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I have not solved or tried to solve any of the six A178 killer/assassin puzzles myself. This is what I tried to say with the sentence you have quoted. Sorry that I did not express myself clearly enough.

_________________
Quis custodiet ipsos custodes?

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That's certainly true. "The Short Redhead" was more of a challenge than "the Short Blonde".

Afmob and manu both had interesting ways to crack V1.


Here is my walkthrough for A178 V1. Thanks Afmob for pointing out typos and a combo elimination that I'd overlooked.

Prelims

a) 11(2) cage in N1 = {29/38/47/56}, no 1
b) R1C34 = {18/27/36/45}, no 9
c) R1C67 = (49/58/67}, no 1,2,3
d) 11(2) cage in N3 = {29/38/47/56}, no 1
e) R2C34 = {18/27/36/45}, no 9
f) R2C67 = {18/27/36/45}, no 9
g) R34C1 = {14/23}
h) 10(2) cage at R3C3 = {19/28/37/46}, no 5
i) 7(2) cage at R3C7 = {16/25/34}, no 7,8,9
j) R34C9 = {39/48/57}, no 1,2,6
k) R67C1 = {18/27/36/45}, no 9
l) 15(2) cage at R6C2 = {69/78}
m) 12(2) cage at R6C8 = {39/48/57}, no 1,2,6
n) R67C9 = {49/58/67}, no 1,2,3
o) 7(2) cage in N7 = {16/25/34}, no 7,8,9
p) R8C34 = {29/38/47/56}, no 1
q) R8C67 = {39/48/57}, no 1,2,6
r) 12(2) cage in N9 = {39/48/57}, no 1,2,6
s) R9C34 = {18/27/36/45}, no 9
t) R9C67 = {18/27/36/45}, no 9
u) 20(3) cage in N1 = {389/479/569/578}, no 1,2
v) 11(3) cage in N3 = {128/137/146/236/245}, no 1
w) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
x) 11(3) cage at R5C1 = {128/137/146/236/245}, no 9
y) 10(3) cage in N9 = {127/136/145/235}, no 8,9

1. 45 rule on C1234 1 innie R5C4 = 5, clean-up: no 4 in R12C3, no 6 in R8C3, no 4 in R9C3
1a. 45 rule on R6789 1 innie R6C5 = 2, clean-up: no 7 in R7C1
1b. R5C4 + R6C5 = 7 -> R4C5 + R5C6 = 15 = {69/78}

2. 45 rule on C6789 1 innie R5C6 = 1 outie R5C5 + 4 -> R5C5 = {34}, R5C6 = {78}, clean-up: no 6,9 in R4C5 (step 1b)
2a. 45 rule on R1234 1 innie R4C5 = 1 outie R5C5 + 3 -> R4C5 = 7, R5C5 = 4, R5C6 = 8, clean-up: no 5 in R1C7, no 1 in R2C7, no 3 in R3C3, no 5 in R3C9, no 4 in R8C7, no 1 in R9C7
2b. 15(4) cage at R3C6 = 4{128/137/236}, no 5,9
2c. 1 of {128} must be in R4C6, 7 of {137} must be in R3C6 -> no 1 in R3C6
2d. 1 in C7 locked in R3456C7, CPE no 1 in R4C8, clean-up: no 6 in R3C7

3. 11(3) cage at R5C1 = {137/236}, 3 locked for R5 and N4, clean-up: no 2 in R3C1, no 7 in R3C3, no 6 in R7C1
3a. 9 in R5 locked in 17(3) cage at R5C7, locked for N6, clean-up: no 3 in R3C9, no 3 in R7C7, no 4 in R7C9

4. 19(3) cage at R3C4 = {289/379/469/568} (cannot be {478} because R4C4 only contains 3,6,9)
4a. 7 of {379} must be in R3C4 -> no 3 in R3C4

5. 45 rule on C12 3 outies R357C3 = 11 = {128/137/146/236}, no 9, clean-up: no 1 in R4C2, no 6 in R6C2
5a. 45 rule on C12 2 innies R46C2 = 1 outie R5C3 + 14
5b. Min R46C2 = 15 -> no 2,4 in R4C2, clean-up: no 6,8 in R3C3
5c. Max R46C2 = 17 -> max R5C3 = 3

6. 45 rule on C89 2 outies R35C7 = 1 innie R6C8 + 3, IOU no 3 in R3C7, clean-up: no 4 in R4C8
6a. 45 rule on C89 2 outies R57C7 = 1 innie R4C8 + 8, IOU no 8 in R7C7, clean-up: no 4 in R6C8
6b. 45 rule on C89 2 innies R46C8 = 1 outie R5C7 + 4
6c. R46C8 cannot total 6 -> no 2 in R5C7
6d. 45 rule on C89 3 outies R357C7 = 15 = {159/249/267/456}
6e. 6 of {267} must be in R5C7 -> no 7 in R5C7
6f. R5C7 = {169} -> R46C8 = 5,10,13 = [23/28/37/58/67], no 5 in R6C8, clean-up: no 7 in R7C7
[I originally saw that R357C7 cannot be [267] because R46C8 cannot be [55]. Then I looked for simpler steps to avoid this two column clash.]

7. 45 rule on R12 3 outies R3C258 = 19 = {289/379/469/478/568}, no 1

8. 45 rule on R89 3 outies R7C258 = 9 = {126/135/234}, no 7,8,9

9. 45 rule on N7 4 innies R7C13 + R89C3 = 25
9a. Max R7C13 + R9C3 = 21 -> min R8C3 = 4, clean-up: no 8,9 in R8C4
9b. 25(4) has five combinations containing 9, which must be in R8C3, and {4678} -> no 5 in R8C3, clean-up: no 6 in R8C4
[Alternatively for step 9b, the only way R7C13 + R9C3 can total 20 is {578} -> no 5 in R8C3 ...]

10. 45 rule on N9 4 innies R7C79 + R89C7 = 23 = {2489/2579/3569/4568} (cannot be {2678} because R7C7 only contains 4,5,9, cannot be {3479/3578} which clash with the 12(2) cage)
10a. 2 of {2579/2678} must be in R9C7 -> no 7 in R9C7, clean-up: no 2 in R9C6

11. R46C2 = R5C3 + 14 (step 5a)
11a. R5C3 = {123} -> R46C2 = 15,16,17 = {69/78/79/89}
11b. 20(3) cage in N1 = {389/479/569/578}
11c. 3,4 of {389/479} must be in R13C2 (R13C2 cannot be {79/89} which clash with R46C2), no 3,4 in R2C1

12. 45 rule on C12 4 innies R456C2 + R5C1 = 25 = {1789/2689/3679}, 9 locked for C2 and N4, clean-up: no 2 in R1C1
12a. 20(3) cage in N1 = {389/479/569/578}
12b. 9 of {569} must be in R2C1 -> no 6 in R2C1

