "easy" for SudokuSolver and have an"ruudiculous" solver log for JS.

I found a couple of ways to solve it including a really interesting Over-The-Top (OTT) way. If no one finds the OTT I'll make a V2 to give a bit of extra incentive for you guys to find it. Someone needs to claim A192 first though.

Coming up to two years here.

Assassin 191
Thanks to Børge for the pics

Cheers
Ed

No walkthrough yet? Strange . Anyways, thanks for this Assassin, Ed! You only need to work on one region to crack it but maybe there are other ways to solve this Killer.

A191 Walkthrough:

1. R123 !
a) Innies N1 = 11(3) <> 9
b) Innies+Outies N2: 9 = R2C7+R4C5 - R2C4 -> R4C5 <> 9 (IOU @ R2)
c) Outies N1 = 12(1+1) <> 1,2
d) Innies R12 = 7(2) <> 7,8,9; R2C9 = (123)
e) Outies N2 = 20(2+1): R2C3 <> 2 since R4C5 <> 9
f) 11(2) @ N2 <> 9
g) Innies R12 + 11(2) @ N2 = 18(4) = {1368/1467/2358/2457/3456}
h) ! 10(2) @ N3 <> 3,7 since it's a Killer pair of combined cage in step 1g
i) Outies N3 = 8(1+1) <> 8,9; R4C8 <> 1,3,5

2. R123 !
a) Outies R123 = 19(3): R4C2 <> 6 since R4C58 <> 9 and R4C8 <> 5,8
b) Outies N1 = 12(1+1): R2C4 <> 6; R4C2 <> 3
c) 11(2) @ N2: R2C3 <> 5
d) Innies N1 = 11(3) <> 5 since 12(3) can't have both of {25}
e) ! 13(2) <> {67} because it's blocked by Killer quad (6789) @ N1 in 10(2), 11(2) @ R1C1 and Innies N1
f) 13(2): R3C1 = (89)
g) Innies R12 = 7(2) <> 1
h) 9(2): R3C9 = (67)
i) 10(2) @ N3: R2C7 <> 1,2
j) 1 locked in 11(3) @ N3 <> 5 for R3

3. R123
a) Innies N1 = 11(3) = {236} locked for N1; 2 also locked for R3
b) 10(2) @ N1 = {19} locked for R1+N1
c) R3C1 = 8 -> R2C1 = 5
d) Innie R12 = R2C9 = 2
e) Cage sum: R3C9 = 7
f) 11(2) @ N2 = {38} -> R2C3 = 3, R2C4 = 8
g) Outie N1 = R4C2 = 4
h) R2C2 = 7, R1C1 = 4
i) Outies R123 = 15(2) = {78} -> R4C8 = 7, R4C5 = 8
j) 11(3) = {137} -> 3 locked for R3+N3
k) 12(2) = {48} -> R1C9 = 8, R2C8 = 4
l) 10(2) @ N3 = {19} -> R2C6 = 1, R2C7 = 9

4. R456
a) 13(4) = {1237} locked for N4, 7 also locked for C1
b) Killer triple (123) locked in R4C2 + 8(3) for R5
c) 25(4) = {3589} -> R5C8 = 8; 3,5,9 locked for C9+N6
d) 17(3) = {269} since R5C7 = (46) -> R5C7 = 6, R4C7 = 2, R4C6 = 9
e) R6C8 = 1, R6C7 = 4 -> R6C6 = 6, R1C7 = 5, R1C8 = 6
f) 15(3) = {258} since R56C3 = (589) -> R5C3 = 5, R6C3 = 8, R6C4 = 2

5. R789
a) 9(2) = {27} -> R9C8 = 2, R9C7 = 7
b) 14(3) = {158} -> R7C7 = 8, R7C8 = 5
c) Hidden Single: R6C5 = 7 @ N5
d) 16(4) = 27{16/34} -> 2 locked for R7+N8
e) 12(2) = [39/84]

6. Rest is singles.

Thanks Ed for another challenging Assassin. I found it a lot harder than Afmob did and I probably never found the steps which Ed intended us to find for this puzzle. My "killer brain" seems to have gone to sleep recently; it took me until my step 16a to find an important elimination which Afmob had in step 1b and, even then, I found it using a slightly harder way.


Here is my walkthrough for A191.

