SudokuSolver Forum

Est = Estimated rating by puzzle maker
E = Easy
H = Hard
Score = SudokuSolver v3.3 score, rounded to nearest 0.05
** in the Afmob column indicates that this puzzle was made by him, for this puzzle the estimate is his rating.

3x3::k:1792:3329:2562:2562:3332:3332:4102:4871:3336:1792:3329:2562:1036:2573:4102:4871:3336:3336:5650:5650:9492:2837:1036:2573:4102:4871:4378:5650:4380:9492:2837:9492:4896:4378:4378:4378:4380:4380:9492:9492:4896:2857:2857:2859:2859:3629:4380:9492:4400:9492:4896:4403:4403:4403:3629:3629:9492:4400:1850:2107:3644:4413:4403:2623:1856:3905:1850:2107:3644:4413:4678:4678:2623:1856:3905:3905:2892:2892:3644:4413:4678:

I'm not sure that I'm an expert , I'm still struggling with JFF1 . However JFF2 lives up to its name, it's a fun puzzle.

One of the hardest things was colouring the cages on my Excel worksheet.

I'll rate JFF2 at 1.0 because I used a naked quad for one of the key steps and because I feel that it would be harder without using elimination solving; that's the main thing that separates 1.0 puzzles from lower rated ones which are mainly on other sites.

Here is my walkthrough. If you are doing eliminations manually, be particularly careful for the diagonally-linked cages; my walkthrough was originally slightly longer because I'd missed one.

Prelims

a) R12C1 = {16/25/34}, no 7,8,9
b) R12C2 = {49/58/67}, no 1,2,3
c) R1C56 = {49/58/67}, no 1,2,3
d) 10(2) diagonal cage at R2C5 = {19/28/37/46}, no 5
e) R34C4 = {29/38/47/56}, no 1
f) 4(2) diagonal cage at R2C4 = {13}, locked for N2, clean-up: no 7,9 in R2C5 and R3C6, no 8 in R4C4
g) R5C67 = {29/38/47/56}, no 1
h) R5C89 = {29/38/47/56}, no 1
i) R67C4 = {89}, locked for C4, clean-up: no 2,3 in R34C4
j) 7(2) diagonal cage at R7C5 = {16/25/34}, no 7,8,9
k) 8(2) diagonal cage at R7C6 = {17/26/35}, no 4,8,9
l) R89C1 = {19/28/37/46}, no 5
m) R89C2 = {16/25/34}, no 7,8,9
n) R9C56 = {29/38/47/56}, no 1
o) 10(3) cage at R1C3 = {127/136/145/235}, no 8,9
p) 19(3) diagonal cage in N3 = {289/379/469/478/568}, no 1
q) 22(3) cage at R3C1 = {589/679}
r) 19(3) diagonal cage in N5 = {289/379/469/478/568}, no 1
s) 37(8) diagonally-linked cage at R3C3 = {12345679}, no 8

1. 45 rule on N3 1 outie R2C6 = 1 innie R3C9 + 3, no 2 in R2C6, no 7,8,9 in R3C9

2. 45 rule on N9 1 outies R8C6 = 1 innie R7C9 + 4, no 1,2,3,4 in R8C6, no 6,7,8,9 in R7C9

3. R7C6 = 1 (hidden single in C6), R8C5 = 7, clean-up: no 6 in R1C6, no 6 in R7C5 and R8C4, no 3 in R7C9, no 5 in R8C6 (both step 2), no 3 in R9C1, no 4 in R9C56

4. 45 rule on N6 2 outies R37C9 = 1 innie R5C7, min R37C9 = 3 -> min R5C7 = 3, clean-up: no 9 in R5C6

5. 45 rule on N2 3 innies R13C4 + R2C6 = 18 = {279/459/567} (cannot be {468} which clashes with 10(2) diagonal cage at R2C5), no 8, clean-up: no 5 in R3C9 (step 1)
5a. 9 of {459} must be in R2C6 -> no 4 in R2C6, clean-up: no 1 in R3C9 (step 1)

6. 45 rule on N8 3 innies R79C4 + R8C6 = 19 = {289/469/568}, no 3

7. 45 rule on C1234 4 outies R3467C5 = 11 = {1235}, locked for C5, clean-up: no 8 in R1C6, no 8 in R3C6, no 3 in R8C4, no 6,8,9 in R9C6
7a. 4 in N8 locked in R89C4, locked for C4, clean-up: no 7 in R34C4
7b. Naked pair {56} in R34C4, locked for C4, clean-up: no 2 in R7C5
7c. Naked pair {24} in R89C4, locked for C4 and N8 -> R1C4 = 7, clean-up: no 6 in R1C5, no 6 in R2C2, no 4 in R3C9 (step 1), no 9 in R9C5