13. R8C3 = 9 (hidden single in C3), R8C4 = 2, clean-up: no 7 in R12C3, no 3 in R8C67, no 5 in R9C1, no 7 in R9C3, no 3 in R9C9
13a. 7 in C3 locked in R67C3, CPE no 7 in R6C2 + R7C4, clean-up: no 8 in R7C3
13b. 9 in N4 locked in R46C2
13c. R46C2 = R5C3 + 14 (step 5a)
13d. R46C2 = {69/89} = 15,17 -> R5C3 = {13}

14. 17(3) cage at R5C7 = {179/269}
14a. 45 rule on C89 4 innies R456C8 + R5C9 = 21 = {1578/2379/2568} (cannot be {1389/1569} because no 7 in R5C7 so R5C89 cannot be {19}, cannot be {3567} because 17(3) cannot have both of 6,7)
14b. 2,6 of {2568} must be in R5C89 -> no 6 in R4C8, clean-up: no 1 in R3C7
14c. 1 in C7 locked in R456C7, locked for N6
14d. R456C8 + R5C9 = {2379/2568}, 2 locked for N6

15. 15(4) cage at R3C6 (step 2b) = 4{128/137/236}
15a. 2,7 only in R3C6 -> R3C6 = {27}

16. 1 in R3 locked in R3C13, locked for N1, clean-up: no 8 in R12C4

17. 19(3) cage at R3C4 (step 4) = {289/469/568} (cannot be {379} because no 3,7,9 in R4C3), no 3,7
17a. 2,5 of {289/568} must be in R4C3 -> no 8 in R4C3

18. 1 in N1 locked in R3C13
18a. 45 rule on N1 4 innies R12C3 + R3C13 = 14 = {1238/1256/1346} with 6 or 8 in R12C3
18b. 45 rule on N7 3 remaining innies R7C13 + R9C3 = 16 = {178/268/367/457} (cannot be {358} because R7C3 only contains 6,7)
18c. 2 of {268} must be in R9C3 (R79C3 cannot be {68} which clashes with R12C3), no 2 in R7C1, clean-up: no 7 in R6C1

19. 45 rule on N7 3(2+1) remaining outies R6C12 + R9C4 = 17
19a. R6C12 cannot total 16 -> no 1 in R9C4, clean-up: no 8 in R9C3
19b. Min R6C2 + R9C4 = 11 -> no 8 in R6C1, clean-up: no 1 in R7C1

20. 17(3) cage at R6C3 = {179/359/368/467} (cannot be {458} because no 4,5,8 in R6C4)
20a. 7 of {179/467} must be in R6C3 -> no 1,4 in R6C3
20b. 4 in C3 locked in R34C3, CPE no 4 in R3C4

21. 7 in C4 locked in R129C4 -> 2 in C3 locked in R129C3 (locking 9(2) cages), locked for C3, clean-up: no 8 in R4C2
21a. Naked pair {69} in R4C24, locked for R4

22. 19(3) cage at R3C4 (step 17) = {469/568}
22a. 6 locked in R34C4, locked for C4, clean-up: no 3 in R129C3

23. R5C3 = 3 (hidden single in C3)
23a. R46C2 = R5C3 + 14 (step 5a)
23b. R5C3 = 3 -> R46C2 = 17 = [98], R3C3 = 1, R7C3 = 7, R4C4 = 6, clean-up: no 3 in R1C1, no 4 in R4C1, no 6 in R6C9, no 4 in R7C7, no 5 in R7C9, no 8 in R9C4

24. 15(4) cage at R3C6 (step 2b) = 4{128/137}, 1 locked for R4 -> R4C1 = 2, R3C1 = 3, clean-up: no 8 in R1C1, no 5 in R3C7, no 6 in R5C12 (step 3), no 6 in R6C1, no 4,5 in R8C2
24a. Naked pair {17} in R5C12, locked for R5 and N4, clean-up: no 8 in R7C1
24b. Naked triple {269} in R5C789, locked for N6
24c. Naked pair {45} in R67C1, locked for C1, clean-up: no 6,7 in R2C2, no 3 in R8C2

25. Naked pair {16} in 7(2) cage in N7, locked for N7 -> R8C1 = 8, clean-up: no 4 in R8C6, no 3 in R9C4, no 4 in R9C9
25a. R8C1 = 8 -> R79C2 = 5 = {23}, locked for C2 and N7 -> R9C3 = 5, R9C4 = 4, R67C1 = [54], R4C3 = 4, R3C4 = 9 (step 22), R6C3 = 6, clean-up: no 9 in R1C1, no 3 in R12C4, no 8 in R3C9, no 3 in R4C9, no 8 in R7C9, no 7 in R8C8

26. Naked pair {17} in R12C4, locked for C4 and N2 -> R67C4 = [38], R34C6 = [21], R4C7 = 8 (step 24), R6C6 = 9, R6C8 = 7, R7C7 = 5, R6C9 = 4, R7C9 = 9, R6C7 = 1, R7C6 = 3 (cage sum), R79C2 = [23], R3C7 = 4, R4C8 = 3, R34C9 = [75], R8C8 = 4, R9C9 = 8, R8C67 = [57], clean-up: no 6 in R1C67, no 4 in R2C6, no 2,6 in R2C7, no 2,6 in R2C8, no 6 in R9C67

and the rest is naked singles and a cage sum.

I decided to have one more try at these puzzles, having started A178 V1.5 after finishing the V1.

They certainly are. I found the "Tall Blonde" and later the "Tall Redhead" very hard going, to the extent that these "young women" got some fairly rough handling in the form of contradiction moves. Also if the 16(3) cages at R1C5 and R7C5, 11(3) cage at R5C1 and 17(3) cage at R5C7 hadn’t quickly reduced to two combinations I probably wouldn’t have been able to solve it; those pairs of combinations were very helpful for some of the contradiction moves.


Here is my walkthrough for A178 V1.5 "Tall Blonde".

Prelims

a) 11(2) cage in N1 = {29/38/47/56}, no 1
b) 11(2) cage in N3 = {29/38/47/56}, no 1
c) R2C34 = {18/27/36/45}, no 9
d) R2C67 = {18/27/36/45}, no 9
e) R34C1 = {14/23}
f) 10(2) cage at R3C3 = {19/28/37/46}, no 5
g) 7(2) cage at R3C7 = {16/25/34}, no 7,8,9
h) R34C9 = {39/48/57}, no 1,2,6
i) R67C1 = {18/27/36/45}, no 9
j) 15(2) cage at R6C2 = {69/78}
k) 12(2) cage at R6C8 = {39/48/57}, no 1,2,6
l) R67C9 = {49/58/67}, no 1,2,3
m) 7(2) cage at R8C2 = {16/25/34}, no 7,8,9
n) R8C34 = {29/38/47/56}, no 1
o) R8C67 = {39/48/57}, no 1,2,6
p) 12(2) cage at R8C8 = {39/48/57}, no 1,2,6
q) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
r) 11(3) cage at R5C1 = {128/137/146/236/245}, no 9

1. 45 rule on C1234 1 innie R5C4 = 5, clean-up: no 4 in R2C3, no 6 in R8C3
1a. 45 rule on R6789 1 innie R6C5 = 2, clean-up: no 7 in R7C1
1b. R5C4 + R6C5 = 7 -> R4C5 + R5C6 = 15 = {69/78}