Prelims

a) 11(2) cage in N1 = {29/38/47/56}, no 1
b) R1C23 = {19/28/37/46}, no 5
c) R1C78 = {29/38/47/56}, no 1
d) 12(2) cage in N3 = {39/48/57}, no 1,2,6
e) R23C1 = {49/58/67}, no 1,2,3
f) R2C34 = {29/38/47/56}, no 1
g) R2C67 = {19/28/37/46}, no 5
h) R23C9 = {18/27/36/45}, no 9
i) R4C34 = {29/38/47/56}, no 1
j) R6C67 = {19/28/37/46}, no 5
k) R9C23 = {39/47/56}, no 1,2,6
l) R9C78 = {18/27/36/45}, no 9
m) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
n) 8(3) cage in N5 = {125/134}
o) 19(3) cage at R6C2 = {289/379/469/478/568}, no 1
p) 26(4) cage at R3C4 = {2789/3689/4589/4679/5678}, no 1
q) 13(4) cage in N4 = {1237/1246/1345}, no 8,9

Steps resulting from Prelims
1a. 8(3) cage in N5 = {125/134}, 1 locked for R5 and N5, clean-up: no 9 in R6C7
1b. 13(4) cage in N4 = {1237/1246/1345}, 1 locked for C1 and N4
1c. 1 in N7 only in R8C23, locked for R8

2. 45 rule on N1 2(1+1) outies R2C4 + R4C2 = 12 = {39/48/57}/[66], no 2, clean-up: no 9 in R2C3

3. 45 rule on N3 2(1+1) outies R2C6 + R4C8 = 8 = {17/26}/[35/44], no 8,9, no 3 in R4C8, clean-up: no 1,2 in R2C7

4. 45 rule on N7 2(1+1) outies R6C2 + R8C4 = 16 = {79}/[88], no 2,3,4,5,6

5. 45 rule on N9 2(1+1) outies R6C8 + R8C6 = 9 = [18]/ {27/36/45}, no 9, no 8 in R6C8

6. 45 rule on R12 2 outies R3C19 = 15 = [78/87/96], clean-up: R2C1 = {456}, R2C9 = {123}

7. 45 rule on R89 2 outies R7C19 = 13 = {49/58/67}, no 1,2,3

8. 45 rule on R123 3 outies R4C258 = 19 = {289/379/469/478/568}, no 1, clean-up: no 7 in R2C6 (step 3), no 3 in R2C7
8a. 2 of {289} must be in R4C8 -> no 2 in R4C5

9. 45 rule on N1 3 innies R2C3 + R3C23 = 11 = {128/137/146/236/245}, no 9

10. 45 rule on R1234 1 outie R5C7 = 2 innies R4C19 + 2
10a. Min R4C19 = 3 -> min R5C7 = 5
10b. Max R4C19 = 7, no 7,8,9 in R4C19

11. 45 rule on R123 4 innies R3C2378 = 1 outie R4C5 + 4
11a. Min R3C2378 = 10 -> min R4C5 = 6
11b. Max R3C2378 = 13, no 8 in R3C2378

12. 13(4) cage in N4 = {1237/1246/1345}
12a. 6,7 of {1237/1246} must be in R5C12 (R5C12 cannot be {23/24} which clash with 8(3) cage in N5) -> no 6 in R4C1, no 6,7 in R6C1

13. 45 rule on N4 3 innies R4C23 + R6C2 = 1 outie R6C4 + 17
13a. Max R4C23 + R6C2 = 24 -> max R6C4 = 7

14. 45 rule on N6 3 innies R4C8 + R6C78 = 1 outie R4C6 + 3
14a. Min R4C8 + R6C78 = 6 -> min R4C6 = 3

15. 45 rule on N3 3 innies R2C7 + R3C78 = 13 = {139/148/247/256/346} (cannot be {238} which clashes with R23C9, cannot be {157} because 11(3) cage at R3C7 cannot be {15}5)
15a. 7 of {247} must be in R2C7 (R3C78 cannot be {27} because 11(3) cage at R3C7 cannot be {27}2), no 7 in R3C78

16. 45 rule on N2 2 innies R2C46 = 1 outie R4C5 + 1
16a. R2C46 cannot total 10, which clashes with R2C67 (CCC, without needing to look at combinations) -> no 9 in R4C5
16b. Max R2C46 = 9, no 9 in R2C4, clean-up: no 2 in R2C3, no 3 in R4C2 (step 2)