8. R1C4 = 7 -> R12C3 = 3 = {12}, locked for C3 and N1, clean-up: no 5,6 in R12C1

9. R1C4 = 7 -> R2C6 + R3C4 = {56} (step 5), locked for N2, clean-up: no 8 in R1C5, no 4 in 10(2) diagonal cage at R2C5, no 6 in R3C9 (step 1)
9a. R2C5 = 8, R3C6 = 2, R9C5 = 6, R9C6 = 5, R7C5 = 3, R8C4 = 4, R9C4 = 2, R3C5 = 1, R2C4 = 3, R2C6 = 6, R34C4 = [56], R12C1 = [34], R5C4 = 1, R3C9 = 3, clean-up: no 5,9 in R1C2, no 9 in R2C2, no 5,6,9 in R5C7, no 8 in R5C8, no 2 in R7C9 (step 2), no 6,8 in R8C1, no 1,2,5 in R8C2, no 7 in R9C1, no 3 in R9C2
9b. 5 in N5 locked in R46C5, locked for 37(8) diagonally-linked cage at R3C3

10. R2C2 = 5 (hidden single in N1), R1C2 = 8

11. R89C3 = [58] (hidden pair in C3), clean-up: no 2 in R8C1
11a. 3 in C3 locked in R456C3, locked for N4

12. R8C2 = 3 (hidden single in C2), R9C2 = 4

13. Naked pair {19} in R89C1, locked for C1 and N7
13a. 22(3) cage at R3C1 = {679} (cannot be {589} because 5,8 only in R4C1) -> R34C1 = [67], R3C2 = 9, R3C3 = 7, R7C3 = 6, R7C12 = [27], R6C1 = 5 (cage sum), R5C1 = 8, R46C5 = [52], clean-up: no 3 in R5C678

14. Naked pair {47} in R5C67, locked for R5 -> R5C5 = 9, R5C3 = 3, R1C56 = [49], R67C4 = [89], R8C6 = 8, R7C9 = 4 (step 2), R7C7 = 5, R9C7 = 1 (cage sum), R7C8 = 8, R3C8 = 4, R13C7 = [28], clean-up: no 2 in R5C89

15. R5C5 = 9 -> R46C6 = 10 = [37], R5C67 = [47], R2C7 = 9, R1C8 = 6 (cage sum)

16. R5C2 = 2 (hidden single in R5), R46C2 = [16]

and the rest is naked singles.

3x3::k:6144:6144:6144:6144:10500:6405:6405:6405:6405:6144:5386:10500:10500:10500:10500:10500:6928:6405:5386:5386:5386:3349:10500:3863:6928:6928:6928:2331:10012:3349:3349:10500:3863:3863:7458:1315:2331:10012:10012:10012:1320:7458:7458:7458:1315:1325:2350:2350:10012:1320:7458:2611:2611:4149:1325:3639:3639:10012:4410:7458:4668:4668:4149:3903:2624:3639:4410:4410:4410:4668:2630:1863:3903:2624:3402:3402:4410:2125:2125:2630:1863:

I think only one version should have been posted according to our rules. But thanks anyway, manu, for making A143!

SudokuSolver misses steps 1d and 2a and therefore takes a much harder path. I think the technique for step 1d hasn't been implemented yet but I'm wondering why it misses step 2a?

A143 Walkthrough:

1. R123
a) Innies+Outies N1: R2C3 = R1C4 <> 4
b) Innies+Outies N3: 7 = R1C6 - R2C7 -> R1C6 = (89), R2C7 = (12)
c) 4 locked in R3C46 @ N2 for R3
d) Innies+Outies R123: 3 = R4C5 - R3C46: R34C6 = 4{1/2} -> R4C5 = (89)

2. C456 !
a) ! Outies N47 = 37(6) -> Innies C4 = 8(3) = 1{25/34} -> 1 locked for C4
b) Killer pair (24) locked in Innies C4 + R3C4 for C4
c) 39(6) = {456789} -> 4 locked for N4