2. 45 rule on R5 2 remaining innies R5C56 = 12 = [39/48]
2a. 45 rule on C6789 1 innie R5C6 = 1 outie R5C5 + 4 -> R5C5 = 4, R5C6 = 8, R4C5 = 7 (step 1b), clean-up: no 1 in R2C7, no 3 in R3C3, no 5 in R3C9, no 4 in R8C7
2b. 15(4) cage at R3C6 = 4{128/137/236}, no 5,9
2c. 1 of {128} must be in R4C6, 7 of {137} must be in R3C6 -> no 1 in R3C6

3. 11(3) cage at R5C1 = {137/236}, 3 locked for R5 and N4, clean-up: no 2 in R3C1, no 7 in R3C3, no 6 in R7C1
3a. 9 in R5 only in 17(3) cage at R5C7, locked for N6, clean-up: no 3 in R3C9, no 3 in R7C7, no 4 in R7C9

4. 1,2 in N9 only in R7C8 + R8C9 + R9C78, locked for 19(5) cage at R7C8, no 1,2 in R9C6

5. 45 rule on R12 3 outies R3C258 = 19, no 1

6. 45 rule on R89 3 outies R7C258 = 9 = {126/135/234}, no 7,8,9

7. 19(3) cage at R3C4 = {289/379/469/568} (cannot be {478} because R4C4 only contains 3,6,9)
7a. 7 of {379} must be in R3C4 -> no 3 in R3C4

8. 45 rule on N7 3 innies R7C13 + R8C3 = 1 outie R9C4 + 16
8a. Max R7C13 + R8C3 = 24 -> max R9C4 = 8

9. R34C1 = {14}/[32], R67C1 = {18/45}/[63/72] -> combined cage R3467C1 = {14}[63]/{14}[72]/[32]{18}/[32]{45}
9a. R3467C1 = {14}[63] => 11(3) cage at R5C1 (step 3) = {137} => no 2 in R5C1
or R3467C1 = {14}[72]/[32]{18}/[32]{45}, 2 locked for C1
-> no 2 in R5C1

10. 5 in R3 only in R3C2578
10a. R3C258 = 19 (step 5) = {289/379/469/478/568}
10b. R3C258 = {568} or 7(2) cage at R3C7 = [52] -> 2 of {289} must be in R3C2, no 2 in R3C8 (blocking cages)

11. 19(5) cage at R7C8 = {12349/12358/12367/12457}
11a. 8 of {12358} must be in N9 => 12(2) cage at R8C8 = {39/57} => R7C7 = 4 (hidden single in N7), R6C8 = 8 -> no 8 in R9C8

12. 19(5) cage at R7C8 = {12349/12358/12367/12457}
12a. {12349/12358} => R7C9 = 6 (hidden single in N9), R6C9 = 7 => no 7 in R9C9
or {12367/12457} => no 7 in R9C9
-> no 7 in R9C9, clean-up: no 5 in R8C8

[I then had a forcing chain which eliminated 8 from R8C9 but that was superseded by the following contradiction move.]

13. 9 in R5 locked in 17(3) cage at R5C7 (step 3a) = {179/269}
13a. R3C258 = {568} or 7(2) cage at R3C7 = [52] (step 10b)
13b. 19(5) cage at R7C8 = {12349/12358/12367/12457} cannot be {12358}, here’s how
8 of {12358} must be in N9 => 12(2) cage at R8C8 = {39} (cannot be [75] because {12358} “sees” R9C9), locked for N9 => 3 of {12358} must be in R9C6 => R9C9 = 9, R7C9 = 6 (hidden single in N9), R6C9 = 7, R7C7 = 4 (hidden single in N9) => R6C8 = 8, R34C9 = {48} (only remaining combination) => R3C9 = 8, 17(3) cage at R5C7 = {269} (only remaining combination) => R5C9 = 2
so cannot place 5 in R3 because R3C9 = 8 blocked R3C258 = {568} and R5C9 = 2 blocks 7(2) cage at R3C7 = [52]
-> 19(5) cage at R7C8 = {12349/12367/12457}, no 8

[At this stage I can see that if 19(5) cage = {12349/12457} then R7C9 = 6, R6C9 = 7, 17(3) cage at R5C7 = {269}, no 5 in R3C7 so R3C258 = {568}. What I don’t yet know is what happens if 19(5) cage = {12367}.]

14. 19(5) cage at R7C8 = {12349/12367/12457}
5 of {12457} cannot be in R9C6, here’s how
R9C6 = 5 => 4,7 of {12457} locked for N9 => 12(2) cage at R8C8 = {39}, R7C9 = 6 (hidden single in N9), R6C9 = 7, R78C7 = {58} (hidden pair in N9) => R7C7 = 8 (12(2) cage at R6C8 cannot be [75] which clashes with R6C9), R6C8 = 4, R8C7 = 5, R8C6 = 7, R34C9 = [48] (cannot be [93] which clashes with R9C9), R4C8 = 5 (hidden single in N6), R3C7 = 2 => all combinations for 15(4) cage at R3C6 (step 2b) = 4{128/137/236} because is blocked by R3C7 = 2 and R8C6 = 7
-> no 5 in R9C6

15. 19(5) cage at R7C8 = {12349/12367/12457}
6 of {12367} cannot be in R9C6, here’s how
R9C6 = 6 => 3,7 of {12367} locked for N9 => 12(2) cage at R8C8 = {48}, R7C9 = 6 (hidden single in N9), R6C9 = 7, R78C7 = {59} (hidden pair in N9) => R7C7 = 9 (12(2) cage at R6C8 cannot be [75] which clashes with R6C9), R6C8 = 3 => all combinations for R34C9 blocked by R6C8 = 3, R6C9 = 7 and R9C9 = {48}
-> no 6 in R9C6

16. R34C9 = {48}/[75/93], R67C9 = [49]/{58/67} -> combined cage R3467C9 = {48}{67}/[75][49]/[93]{58}/[93]{67}
16a. 16(3) cage at R7C5 = {169/358}
[These are for use in later steps.]