17. R3C2378 = R4C5 + 4 (step 11)
17a. Max R4C5 = 8 -> max R3C2378 = 12, no 7, 2 locked for R3

18. R2C3 + R3C23 (step 9) = {128/137/146/236/245}
18a. 5 of {245} must be in R2C3 (R3C23 cannot be {25} because 12(3) cage at R3C2 cannot be {25}5), no 5 in R3C23

19. R4C258 (step 8) = {289/469/478/568}
19a. 1 in R4 must be in R4C179
19b. 45 rule on R1234 4 innies R4C1679 = 15 = {1239/1257/1347/1356} (cannot be {1248} which clashes with R4C258), no 8 in R4C67

20. 45 rule on N2 3(2+1) outies R2C37 + R4C5 = 20
20a. R4C5 = {678} -> R2C37 = 12,13,14 = [39/48/57/84/49/58/67/59/68/86] (cannot be [76] because R2C46 cannot be [44]), no 7 in R2C3, clean-up: no 4 in R2C4, no 8 in R4C2 (step 2)

21. R4C258 (step 8) = {289/469/478/568}
21a. 8 of {478} must be in R4C5 -> no 7 in R4C5

22. 26(4) cage at R3C4 = {3689/4589/5678} (cannot be {4679} which clashes with R3C19), CPE no 8 in R12C5

23. R3C2378 = R4C5 + 4 (step 11)
23a. R4C5 = {68} -> R3C2378 = 10,12 = {1234/1236/1245}
23b. R3C78 cannot contain both of 1,2 (because no 8 in R4C8) -> R3C23 must contain at least one of 1,2

24. R4C258 (step 8) = {289/469/478/568} = [487/586/685/784/964/982]
24a. Cannot be [685], here’s how
R4C2 = 6 => R3C23 = {24}, R4C8 = 5 => R3C78 = {24} clashes with R3C23
24b. -> no 6 in R4C2, no 5 in R4C8, clean-up: no 6 in R2C4 (step 2), no 5 in R2C3, no 3 in R2C6 (step 3), no 7 in R2C7

25. R2C46 = R4C5 + 1 (step 16)
25a. R4C5 = {68} -> R2C46 = 7,9 = [34/52/36/72/81] (cannot be [54] because R2C37 cannot be [66]) -> R2C3467 = [8346/6528/8364/4728/3819], 8 locked in R2C347, locked for R2, clean-up: no 3 in R1C1, no 4 in R1C9

26. 45 rule on R1 3 outies R2C258 = 17 = {179/359/467} (cannot be {269} which clashes with R2C3467), no 2, clean-up: no 9 in R1C1

27. 26(4) cage at R3C4 = {3689/4589/5678} = {369}8/{459}8/{578}6 (cannot be {389}6/{567}8 which clash with R3C19)
27a. R2C46 + R4C5 (step 25a) = [346/368/728/818] (cannot be [526] which clashes with 26(4) cage = {578}6), no 5 in R2C4, clean-up: no 6 in R2C3, no 7 in R4C2 (step 2)

28. R2C3 + R3C23 (step 9) = {128/146/236}
28a. 3,4 of {146/236} must be in R2C3 -> no 3,4 in R3C23

29. R3C2378 (step 23a) = {1236/1245} (cannot be {1234} because 11(3) cage at R3C7 cannot be {34}4) = 12 -> R4C5 = 8 (step 11), clean-up: no 3 in R4C34, no 2 in R6C7
29a. 26(4) cage at R3C4 (step 27) = {369}8/{459}8, no 7, 9 locked for R3 and N2, clean-up: no 4 in R2C1

30. Hidden pair {78} in R3C19 for R3, clean-up: no 3 in R2C9
30a. Killer pair 6,8 in R23C1 and R2C3 + R3C23, locked for N1, clean-up: no 3,5 in 11(2) cage at R1C1, no 2,4 in R1C23

31. R2C258 (step 26) = {179/359/467}
31a. 1,6 of {179/467} must be in R2C5 -> no 4,7 in R2C5

32. R4C5 = 8 -> R2C46 (step 27a) = [36/72/81], no 4 in R2C6, clean-up: no 6 in R2C7, no 4 in R4C8 (step 3)

33. R2C7 + R3C78 (step 15) = {139/148/346} (cannot be {256} because 2,5,6 only in R3C78), no 2,5

34. 5 in R3 only in R3C456, locked for N2
34a. 26(4) cage at R3C4 (step 29a) = {459}8 (only remaining combination), 4 locked for R3 and N2