3. C123
a) Outies N7 = 12(1+1) = [39] -> R6C1 = 3, R9C4 = 9
b) Cage sums: R7C2 = 2, R9C3 = 4
c) 9(2) @ C1 = {18} locked for C1+N4
d) 15(2) = {69} -> R9C1 = 6, R8C1 = 9
e) 10(2) = {37} locked for C2+N7
f) 9(2) @ R6C2 = {27} -> R6C2 = 2, R6C3 = 7
g) 39(6) = {456789} -> 7,8 locked for C4
h) 13(3) = 6{25/34} -> 6 locked for R4

4. C789
a) R6C9 = 9, R7C9 = 7
b) 10(2) @ N6 = {46} locked for R6+N6
c) Innie N9 = R9C7 = 3
d) Cage sum: R9C6 = 5
e) 5(2) = {23} locked for C9+N6
f) R9C9 = 1 -> R8C9 = 6, R6C5 = 1 -> R5C5 = 4, R6C6 = 8
g) Hidden Single: R4C7 = 8 @ N6
h) 15(3) = {348} -> R3C6 = 4, R4C6 = 3

5. R123
a) R3C4 = 2, R6C4 = 5
b) 1 locked in R3C23 @ R3 for N1
c) Innies+Outies N1: R1C4 = R2C3 = 3
d) Hidden Single: R3C8 = 3 @ R3
e) 27(4) = {3789} -> R3C9 = 8; {79} locked for N3

6. Rest is singles.

Rating: Hard 1.0 - Easy 1.25. I used IOD, large Outies and a Killer pair.

Thanks Manu for a nice puzzle!

In case anyone is concerned about trying both A143 and A143-Lite, the transfer of cells R4C2, R4C3, R4C7 and R4C8 to different cages makes them very different puzzles; my first two steps for A143-Lite no longer work for A143.

I took some time to find the breakthrough move and before that found the interesting step 12, which proved not to be needed. Then I found the breakthrough in step 13 by a different route than Afmob. My version of step 13 is I think technically slightly harder but IMHO possibly more easy to spot.

I'll rate A143 at 1.25 the way I solved it, because of step 13. I'll be interested to see whether Afmob or Ed have any comments on the rating of this step.

Here is my walkthrough for A143.

Prelims

a) R45C1 = {18/27/36/45}, no 9
b) R45C9 = {14/23}
c) R56C5 = {14/23}
d) R67C1 = {14/23}
e) R6C23 = {18/27/36/45}, no 9
f) R6C78 = {19/28/37/46}, no 5
g) R67C9 = {79}, locked for C9
h) R89C1 = {69/78}
i) R89C2 = {19/28/37/46}, no 5
j) R89C8 = {19/28/37/46}, no 5
k) R89C9 = {16/25/34}, no 7,8,9
l) R9C34 = {49/58/67}, no 1,2,3
m) R9C67 = {17/26/35}, no 4,8,9
n) 27(4) cage in N3 = {3789/4689/5679}, no 1,2, 9 locked for N3
o) 17(5) cage in N8 = {12347/12356}, no 8,9, 1,2,3 locked for N8, clean-up: no 5,6,7 in R9C7
p) 39(6) cage at R4C2 = {456789}
q) 41(8) cage at R1C5 = {12356789}

1. 8,9 in C5 locked in R1234C5, locked for 41(8) cage at R1C5
1a. 8 in C9 locked in R123C9, locked for N3

2. 45 rule on N3 1 outie R1C6 = 1 innie R2C7 + 7, R1C6 = {89}, R2C7 = {12}

3. 45 rule on N1 1 outie R1C4 = 1 innie R2C3, no 4,8,9 in R1C4
3a. 4 in N2 locked in R3C46, locked for R3

4. 45 rule on N7 2 innies R7C1 + R9C3 = 6 = [15/24], clean-up: R6C1 = {34}, R9C4 = {89}

5. 45 rule on N9 2 innies R7C9 + R9C7 = 10 = [73/91], no 2 in R9C7, clean-up: no 6 in R9C6

6. R89C9 = {16/25} (cannot be {34} which clashes with R45C9), no 3,4
6a. Killer pair 1,2 in R45C9 and R89C9, locked for C9

7. 45 rule on N8 4 innies R79C46 = 28 = {4789/5689}
7a. R9C6 = {57} -> no 5,7 in R7C46