17. 19(5) cage at R7C8 = {12349/12367/12457}
3 cannot be in R9C6, here’s how
R9C6 = 3 => R8C8 = 3 (hidden single in N9, R8C67 cannot be [93] because R89C6 = [93] clashes with 16(3) cage at R7C5), R9C9 = 9, R3467C9 = {48}{67} (only remaining combination) => R7C9 = {67} => {12349} clashes with R9C9 and {12367} clashes with R7C9
-> no 3 in R9C6

18. 45 rule on N9 3 innies R7C79 + R8C7 = 1 outie R9C6 + 14
18a. R9C6 = {479} => R7C79 + R8C7 = 18,21,23
R9C6 = 4 => 19(5) cage at R7C8 = {12349/12457}, R7C9 = 6 (hidden single in N9), R6C9 = 7, R78C7 = 12 cannot be [93] because R7C7 = 9, R6C8 = 3, R8C8 = 4 (hidden single in N9), R9C9 = 8 => all combinations for R34C9 blocked by R6C8 = 3, R6C9 = 7 and R9C9 = 8
or R6C6 = {79} => R7C79 + R8C7 = 21,23 cannot contain 3
-> no 3 in R8C7, clean-up: no 9 in R8C6

19. R9C6 = {479} => R7C79 + R8C7 = 18,21,23 (step 18a)
R9C6 = 4 => 19(5) cage at R7C8 = {12349/12457}, R7C9 = 6 (hidden single in N9), R6C9 = 7 => R7C79 + R8C7 = 18 = [765] (cannot be [468] because R8C67 = [48] clashes with R9C6, cannot be [567] because 12(2) cage at R6C8 = [75] clashes with R6C9)
or R9C6 = 7 => R7C79 + R8C7 = 21 = {579/678} (cannot be {489}, locked for N9 => 12(2) cage at R8C8 = [75] because [489] => R6C9 = 5 clashes with R9C9 and [498] => R6C9 = 4 => all combinations for R34C9 blocked by R6C9 = 4, R7C9 = 9 and R9C9 = 5
or R9C6 = 9 => R7C79 + R8C7 = 23 = {689} => R7C9 = 6
-> R7C79 + R8C7 = [765]/{579/678/689}, no 4, clean-up: no 8 in R6C8
19a. 6 of {678/689} must be in R7C9 -> no 8 in R7C9, clean-up: no 5 in R6C9

20. 17(3) cage at R5C7 = {179/269}
20a. R7C79 + R8C7 = [765]/{579/678/689} (step 19)
{579} = 21 => R9C6 = 7 (step 18)
{579} cannot be [579] (because R6C89 = [76] clashes with 17(3) cage at R5C7), cannot be [975] because R8C67 = [75] clashes with R9C6 = 7)
6 of other combinations must be in R7C9
-> no 7 in R7C9, clean-up: no 6 in R6C9
20b. 8 cannot be in R7C7, here’s how
{678} = [867] = 21, R9C6 = 7 (step 18), R6C8 = 4, R6C9 = 7, R4C9 = 8 (hidden single in N6), 17(3) cage at R5C7 = {269} (only remaining combination), locked for N6, 15(4) cage at R3C6 (step 2b) = 4{236} (only remaining combination) => R4C7 = 3, R34C6 = [26], R6C7 = 5 (hidden single in N6, 5 cannot be in R4C8 because 7(2) cage at R3C7 = [25] clashes with R3C6), R67C6 = 8 = [17/62] which clash with R9C6 and R34C6
or {689} = [869] = 23, R9C6 = 9 (step 18), R8C6 = 3 -> R89C6 = [39] clashes with 16(3) cage at R7C5
-> no 8 in R7C7, clean-up: no 4 in R6C8
20c. R7C79 + R8C7 cannot be {678}, here’s how
{678} = [768] = 21, R9C6 = 7 (step 18), R6C8 = 5, R6C9 = 7, R4C9 = 8 (hidden single in N6), 17(3) cage at R5C7 = {269} (only remaining combination), locked for N6, 15(4) cage at R3C6 (step 2b) = 4{236} (only remaining combination) => R4C7 = 3, R34C6 = [26], R6C7 = 4 (hidden single in N6, 4 cannot be in R4C8 because 7(2) cage at R3C7 = [34] clashes with R3C6), R67C6 = 9 = {36} clashes with R4C6
-> R7C79 + R8C7 = [765]/{579}/[968]

21. R7C79 + R8C7 = [765]/{579}/[968]
21a. R7C79 + R8C7 = [765]/{579}
or R7C79 + R8C7 = [968] => 12(2) cage at R8C8 = [75]
-> 5 must be in R7C79 + R8C7 + R9C9, locked for N9

22. 19(5) cage at R7C8 (step 13b) = {12349/12367}, 3 locked for N9, clean-up: no 9 in 12(2) cage at R8C8
22a. 4 of {12349} cannot be in R9C6, here’s how
R9C6 = 4 => R7C79 + R8C7 = 18 (step 18a) = [765], R6C8 = 5, R6C9 = 7, R8C6 = 7, 12(2) cage at R8C8 = [48], R34C9 = [93] (cannot be {48} which clashes with R9C9), R6C7 = 4 (hidden single in N6), R67C6 = 9 = [63], 16(3) cage at R7C5 = {169} (only remaining combination), locked for N8, R7C3 = 9 (hidden single in R7), R6C2 = 6 clashes with R6C6
-> no 4 in R9C6

23. 19(5) cage at R7C8 (step 13b) = {12349/12367}
23a. R9C6 = {79} -> no 7,9 in R8C9 + R9C78

24. R9C6 = {79} -> R7C79 + R8C7 = 21,23 (step 18) = {579}/[968]
[Just restating this for the next two steps.]

25. Consider placements for R9C6
R9C6 = 7
or R9C9 = 9 => R7C79 + R8C7 = 21 = [968] (step 24) => R8C8 = 7 (hidden single in N9)
-> 7 must be in R8C8 + R9C6, CPE no 7 in R8C46, clean-up: no 4 in R8C3, no 5 in R8C7

26. Consider placements for R9C6
R9C6 = 7 => R7C79 + R8C7 = 21 = {579} (step 24) => R8C7 = {79} => R8C6 = {35} => 16(3) cage at R7C5 = {169} (only remaining combination)
or R9C6 = 9
-> 9 must be in R89C5 + R9C6, locked for N8, clean-up: no 2 in R8C3

27. 19(5) cage at R7C8 (step 13b) = {12349/12367} cannot be {12349}, here’s how
{12349} => R9C6 = 9, 16(3) cage at R7C5 (step 16a) = {358} (only remaining combination), locked for N8, R7C79 + R8C7 = 21 = [968] (step 24), R6C9 = 7, 17(3) cage at R5C7 (step 13) = {269} (only remaining combination), locked for R5 => 11(3) cage at R5C1 = {137}, 15(2) cage at R6C2 = {78} => R6C2 = 8, R7C3 = 7, R7C1 = 8 (hidden single in R7), R6C1 = 1 clashes with 11(3) cage at R5C1
-> 19(5) cage at R7C8 = {12367}, no 4,9

[No more contradiction moves!]