35. 3 in R3 only in R3C78, locked for N3, clean-up: no 8 in R1C78, no 9 in 12(2) cage at R1C9
35a. R2C7 + R3C78 (step 33) must contain 3 = {139/346}, no 8, clean-up: no 2 in R2C6, no 6 in R4C8 (step 3)

36. 45 rule on R123 2 remaining outies R4C28 = 11 = [47/92], no 5, clean-up: no 7 in R2C4 (step 2), no 4 in R2C3

37. Naked pair {38} in R2C34, locked for R2
37a. Naked pair {16} in R2C56, locked for R2 and N2 -> R2C1 = 5, R3C1 = 8, R2C9 = 2, R3C9 = 7, R2C8 = 4, R1C9 = 8, R2C7 = 9, R2C6 = 1, R2C5 = 6, R2C2 = 7, R1C1 = 4, R2C3 = 3, R2C4 = 8, R4C2 = 4 (step 2), R4C8 = 7 (step 3)
37b. Naked pair {19} in R1C23, locked for N1
37c. Naked pair {56} in R1C78, locked for N3
37d. Clean-up: no 8 in R6C2 (step 4), no 3 in R6C6, no 6 in R7C1, no 5,9 in R7C9 (both step 7), no 9 in R8C4 (step 4), no 2,5 in R8C6 (step 5), no 9 in R9C2, no 5,8 in R9C3, no 2,5 in R9C7

38. R8C4 = 7, R7C1 = 9, R7C9 = 4 (step 7), clean-up: no 2,5 in R6C8 (step 5), no 3 in R9C2, no 5 in R9C8

39. R6C2 = 9, R1C23 = [19], clean-up: no 2 in R4C4, no 1 in R6C7
39a. R6C2 = 9 -> R7C23 = 10 = [28/37/82], no 5,6

40. R8C3 = 1 (hidden single in N7)
40a. R9C3 = 4 (hidden single in N7), R9C2 = 8, clean-up: no 2 in R7C23, no 1 in R9C78
40b. R7C23 = [37]

41. Naked pair {26} in R89C1, locked for C1 and N7 -> R8C2 = 5

42. Naked pair {13} in R46C1, locked for N4 -> R5C1 = 7, R5C2 = 2 (step 1b), R3C23 = [62], clean-up: no 9 in R4C4

43. 8(3) cage in N5 = {134} (only remaining combination), locked for R5 and N5, clean-up: no 6 in R6C7

44. 8 in N4 only in 15(4) cage at R5C3 = {258} (only remaining combination) -> R6C4 = 2, R56C3 = {58}, locked for C3 -> R4C34 = [65], R4C6 = 9, R6C5 = 7, R6C6 = 6, R6C7 = 4, clean-up: no 3 in R6C8 + R8C6 (step 5)

45. R6C8 = 1, R4C9 = 3, R4C7 = 2, R5C7= 6 (cage sum)

and the rest is naked singles.

I used a different way to get into A191 with a variation on what's become a favourite move of mine (step 6). Loved finding it.

Thanks to HATMAN for taking the next Assassin! I'm struggling to find a V2 for A191 that's not just a one-trick pony but will keep trying on the weekend.

[edit: Thanks Andrew for some corrections and clarifications.]
Start to A191
Cheers
Ed

Thanks for your patience. This took forever to get right but am really happy with the result. A warning, JSudoku (JS) can't finish it. I used a couple of very short (but interesting) chains but they must be contradiction ones. SudokuSolver doesn't use any T&E. Good luck!

Assassin 191 v2
NOTE: 1-9 cannot repeat on either diagonal. A remote cage 21(4) at r2c3467.

Cheers
Ed

Thanks! And thanks for an interesting, challenging and well-balanced puzzle! Also thanks to HATMAN for volunteering for A192 and thus making this puzzle possible (even if these beasts are not always good for my health! )


What's the rationale behind that? Both are IMHO excellent solvers. Won't always concentrating on the relatively few weaknesses that JS has in comparison to SS run the risk of making the puzzles rather "samey" in the long run? Furthermore, JS is traditionally very strong on chains and has (for me) the big advantage that I know what it's talking about! By contrast, SS uses lots of terminology that AFAIK has not been so well defined (if at all!) by the Sudoku community.