8. 45 rule on C1234 3(2+1) innies R2C34 + R8C4 = 8
8a. Min R28C4 = 3 -> max R2C3 = 5, clean-up: no 6,7 in R1C4 (step 3)
8b. Min R2C34 = 3 -> max R8C4 = 5
8c. Max R28C4 = 7, no 7 in R2C4

9. 45 rule on R1234 4 innies R4C1289 = 14 = {1238/1247/1256/1346/2345}, no 9
9a. 8 of {1238} must be in R4C2 -> no 8 in R4C18, clean-up: no 1 in R5C1

10. 45 rule on R123 1 outie R4C5 = 2 innies R3C46 + 3
10a. Max R3C46 = 6 and must contain 4 -> R3C46 = {14/24}
10b. R3C46 = 5,6 -> R4C5 = {89}

11. 45 rule on R89 2 innies R8C37 = 1 outie R7C5 + 10
11a. Min R8C37 = 11, no 1

Next I first saw
12. 45 rule on C5 6(4+2) outies R2C3467 + R8C46 = 18
12a. Min R2C3467 = 11 -> max R8C46 = 7, no 7
12b. Min R8C46 = 3 -> max R2C3467 = 15
12c. R2C3467 must contain 1 (because it doesn’t contain 4), locked for R2 and 41(8) cage at R1C5

Then I saw the simpler
12. 45 rule on C5 4 innies R1234C5 = 2 outies R8C46 + 23
12a. Max R1234C5 = 30 -> max R8C46 = 7, no 7
12b. Min R8C46 = 3 -> min R1234C5 = 26, no 1
12c. 1 in 41(8) cage locked in R2C3467, locked for R2

13. R2C34 + R8C4 = 8 (step 8), R1C4 = R2C3 (step 3) -> R128C4 = 8 = {125/134}, no 6, 1 locked for C4
13a. 4 of {134} must be in R8C4 -> no 3 in R8C4
13b. Killer pair 2,4 in R128C4 and R3C4, locked for C4
13c. 4 in 39(6) cage at R4C2 locked in R4C2 + R5C23, locked for N4 -> R6C1 = 3, R7C1 = 2, R9C3 = 4 (step 4), R9C4 = 9, clean-up: no 5,6,7 in R45C1, no 2 in R5C5, no 5,6 in R6C23, no 7 in R6C78, no 6 in R8C1, no 1,6,8 in R8C2, no 1,6 in R8C8, no 6,8 in R9C2

14. R45C1 = [18], clean-up: no 4 in R5C9, no 7 in R89C1
14a. R89C1 = [96], clean-up: no 4 in R8C8, no 1 in R8C9, no 1 in R9C2, no 1 in R9C8
14b. Naked pair {37} in R89C2, locked for C2 and N7 -> R6C23 = [27], R67C9 = [97], R9C7 = 3 (step 5), R89C2 = [37], R9C6 = 5, clean-up: no 3 in R5C5, no 1,8 in R6C78, no 2 in R8C9
14c. Naked pair {46} in R6C78, locked for R6 and N6 -> R56C5 = [41], R6C46 = [58], R1C6 = 9, R4C5 = 9, R9C5 = 2, R89C8 = [28], R9C9 = 1, R8C9 = 6, R8C5 = 7
14d. Naked pair {14} in R8C46, locked for R8 and N8 -> R7C6 = 6, R7C45 = [83], R8C7 = 5, R8C3 = 8, clean-up: no 5 in R2C3 (step 3)

15. Naked pair {69} in R5C23, locked for R5 and N4 -> R4C23 = [45], R5C4 = 7, R7C23 = [51], clean-up: no 1 in R1C4 (step 3)

16. Naked pair {23} in R4C69, locked for R4 -> R4C78 = [87], R4C4 = 6, R3C4 = 2 (cage sum), R12C4 = [31], R2C7 = 2, R2C3 = 3, R2C6 = 7, R3C6 = 4, R4C6 = 3 (cage sum), R45C9 = [23], R5C678 = [215], R8C46 = [41]

17. R1C8 = 1 (hidden single in C8), R3C2 = 1, R3C8 = 3 (hidden singles in R3)
17a. 27(4) cage in N3 = {3789} (only remaining combination), no 4,5,6

and the rest is naked singles.