28. 19(5) cage at R7C8 = {12367} -> R9C6 = 7, 6 locked for N9, clean-up: no 2 in R2C7, no 7 in R6C9
28a. R9C6 = 7 -> R7C79 + R8C7 = 21 = {579} (step 24), locked for N9, 5 also locked for R7, 7 also locked for C7, clean-up: no 2 in R2C6, no 4 in R6C1, no 4 in R8C6
28b. Naked pair {48} in R69C9, locked for C9, clean-up: no 3,7 in R2C8
28c. Killer pair 5,9 in R34C9 and R7C9, locked for C9, clean-up: no 2,6 in R2C8

29. 16(3) cage at R7C5 (step 16a) = {169} (cannot be {358} which clashes with R8C6), locked for C5 and N8, clean-up: no 5 in R8C3
29a. Naked triple {358} in 16(3) cage at R1C5, locked for N2, clean-up: no 1,6 in R2C3, no 4,6 in R2C7

30. R8C6 = 5 (hidden single in N8), R8C7 = 7, clean-up: no 5 in R6C8, no 4 in R8C4
30a. Naked pair {59} in R7C79, locked for R7, clean-up: no 6 in R6C2

31. 15(4) cage at R3C6 (step 2b) = 4{128/236}, CPE no 2 in R3C7, clean-up: no 5 in R4C8
31a. 8 of 4{128} must be in R4C7 -> no 1 in R4C7

32. 19(3) cage at R3C4 (step 7) = {289/379/469} (cannot be {568} because 5,8 only in R4C3), no 5
32a. 8 of {289} must be in R4C3 -> no 2 in R4C3

33. 17(3) cage at R6C3 = {269/359/368/467} (cannot be {179} because no 1,7,9 in R7C4, cannot be {278/458} because R6C4 only contains 3,6,9), no 1
33a. 7 of {467} must be in R6C3 -> no 4 in R6C3
33b. 4 in N4 only in R4C123, locked for R4, clean-up: no 3 in R3C7
33c. 1 in N5 only in R46C6, locked for C6, clean-up: no 8 in R2C7

34. 45 rule on N3 3 innies R2C7 + R3C79 = 1 outie R1C6 + 10
34a. R2C7 + R3C79 cannot total 12,19 -> no 2,9 in R1C6

35. Naked pair {46} in R12C6, locked for C6 and N2 -> R3C6 = 2, R7C6 = 3, R4C6 = 1, R4C7 = 8 (cage sum), R6C6 = 9, R6C7 = 1 (cage sum), clean-up: no 3,5,7 in R2C3, no 4 in R3C1, no 9 in R3C3, no 6 in 7(2) cage at R3C7, no 7 in 17(3) cage at R5C7 (step 13), no 6 in R6C1, no 8 in R7C1, no 6 in R7C3

36. Naked triple {269} in 17(3) cage at R5C7, locked for R5 and N6 -> R4C8 = 3, R3C7 = 4, R4C9 = 5, R3C9 = 7, R67C9 = [49], R6C8 = 7, R7C7 = 5, R2C7 = 3, R2C6 = 6, R1C6 = 4, R3C4 = 9, R4C4 = 6, R4C3 = 4, R4C1 = 2, R3C1 = 3, R4C2 = 9, R3C3 = 1, R6C2 = 8, R7C3 = 7, R5C3 = 3, R6C1 = 5, R7C1 = 4, R6C34 = [63], R7C4 = 8 (step 33), R9C9 = 8, R8C8 = 4, R8C4 = 2, R8C3 = 9, R9C4 = 4, clean-up: no 8 in R1C1, no 7 in R2C2, no 8 in R2C8, no 3 in R8C2

37. Naked pair {16} in 7(2) cage at R8C2, locked for N7 -> R7C2 = 2, R8C1 = 8, R9C23 = [35]

38. Naked pair {26} in R15C9, locked for C9 -> R2C9 = 1, R8C9 = 3, R2C4 = 7, R2C3 = 2, R1C34 = [81], R2C1 = 9, R2C8 = 5, R1C9 = 6

and the rest is naked singles.

And then the "Tall Redhead" got even more rough handling in the form of contradiction moves and, in at least one case, a contradiction within a contradition. Again if the 16(3) cages at R1C5 and R7C5, 11(3) cage at R5C1 and 17(3) cage at R5C7 hadn’t quickly reduced to two combinations I probably wouldn’t have been able to solve it; those pairs of combinations were very helpful for some of the contradiction moves. Also in this case the three 9(2) cages in C34 and the two 9(2) cages in C67 were very helpful and provided interest to some of the contradiction moves.


Here is my walkthrough for A178 V2 "Tall Redhead"

Prelims

a) R1C34 = {18/27/36/45}, no 9
b) R1C67 = {49/58/67}, no 1,2,3
c) R2C34 = {18/27/36/45}, no 9
d) R2C67 = {18/27/36/45}, no 9
e) R34C1 = {14/23}
f) R34C9 = {39/48/57}, no 1,2,6
g) R67C1 = {18/27/36/45}, no 9
h) R67C9 = {49/58/67}, no 1,2,3
i) R8C34 = {29/38/47/56}, no 1
j) R8C67 = {39/48/57}, no 1,2,6
k) R9C34 = {18/27/36/45}, no 9
l) R9C67 = {18/27/36/45}, no 9
m) 20(3) cage in N1 = {389/479/569/578}, no 1,2
n) 11(3) cage in N3 = {128/137/146/236/245}, no 9
o) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
p) 11(3) cage at R5C1 = {128/137/146/236/245}, no 9
q) 10(3) cage in N9 = {127/136/145/235}, no 8,9

1. 45 rule on C1234 1 innie R5C4 = 5, clean-up: no 4 in R1C3, no 4 in R2C3, no 6 in R8C3, no 4 in R9C3
1a. 45 rule on R6789 1 innie R6C5 = 2, clean-up: no 7 in R7C1
1b. R5C4 + R6C5 = 7 -> R4C5 + R5C6 = 15 = {69/78}

2. 45 rule on R5 2 remaining innies R5C56 = 12 = [39/48]
2a. 45 rule on C6789 1 innie R5C6 = 1 outie R5C5 + 4 -> R5C5 = 4, R5C6 = 8, R4C5 = 7 (step 1b), clean-up: no 5 in R1C7, no 1 in R2C7, no 5 in R3C9, no 4 in R8C7, no 1 in R9C7
2b. 15(4) cage at R3C6 = 4{128/137/236}, no 5,9
2c. 1 of {128} must be in R4C6, 7 of {137} must be in R3C6 -> no 1 in R3C6

3. 11(3) cage at R5C1 = {137/236}, 3 locked for R5 and N4, clean-up: no 2 in R3C1, no 6 in R7C1
3a. 9 in R5 locked in 17(3) cage at R5C7, locked for N6, clean-up: no 3 in R3C9, no 4 in R7C9
3b. 17(3) cage at R5C7 = {179/269}
3c. 16(3) cages at R1C5 and R7C5 = {169/358}
[For use with later contradiction moves]

4. 45 rule on C12 3 outies R357C3 = 11 = {128/137/146/236/245}, no 9

5. 19(3) cage at R3C4 = {289/379/469/568} (cannot be {478} because R4C4 only contains 3,6,9)
5a. 7 of {379} must be in R3C4 -> no 3 in R3C4

6. R34C1 = {14}/[32], R67C1 = {18/45}/[63/72] -> combined cage R3467C1 = {14}[63]/{14}[72]/[32]{18}/[32]{45}
6a. R3467C1 = {14}[63] => 11(3) cage at R5C1 (step 3) = {137} => no 2 in R5C1
or R3467C1 = {14}[72]/[32]{18}/[32]{45}, 2 locked for C1
-> no 2 in R5C1

7. 1 in C4 only in R12679C4 -> R1C34 = [81] or R2C34 = [81] or 17(3) cage at R6C3 = {179} with R6C3 = {79} or R9C34 = [81] -> no 8 in R6C3 (locking-out cages)