Anyway, without further ado, here's my WT for the A191 V2. It'll be interesting to compare Ed's "couple of very short (but interesting) chains" with the approach I used:

_________________
Cheers,
Mike

Mike

You probably have a point as I tend to do it the other way round to Ed.

Maurice

_________________
Quis custodiet ipsos custodes?

Normal: [D  Y-m-d,  G:i]     PM->email: [D, d M Y H:i:s]

Thanks Ed for an extremely challenging V2.

Congratulations to Mike for finding what I assume was the way that Ed intended it to be solved. Your steps 4c and 4d, which clearly depend on spotting step 4b first, were neat and very powerful. After them the puzzle was effectively cracked.

My solving path was very different and much harder work but at least I think I can say that this puzzle isn't a one-trick pony. I found it very hard going when I was analysing the 19(4) cage at R8C2 but the puzzle got more interesting when I was able to move on to other parts of the grid after step 21.


Here is my walkthrough for A191 V2.

Prelims

a) 11(2) cage in N1 = {29/38/47/56}, no 1
b) R1C23 = {19/28/37/46}, no 5
c) R1C78 = {29/38/47/56}, no 1
d) 12(2) cage in N3 = {39/48/57}, no 1,2,6
e) R23C1 = {49/58/67}, no 1,2,3
f) R23C9 = {18/27/36/45}, no 9
g) R4C34 = {29/38/47/56}, no 1
h) R4C67 = {29/38/47/56}, no 1
i) R5C34 = {15/24}
j) R5C67 = {19/28/37/46}, no 5
k) R6C34 = {19/28/37/46}, no 5
l) R6C67 = {19/28/37/46}, no 5
m) R78C1 = {29/38/47/56}, no 1
n) R78C9 = {19/28/37/46}, no 5
o) R9C23 = {39/47/56}, no 1,2,6
p) R9C78 = {18/27/36/45}, no 9
q) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
r) 19(3) cage at R6C2 = {289/379/469/478/568}, no 1
s) 13(4) cage at R3C2 = {1237/1246/1345}, no 8,9

1. 45 rule on R12 2 outies R3C19 = 15 = [78/87/96], clean-up: no 7,8,9 in R2C1, R2C9 = {123}

2. 45 rule on R89 2 innies R8C19 = 8 = [26/53/62/71], no 4,8,9, no 3 in R8C1, no 7 in R8C9, clean-up: R7C1 = {4569}, R7C9 = {4789}
2a. 45 rule on R89 2 outies R7C19 = 13 [Added to simplify later steps]

3. 45 rule on C9 2 outies R25C8 = 1 innie R9C9 + 11
3a. Max R25C8 = 17 -> max R9C9 = 6
3b. Min R25C8 = 12, no 1,2 in R5C8

4. 45 rule on N1 3 innies R2C3 + R3C23 = 11 = {128/137/146/236/245}, no 9

5. 45 rule on N3 1 innie R2C7 = 1 outie R4C8 + 2, no 1,2 in R2C7, no 8 in R4C8

6. 45 rule on N7 2(1+1) outies R6C2 + R8C4 = 16 = [79/88/97]

7. 45 rule on N9 2(1+1) outies R6C8 + R8C6 = 9 = {18/27/36/45}, no 9

8. Min R5C12 = 5 (cannot be {12} which clashes with R5C34, cannot be {13} because R5C1234 = 10(4) = {1234} clashes with R5C67) -> max R6C1 = 7

9. 12(2) cage at R1C9 = {39/48/57}, R23C9 = [18/27/36] -> combined cage 12(2) + R23C9 must contain at least one of 3,8
9a. R1C78 = {29/47/56} (cannot be {38} which clashes with combined cage 12(2) + R23C9), no 3,8

10. Hidden killer quad 2,3,4,5 in R78C1, R7C23, R9C23 and 19(4) cage for N7, R7C23 contains one of 2,3,4,5, R78C1 contains one of 2,4,5, R9C23 contains one of 3,4,5 -> 19(4) cage must contain one of 2,3,4,5
10a. 1 in N7 only in 19(4) cage at R8C2 = {1279/1369/1378/1468/1567} (cannot be {1459} which contains two of 2,3,4,5)
10b. Cannot be {1468}, here’s how
19(4) cage = {146}8 => R78C1 = [92] => R9C23 = {57} => R7C23 cannot be {38} because 19(3) cage at R6C2 cannot be 8{38}
10c. 19(4) cage at R8C2 = {1279/1369/1378/1567}, no 4

11. R78C1 = [56/65/92] (cannot be [47] because R78C1 = [47] + 19(4) cage = {136}9 clashes with R9C23 and R8C1 = 7 clashes with all others combinations for 19(4) because R8C1 “sees” all the cells of the 19(4) cage), no 4 in R7C1, no 7 in R8C1, clean-up: no 1 in R8C9 (step 2), no 9 in R7C9

12. R23C1 = [49/58/67], R78C1 = {56}/[92] -> combined cage R2378C1 = [49]{56}/[58][92]/[67][92], 9 locked for C1, clean-up: no 2 in R2C2

13. 19(3) cage at R6C2 = {289/379/478/568} (cannot be {469} which clashes with R78C1 = {56} or R7C19 = [94])
[With hindsight this elimination of {469} could have been done after step 2.]

14. 19(4) cage at R8C2 = {1279/1369/1378/1567} (step 10c)
14a. Cannot be {1369}, here’s how
19(4) cage = {136}9 => R78C1 = [92] => R7C9 = 4 (step 2a), R9C23 = {48} (only remaining place for 4 in N7) => R7C23 cannot be {57} because 19(3) cage at R6C2 cannot be 7{57}
14b. 19(4) cage = {1378} can only be {137}8, here’s how
19(4) cage = {138}7 => R9C23 = {57} => R78C1 = [92] => R7C23 cannot be {46} because 19(3) cage at R6C2 cannot be {469} (step 13)
-> 19(4) cage at R8C2 = {127}9/{129}7/{137}8/{156}7, no 8 in R8C23 + R9C1

15. 19(4) cage at R8C2 = {127}9/{129}7/{137}8/{156}7
15a. 19(4) cage at R8C2 = {127}9/{137}8/{156}7 => R9C23 cannot be {57}
19(4) cage at R8C2 = {129}7 => R78C1 = {56} => R9C23 cannot be {57}
15b. -> R9C23 = {39/48}, no 5,7
15c. 19(4) cage at R8C2 = {129}7 => R6C2 = 9 (step 6) -> no 9 in R8C2

16. R23C9 = [18/27/36], R78C9 = [46/73/82] -> R2378C9 = [1873/1846/2746/3682]
16a. 25(4) cage in N6 = {1789/2689/3589/3679/4579} (cannot be {4678} which clashes with R2378C9, ALS block), 9 locked for N6, clean-up: no 2 in R4C6, no 1 in R5C6, no 1 in R6C6

17. 19(4) cage at R8C2 (step 15) = {127}9/{129}7/{137}8/{156}7
17a. {127}9 => R8C4 = 9
{129}7/{137}8 => R9C23 = {48} => 9 in R9 only in R9C456
{156}7 => R7C1 = 9 => 9 in R9 only in R9C456
17b. -> 9 in R8C4 + R9C456, locked for N8

18. 9 in 45(9) cage only in R3C456 + R456C5, CPE no 9 in R12C5

19. R2378C9 (step 16) = [1873/1846/2746/3682]
19a. Cannot be [1873], here’s how
[1873] => R3C1 = 7 (step 1), R8C1 = 5 (step 2) => R7C1 = 6 -> no place for 9 in C1
19b. R2378C9 = [1846/2746/3682], 6 locked for C9
19c. R78C9 = [46/82], no 3,7, clean-up: no 5 in R8C1 (step 2), no 6 in R7C1
[With hindsight after step 12 I ought to have spotted 9 in C1 only in R37C1 -> R3C19 = [96] (step 1) or R7C19 = [94] (step 2a) -> R37C9 must contain at least one of 4,6...]