8. 17(3) cage at R6C3 = {179/269/359/368/467} (cannot be {278/458} because R6C4 only contains 1,3,6,9)
8a. 2,8 of {269/368} must be in R7C4, 6 of {467} must be in R6C4 -> no 6 in R7C4

9. 10(3) cage in N9 = {127/136/145/235} cannot be {235}, here’s how
10(3) cage = {235} => 1 in N9 must be in 24(4) cage at R6C8 = {1689}, 9 locked for N9, R6C8 = {68} so consider the two candidates for R6C8
If R6C8 = 6 => R9C7 = 4 (hidden single in N9), R7C9 = 6 (hidden single in N9), R6C9 = 7 but R6C89 = [67] clashes with 17(3) cage at R5C7
Or if R6C8 = 8 => R9C7 = 4 (hidden single in N9), R9C6 = 5, R7C9 + R8C7 = {78} (hidden pair in N9) => R8C7 = 8 (R8C67 cannot be [57] which clashes with R9C6), R8C6 = 4, R7C9 = 7 (hidden single in N9), R6C9 = 6, 17(3) cage at R5C7 (step 3b) = {179} (only remaining combination), locked for R5) => 11(3) cage at R5C1 = {236}, locked for N4 => R34C1 = {14}, locked for C1 => R67C1 = [72], R8C34 = [56/92], R9C4 = 7 (hidden single in N8), R9C3 = 2 clashes with R7C1
-> 10(3) cage in N9 = {127/136/145}, 1 locked for N9

10. 45 rule on N9 3 innies R7C9 + R89C7 = 1 outie R6C8 + 11

11. 24(4) cage at R6C8 cannot be 1{689}, here’s how
24(4) cage = 1{689}, 6,8,9 locked for N9, R6C8 = 1 => R7C9 + R89C7 = 12 (step 10) = {237/345}
Cannot be {237} = [732] => R6C9 = 6 and R6C89 = [16] clashes with 17(3) cage at R5C7
Cannot be {345} = [534] => R8C6 = 9, R9C6 = 5 and R89C6 = [95] clashes with 16(3) cage at R7C5
-> no 1 in R6C8

12. 19(3) cage at R3C4 (step 5) = {289/379/469/568} cannot be {568}, here’s how
19(3) cage = {568} = [856], 9 in N5 only in R6C46, locked for R6, R8C3 = 9 (hidden single in C3), R8C4 = 2, 9 in C4 only in 17(3) cage at R6C3 = {179} (only remaining combination) => 4 in C4 only in R129C4 => 5 in one of R129C3 clashes with R4C3
-> 19(3) cage at R3C4 = {289/379/469}, no 5

13. 19(3) cage at R3C4 = {289/379/469} cannot be {379}, here’s how
19(3) cage = {379} = [793] => 17(3) cage at R6C3 (step 8) = {179/269/467}
Cannot be {179} = 7{19} => 2 in C4 only in R1289C4 => either 7 in one of R129C3 clashes with R6C3 or 9 in R8C3 clashes with R4C3
Cannot be {269} = [692] because R6C6 = 1, R4C6 = 6 => R3C6 + R4C7 = {23} (step 2b) => R4C7 = 2, 17(3) cage at R5C7 (step 3b) = {179} (only remaining combination), locked for R5 => 11(3) cage at R5C1 = {236} which clashes with R6C3
Cannot be {467} = [764] because R4C6 = 1, R6C6 = 9, 13(3) cage at R6C6 = {139} => R7C6 = 3, R8C4 = 9 (hidden single in C4) and R7C6 + R8C4 clash with 16(3) cage at R7C5)
-> 19(3) cage at R3C4 = {289/469}, no 3,7

14. 17(3) cage at R6C3 (step 8) = {179/269/359/368/467} cannot be {269}, here’s how
17(3) cage = {269} => R7C4 = 2, R6C34 = {69} => 1 in C4 only in R129C4 => 8 must be in R129C3, locked for C3 => R8C34 cannot be [83], 3 in C4 only in R129C4 => 6 must be in R129C3, locked for C3 => R6C34 = [96], R4C4 = 9, 19(3) cage at R3C4 (step 13) = {289} (only remaining combination) => R3C4 = 8, R4C3 = 2 => no 7 in R129C4, R8C4 = 7 (hidden single in C4), R8C3 = 4, 16(3) cage at R1C5 (step 3c) = {169} (only remaining combination), locked for C5 and N2, 16(3) cage at R7C5 = {358}, locked for N8, R9C4 = 1 (hidden single in C4), R8C6 = 9, R8C7 = 3 => R9C67 cannot be [63] => R9C6 = 4, R7C6 = 6, R6C67 = 7 = [34], R2C67 cannot be [54], R1C6 = 5 (hidden single in C6), R1C7 = 8, R4C6 = 1, 15(4) cage at R3C6 (step 2b) = 4{128} (only remaining combination) => R4C7 = 8 which clashes with R1C7
-> 17(3) cage at R6C3 = {179/359/368/467}, no 2

15. 17(3) cage at R6C3 = {179/359/368/467} cannot be {467}, here’s how
17(3) cage at R6C3 = {467} => R6C4 = 6, R4C4 = 9, R8C3 = 9 (hidden single in C3), R8C4 = 2, 19(3) cage at R3C4 (step 13) = {289} (cannot be {469} because caged X-Wing for 4,6 in 19(3) and 17(3) cages, no other 4,6 in C34 => no 5 in R129C3, R357C3 (step 4) = {128/137} so cannot place 5 in C3) => R3C4 = 8, 16(3) cage at R1C5 (step 3c) = {169}, locked for C5 and N2, 16(3) cage at R7C5 = {358}, locked for N8, R4C3 = 2 => no 7 in R129C4 => R7C4 = 7 (hidden single in C4), R9C4 = 1 (hidden single in C4), R7C6 = 9 (hidden single in C6) => R6C67 = 4 = {13}, R9C6 = 6 (hidden single in C6), R9C7 = 3, R6C7 = 1, 17(3) cage at R5C7 (step 3b) = {269}, locked for N6, R8C6 = 4, R8C7 = 8 => no remaining candidates in R4C7
-> 17(3) cage at R6C3 = {179/359/368}, no 4
15a. 6 of {638} must be in R6C3 -> no 6 in R6C4