20. Naked pair {26} in R8C19, locked for R8, clean-up: no 3,7 in R6C8 (step 7)

21. 19(4) cage at R8C2 (step 17) = {127}9/{129}7/{137}8/{156}7
21a. Cannot be {127}9, here’s how
[My original way to do this was flawed but I’ve found a slightly longer way]
19(4) cage = {127}9 => R8C1 = 6 => R7C1 = 5 => R7C9 = 8 (step 2a) => R9C23 = {48} (only remaining place for 8 in N7) => 9 in R9 only in R9C456 => no 9 in R8C4
21b. 19(4) cage at R8C2 = {129}7/{137}8/{156}7, no 9 in R8C4, clean-up: no 7 in R6C2 (step 6)
21c. 6 of {156}7 must be in R9C1 -> no 5 in R9C1

22. 9 in N8 only in R9C456, locked for R9, clean-up: no 3 in R9C23
22a. Naked pair {48} in R9C23, locked for R9 and N7, clean-up: no 1,5 in R9C78
22b. Killer pair 2,6 in R8C9 and R9C78, locked for N9

23. 45 rule on R9 2 innies R9C19 = 1 outie R8C5 + 3
23a. R9C19 cannot total 10 (cannot be [73] which clashes with R9C78) -> no 7 in R8C5

24. 21(4) cage at R8C6 = {1389/1479/3459} (cannot be {1578} which clashes with R8C4), 9 locked for R8 and N9
24a. 19(4) cage at R8C2 (step 21b) = {137}8/{156}7, no 2

25. 25(4) cage in N6 (step 16a) = {1789/3589/3679/4579} (cannot be {2689} which clashes with R2378C9, ALS block), no 2

26. 2 in C9 only in R28C9 -> R2378C9 (step 19b) = [2746/3682], no 1, clean-up: no 8 in R3C9, no 7 in R3C1 (step 1), no 6 in R2C1
26a. R2378C1 (step 12) = [49][56]/[58][92], 5 locked for C1, clean-up: no 6 in R2C2

27. R2C3 + R3C23 (step 4) = {128/137/146/236} (cannot be {245} which clashes with R2C1), no 5

28. 45 rule on N3 3 innies R2C7 + R3C78 = 13 = {139/148/157/247/346} (cannot be {238} which clashes with R2C9, cannot be {256} which clashes with R23C9)
28a. R1C78 = {29/56} (cannot be {47} which clashes with R2C7 + R3C78 or with R2C7 + R3C78 + R23C9 when R2C7 + R3C78 = {139}), no 4,7

29. 14(3) cage at R6C8 = {158/167/257/356} (cannot be {248} which clashes with R7C9, cannot be {347} which clashes with R9C78), no 4, clean-up: no 5 in R8C6 (step 7)

30. 45 rule on R1 3 outies R2C258 = 17 = {179/278/368/467} (cannot be {458} which clashes with R2C1, cannot be {359} which clashes with R2C19, cannot be {269} because 2,6 only in R2C5), no 5, clean-up: no 6 in R1C1, no 7 in R1C9
30a. 1,2,6 only in R2C5 -> R2C5 = {126}

31. 45 rule on R1 2 innies R1C19 = 1 outie R2C5 + 6
31a. R2C5 = {126} -> R1C19 = 7,8,12 = {34/35/39/48/57} (cannot be {25} which clashes with R1C78), no 2 in R1C1, clean-up: no 9 in R2C2

32. Killer pair 4,8 in 11(2) cage at R1C1 and R23C1, locked for N1, clean-up: no 2,6 in R1C23

33. R2C3 + R3C23 (step 27) = {236} (only remaining combination, cannot be {137} which clashes with 11(2) cage at R1C1), locked for N1, clean-up: no 8 in 11(2) cage at R1C1, no 7 in R1C23

33. Naked pair {47} in 11(2) cage at R1C1, locked for N1 and D\ -> R2C1 = 5, R3C1 = 8, R7C1 = 9, R8C1 = 2, R8C9 = 6, R7C9 = 4, R3C9 = 7, R2C9 = 2
33a. Naked pair {19} in R1C23, locked for R1
33b. Naked pair {56} in R1C78, locked for R1 and N3
33c. 2 in R1 only in R1C456, locked for N2
33d. 9 in R3 only in R3C456, locked for N2 and 45(9) cage at R3C4, no 9 in R456C5
33e. 9 in C9 only in R456C9, locked for N6
33f. Clean-up: no 3,8 in R2C8, no 4,7 in R4C3, no 3,6 in R6C7, no 3 in R9C78

34. R2C258 (step 30) = {179/467} -> R2C2 = 7, R1C1 = 4

35. 1 in N3 only in R3C78, locked for R3 and 11(3) cage at R3C7
35a. 11(3) cage at R3C7 = {137/146} -> R4C8 = {67}, R3C7 = {89} (step 5)