16. 19(3) cage at R3C4 (step 13) = {289/469} cannot be {289}, here’s how
19(3) cage at R3C4 = {289} => R4C4 = 9, R3C4 + R4C3 = {28}, 17(3) cage at R6C3 (step 15) = {179/368} (cannot be {359} which clashes with R4C4 because 5 only in R6C3)
Cannot be {179} = [917] => R46C6 = {36}, locked for C6, no 1 in R129C3 => no 8 in R129C3, R357C3 (step 4) = {137/146/236/245} (cannot be {128} which clashes with R4C3) => 8 in C3 only in R48C3
If R4C3 = 8 => R3C4 = 2, R3C6 = 7, R4C67 = [31], 17(3) cage at R5C7 (step 3b) = {269} (only remaining combination), locked for R5 => 11(3) cage at R5C1 = {137}, R1289C4 = {3468} with 3,6 in two of the 9(2) cages (because R8C34 = [56] clashes with [54] in one of the 9(2) cages, locking-out cages, and R8C34 = [83] clashes with R4C3) => two 9(2) cages must be [36] and [63], 3,6 locked for C3 => R357C3 (step 4) cannot be {245} because R5C3 only contains 1,7
Or if R8C3 = 8, R8C3 = 3 => 16(3) cage at R7C5 (step 3c) = {169}, R4C3 = 2, R3C4 = 8 => 16(3) cage at R1C5 (step 3c) = {169} clashes with 16(3) cage at R7C5
Cannot be {368} = [638] => R3C4 = 2, R6C6 = 1, R4C6 = 6 => R3C6 + R4C7 (step 2b) = {23} => R4C7 = 2, 17(3) cage at R5C7 (step 3b) = {179} (only remaining combination), locked for R5 => 11(3) cage at R5C1 = {236} which clashes with R6C3
-> 19(3) cage at R3C4 (step 13) = {469}, no 2,8, CPE no 4 in R3C3

17. 17(3) cage at R6C3 (step 15) = {179/359/368} cannot be {359}, here’s how
17(3) cage = {359} => R6C3 = 5, R67C4 = {39}, locked for C4 => R4C4 = 6, R3C4 = 4, R4C3 = 9, no 2 in R8C34, R67C4 = [93] (cannot be [39] because R6C6 = 9 (hidden single in N5), R6C7 + R7C6 = 4 = {13} => R6C7 = 1, R7C6 = 3 and R7C46 = [39] clashes with 17(3) cage at R7C5), R46C6 = {13} (hidden pair in N5), locked for C6, 16(3) cage at R7C5 = {169}, locked for C5 and N8, 16(3) cage at R1C5 = {358}, locked for N2, R1C6 = 9 (hidden single in N2), R1C7 = 4, no 5 in R9C6, R8C34 = [38/47] => R8C67 = {57} (only remaining combination, cannot be [48] which clashes with R8C34) => R8C34 = [38], R9C4 = {27} => R9C34 = {27}, locked for R9, R9C6 = 4, R9C7 = 5, R8C67 = [57], R7C6 = 2 (cannot be 7 because 13(3) cage at R6C6 cannot be [157/337]) => R6C67 = 11 = [38], R4C6 = 1, 15(4) cage at R3C6 (step 2b) = 4{137} (only remaining combination) => R3C6 = 7, R4C7 = 3, R2C6 = 6 (hidden single in C6), R2C7 = 3 clashes with R4C7
-> 17(3) cage at R6C3 = {179/368}, no 5
17a. 8 of {368} must be in R7C4 -> no 3 in R7C4

18. 17(3) cage at R6C3 = {179/368}
18a. Consider 17(3) cage = {179} => caged X-wing for 9 in 19(3) cage at R3C6 and 17(3) cage at R6C3, no other 9 in C34 => no 2 in R8C34, 2 in C4 only in R129C4 => 7 must be in R129C3, locked for C3 => 7 of {179} must be in R7C4
18b. 7,8 of {179/368} only in R7C4 -> R7C4 = {78}, no 7 in R6C3
18c. R6C34 = {19}/[63]

19. 13(3) cage at R6C6 = {139/148/157/238/256/346} (cannot be {247} because no 2,4,7 in R6C6)
19a. 3 of {139} must be in R7C6 (R6C67 cannot be {13}/[93] which clash with R6C34), 1 of {148/157} must be in R6C6 -> no 1,9 in R7C6

20. Consider combinations for 17(3) cage at R6C3 = {179/368}
20a. {179} => caged X-wing for 9 in 19(3) cage at R3C6 and 17(3) cage at R6C3, no other 9 in C34
Or {368} = [638] => 16(3) cage at R7C5 (step 3c) = {169}, locked for N8
-> no 9 in R8C4, clean-up: no 2 in R8C3

21. 15(4) cage at R3C6 (step 2b) = 4{128/137/236}, 2 cannot be in R4C7, here’s how
R4C7 = 2, R34C6 = {36}, locked for C6, 2 in N4 only in 11(3) cage at R5C1 (step 3) = {236}, locked for N4 => R6C3 = {19} => 17(3) cage at R6C3 (step 18) = {179} => R6C34 = {19}, locked for R6 => no remaining candidates in R6C6
-> no 2 in R4C7
21a. 15(4) cage at R3C6 = 4{128/137/236}, 2,7 only in R3C6 -> R3C6 = {27}

22. 45 rule on C89 3 outies R357C7 = 15
22a. Consider placements for R3C6
R3C6 = 2
Or R3C6 = 7, no 6 in R1C7, no 2 in R29C7, R4C67 = {13}, locked for R4, R34C9 = {48}, caged X-Wing for 4 in 19(3) cage at R3C4 and R34C9, no other 4 in R34C1, no 1 in R34C1 => R34C1 = [32], 11(3) cage at R5C1 = {137}, locked for N4 => R6C3 = {69}, 17(3) cage at R6C3 = {179/368} => R6C4 = {13}, naked pair {13} in R4C6 + R6C4, locked for N5 => R6C6 = {69}, naked pair {69} in R6C36, locked for R6, 17(3) cage at R6C3 = {179/368} = [638]/[917] => R6C34 = [63] => R6C6 = 9, R6C7 + R7C6 = [13] or R6C34 = [91], R4C6 = 3 => 3 locked in R47C6, locked for C6, no 6 in R29C7, 2,6 in C7 only in R357C7 = 15 = {267} => R7C7 = 7 => no 2 in R29C6 => R7C6 = 2 (hidden single in C6)
-> 2 must be in R37C6, locked for C6, clean-up: no 7 in R29C7

23. 15(4) cage at R3C6 (step 2b) = 4{128/137/236}
23a. Consider placements for R3C6
R3C6 = 2 => R4C67 = [18/36/63]
Or R3C6 = 7 => R4C67 = {13} => R7C7 = 7 (from analysis in step 22a) => R7C4 = 8, 17(3) cage at R6C3 = [638] => R4C67 = [13]
-> R4C67 = [13/18/36/63], no 1 in R4C7

24. 15(4) cage at R3C6 (step 2b) = 4{128/137/236} cannot be 4{137}, here’s how
R3C6 = 7 => R4C67 = [13], R357C7 = {26}7 and R6C6 = {69} (from analysis in step 22a), R7C6 = 2 (hidden single in C6) => R6C67 = 11 = [65] => cannot place 1 in C7
-> 15(4) cage at R3C6 = 4{128/236} -> R3C6 = 2, clean-up: no 7 in R12C3
24a. R4C67 (step 23a) = [18/36/63]