36. 2 in N1 only in R3C23, locked for 13(4) cage at R3C2, no 2 in R4C2
36a. 13(4) cage at R3C2 = {1237/1246}, no 5, 1 locked for R4 and N4, clean-up: no 5 in R5C4, no 9 in R6C4
36b. 1,4,7 only in R4C12 -> no 3,6 in R4C12

37. Naked pair {27} in R9C78, locked for R9 and N9

38. 14(3) cage at R6C8 (step 29) = {158} (only remaining combination, cannot be {356} because R7C23 = [67] clashes with 19(4) cage at R8C2), CPE no 1,5,8 in R8C8

39. 3 in N9 only in R8C78 + R9C9, locked for 21(4) cage at R8C6, no 3 in R8C6
39a. 21(4) cage at R8C6 (step 24) = {1389/3459}, no 7

40. R56C1 = {367} -> 12(3) cage in N4 = {237} (only combination containing two of 3,6,7) -> R5C2 = 2, R56C1 = {37}, locked for C1 and N4, clean-up: no 8,9 in R4C4, no 4 in R5C34, no 3,7,8 in R6C4

41. R4C1 = 1, R4C2 = 4, R3C3 = 2 (hidden single in N1), placed for D\, R3C2 = 6 (step 36a), R2C3 = 3, R5C34 = [51], R9C23 = [84], R6C2 = 9, R8C4 = 7 (step 6), R9C1 = 6, R7C3 = 7, both placed for D/, R1C23 = [19], R8C3 = 1, R7C2 = 3 (step 13), R8C2 = 5, placed for D/
[No more routine clean-up]

42. R3C7 = 1, R6C4 = 2 (hidden singles on D/), R6C3 = 8, R4C3 = 6, R4C4 = 5, placed for D\, R7C7 = 8, placed for D\, R5C5 = 3, placed for both diagonals, R8C8 = 9, placed for D\, R1C9 = 8, placed for D/

and the rest is naked singles without using the diagonals.

Sorry to take so long to get back about this V2. Thanks to Mike and Andrew for trying it and for your feedback.No rationale. Just being pragmatic. It seems to give me interesting puzzles that I enjoy solving and sharing. That may be a pure fluke. These days I just bash out any old cage pattern that doesn't yield high scoring puzzles, take the highest scoring one that JSudoku also says is interesting (ie, something more than "quadruple innies and outies" in the "Deduce All Moves" log), then solve it myself and hope I enjoy it. If not, move on. So far, it gives me a puzzle first time that I enjoy. Good point. "Samey" puzzles would be terrible. If they start to feel this way, please let me know. I've already been worried about too many small cages.I'm the opposite. The logs look "ruudiculous" to me because I don't really understand them. As long as they are interesting puzzlesBy contrast, I do understand SS! Hence, I try not to look at the solver log when I'm looking for an Assassin, or working on someone elses puzzle for that matter. The score is enough of a hint for me. Don't want to blinker my own solving.

BTW, Richard has described all his solver routines in the Help file with SudokuSolver (Help-Index-Solver Routines-"here" link). It might be useful if I did up a little table to correlate his terminology with ours. Eg, what we call Locking Cages he calls Dependant Cage Sums (though it only covers the simplest case of Locking Cages). Let me know if you think that would be worthwhile. I've talking with Andrew (by PM) before about doing this. Could be good to put on the Killer Techniques forum as a resource. You could add JSudoku's terms Mike!

Great work Mike!!! We worked in the same areas but you expressed it much better. It's like Half-cage combining. Really neat! The way I saw your step 4 was chainy,

4. 1 in n3 in r3 or in r2c9.
4a. If it's in r3 -> 1 in n1 in 10(2)n1 = {19}
4b. If it's in r2c9 -> r2c1 = 6 (h7(2)r2c19) and r3c1 = 7
4c. -> [49] blocked from 13(2)n1 (Locking-out Cages)
4d. and {37/46} blocked from 10(2)n1 (Locking-out Cages)

Note that this move (either variation) is available from step 1 in the original Assassin and effectively cracks it in one step.

I found Mike's 13c but missed the resulting hidden single. Instead I used when outies n7 = [88], 8 in n7 must be in 12(2) = {48} -> combo's in the 19(4)n7 with 8 in r8c4 cannot also have 4. This locks 7 in the cage -> r8c1 = 2.

My apologies to Andrew. I couldn't finish his WT even though he does similar work to my final move. Don't have the patience anymore for more than a couple of steps like that.

Cheers
Ed