25. 13(3) cage at R6C6 (step 19) = {139/148/157/346}
4 cannot be in R6C7, here’s how
R6C7 = 4 => R67C6 = {36}, locked for C6 => R4C67 = [18], R6C34 = [19] (cannot be [63] which clashes with R6C6), R4C4 = 6, R6C6 = 3, R7C6 = 6, 16(3) cage at R7C5 (step 3c) = {358}, locked for N8, R8C6 = 9 (hidden single in N8), no 5 in R29C6 => R1C6 = 5 (hidden single in C6) => R1C7 = 8 clashes with R4C7
-> no 4 in R6C7
25a. 4 of {346} must be in R7C6 -> no 6 in R7C6

26. 13(3) cage at R6C6 (step 19) = {139/148/157/346}
26a. 13(3) cage = {139/148/157}, 1 locked for R6 => 17(3) cage at R6C3 = (step 18) = {368} = [638]
Or 13(3) cage = {346} = {36}4, 3,6 locked for R6 => 17(3) cage at R6C3 = (step 18) = {179} = {19}7, 1 locked for R6
-> Killer triple 1,3,6 R6C34 and R6C67, locked for R6, clean-up: no 3,8 in R7C1, no 7 in R7C9
26b. Combined cage R3467C1 (step 6) = {14}[72]/[32]{18}/[32]{45}, 2 locked for C1

[Something that’s been there for a long time but it only gives one minor elimination.]
27. 45 rule on N1 3 innies R12C3 + R3C1 = 1 outie R4C2 + 4
27a. Min R12C3 + R3C1 = 6 -> min R4C2 = 2

28. R357C3 (step 4) = {128/137/236/245} (cannot be {146} which clashes with R46C3, ALS block)

29. R357C3 = {128/137/236/245} cannot be {128}, here’s how
R357C3 = {128}, locked for C3 => R12C3 = {356}, R9C3 = {3567} => R12C4 = {346}, R9C4 = {2346} => R9C4 = 2 (R129C4 cannot be {346} which clashes with R34C4, ALS block), R12C4 = {34/36} (cannot be {46}, same ALS block), 3 locked for N2 => 16(3) cage at R1C5 (step 3c) = {169}, locked for N2 => R12C4= {34}, locked for N2 => no remaining candidates in R3C4
-> R357C3 = {137/236/245}, no 8
29a. 4 of {245} must be in R7C3 -> no 5 in R7C3

30. 8 in C3 only in R1289C3 cannot be in R8C3, here’s how
R8C3 = 8 => R8C4 = 3, 16(3) cage at R7C5 (step 3c) = {169}, R9C4 = 2 (hidden single in C4), no 1 in R129C4 => R6C4 = 1 (hidden single in C4) => 17(3) cage at R6C3 = {179} => R7C4 = 7 => cannot place 8 in N8
-> no 8 in R8C3, clean-up: no 3 in R8C4
30a. 8 in C3 only in R129C3 -> 1 must be in one of R129C4, locked for C4
30b. 1 in N5 only in R46C6, locked for C6, clean-up: no 8 in R29C7

31. 17(3) cage at R6C3 (step 18) = {179/368}
31a. 1 of {179} must be in R6C3 -> no 9 in R6C3
31b. Killer pair 1,6 in 11(3) cage at R5C1 and R6C3, locked for N4, clean-up: no 4 in R3C1

32. 19(3) cage at R3C4 = {469}, 6 locked for C4, clean-up: no 3 in R129C3, no 5 in R8C3

33. R357C3 (step 29) = {137/236/245} cannot be {245}, here’s how
33a. R357C3 = {245} = [524] => R12C3 = {168}, naked triple {168} in R126C3, locked for C3 => R9C3 = 7, R8C3 = 3 (hidden single in C3), R8C4 = 8, R7C4 = 7, 17(3) cage at R6C3 (step 18) = {179} => R6C34 = [19], R12C3 = {68} => R12C4 = {13} which clashes with 16(3) cage at R1C5
-> R357C3 = {137/236}, no 4,5, 3 locked for C3, clean-up: no 8 in R8C4
33b. Killer pair 1,6 in R357C3 and R6C3, locked for C3, clean-up: no 3,8 in R129C4

34. R6C4 = 3 (hidden single in C4) => 17(3) cage at R6C3 (step 18) = {368} -> R6C3 = 6, R7C4 = 8, clean-up: no 2 in R57C3 (step 33a), no 5 in R6C9, no 3,5 in 16(3) cage at R7C5 (step 3c)

35. Naked triple {169} in 16(3) cage at R7C5, locked for C5 and N8, clean-up: no 3 in R8C7, no 8 in R9C3, no 3 in R9C7

36. Naked triple {358} in 16(3) cage at R1C5, locked for N2, clean-up: no 8 in R1C7, no 4,6 in R2C7

37. R34C4 = {69} (hidden pair in C4) -> R4C3 = 4 (step 32), R4C1 = 2, R3C1 = 3, clean-up: no 8 in R3C9, no 7 in R6C1, no 5 in R7C1, no 7 in R8C4

38. Naked triple {137} in R357C3, locked for C3 -> R8C3 = 9, R8C4 = 2, clean-up: no 3 in R8C6

39. 8 in C3 only in R12C3, locked for N1

40. 1 in N1 only in 21(4) cage at R1C1 = 1{479/569/578}, no 2
40a. R12C3 = {28} (hidden pair in N1), locked for C3 -> R9C3 = 5, R9C4 = 4, clean-up: no 8 in R8C7
40b. Naked pair {17} in R12C4, locked for N2, clean-up: no 6 in R1C7, no 2 in R2C7

41. 45 rule on N1 2 innies R12C3 = 1 outie R4C2 + 1, R12C3 = {28} = 10 -> R4C2 = 9, R34C4 = [96], R4C6 = 1, R4C7 = 8 (cage sum), R6C6 = 9, R6C7 + R7C6 = 4 => R6C7 = 1, R7C6 = 3, R9C6 = 7, R9C7 = 2, R8C67 = [57], clean-up: no 6 in R1C6, no 4 in R1C7, no 7 in 17(3) cage at R5C7 (step 3b), no 5 in R7C9
41a. R6C89 = {47} (hidden pair in N6), locked for R6

42. R1C67 = [49], R2C6 = 6, R2C7 = 3, R5C7 = 6

43. 10(3) cage in N9 (step 9) = {136} (only remaining combination, cannot be {145} which clashes with R7C7), locked for N9 -> R7C9 = 9, R9C9 = 8, R8C8 = 4, R7C7 = 5, R6C8 = 7, R6C9 = 4, R3C7 = 4, R3C9 = 7, R4C9 = 5, R4C8 = 3, R3C3 = 1, R5C89 = [92], R2C9 = 1, R1C9 = 6, R2C8 = 5 (cage sum), R7C2 = 2 (hidden single in R7), R7C1 = 4 (hidden single in R7), R6C1 = 5

and the rest is naked singles.


I think that "Short Brunette" and "Tall Brunette" will probably remain lonely "young women". Their cage patterns are so different from the ones I've just posted that they took away most/all of the steps that I used.

I assume that since Børge posted all of these puzzles, at least one of the software solvers must have been able to solve each of them and determine that they all have a unique solution and can be solved.