3x3::k:6144:6144:6144:6144:6660:6405:6405:6405:6405:6144:5386:6660:6660:6660:6660:6660:6928:6405:5386:5386:5386:2069:5142:1815:6928:6928:6928:2331:2332:2332:2069:5142:1815:3873:3873:1315:2331:8997:8997:8997:5142:5673:5673:5673:1315:1325:2350:2350:8997:5142:5673:2611:2611:4149:1325:3639:3639:8997:4410:5673:4668:4668:4149:3903:2624:3639:4410:4410:4410:4668:2630:1863:3903:2624:3402:3402:4410:2125:2125:2630:1863:

I decided that, since I was going to try both of them, it made more sense to do the easier one first.

I'll rate A143-Lite at 1.0. It doesn't need anything harder than killer pairs and simple combinations.

Here is my walkthrough. It would have been shorter if I'd spotted step 14 a bit earlier, after step 9. Thanks Afmob for pointing out that it was actually down to naked singles after step 16 and for other corrections.

Prelims

a) R34C4 = {17/26/35}, no 4,8,9
b) R34C6 = {16/25/34}, no 7,8,9
c) R45C1 = {18/27/36/45}, no 9
d) R4C23 = {18/27/36/45}, no 9
e) R4C78 = {69/78}
f) R45C9 = {14/23}
g) R67C1 = {14/23}
h) R6C23 = {18/27/36/45}, no 9
i) R6C78 = {19/28/37/46}, no 5
j) R67C9 = {79}, locked for C9
k) R89C1 = {69/78}
l) R89C2 = {19/28/37/46}, no 5
m) R89C8 = {19/28/37/46}, no 5
n) R89C9 = {16/25/34}, no 7,8,9
o) R9C34 = {49/58/67}, no 1,2,3
p) R9C67 = {17/26/35}, no 4,8,9
q) 27(4) cage in N3 = {3789/4689/5679}, no 1,2, 9 locked for N3
r) 35(5) cage at R5C2 = {56789}
s) 17(5) cage in N8 = {12347/12356}, no 8,9, 1,2,3 locked for N8, clean-up: no 5,6,7 in R9C7

1. Killer pair 7,9 in R4C78 and R6C9, locked for N6, clean-up: no 1,3 in R6C78
1a. Killer pair 6,8 in R4C78 and R6C78, locked for N6
1b. Killer pair 2,4 in R45C9 and R6C78, locked for N6

2. 9 in N4 locked in R5C23, locked for R5 and 35(5) cage at R5C2
2a. 5 in N6 locked in R5C78, locked for R5 and 22(5) cage at R5C6, clean-up: no 4 in R4C1

3. 45 rule on N3 1 outie R1C6 = 1 innie R2C7 + 7, R1C6 = {89}, R2C7 = {12}
3a. 8 in C9 locked in R123C9, locked for N3

4. R89C9 = {16/25} (cannot be {34} which clashes with R45C9), no 3,4
4a. Killer pair 1,2 in R45C9 and R89C9, locked for C9

5. 45 rule on N9 2 innies R7C9 + R9C7 = 10 = [73/91], no 2 in R9C7, clean-up: no 6 in R9C6

6. 45 rule on R12 2 innies R2C28 = 15 = [69/87/96]

7. 45 rule on N7 2 innies R7C1 + R9C3 = 6 = [15/24], clean-up: R6C1 = {34}, R9C4 = {89}

8. 45 rule on N8 4 innies R79C46 = 28 = {4789/5689}
8a. R9C6 = {57} -> no 5,7 in R7C46

9. 45 rule on N4 3 innies R5C23 + R6C1 = 18 = {369} (only remaining combination containing 9 in R5C23) -> R6C1 = 3, R7C1 = 2, R9C3 = 4 (step 7), R9C4 = 9, clean-up: no 6,7 in R45C1, no 5,6 in R4C2, no 6 in R4C3, no 5,6 in R6C2, no 6 in R6C3, no 6 in R8C1, no 1,6,8 in R8C2, no 1,6 in R8C8, no 6,8 in R9C2
9a. Naked pair {69} in R5C23, locked for R5 and 35(5) cage at R5C2 -> R7C4 = 8, R56C4 = [75], clean-up: no 1,3 in R34C4, no 2 in R3C6, no 4 in R6C2
9b. Naked pair {26} in R34C4, locked for C4

10. 45 rule on N1 1 outie R1C4 = 1 innies R2C3 -> R2C3 = {13}, no 4 in R1C4

11. 5 in N7 locked in 14(3) cage = {158/356}, no 7,9
11a. 8 of {158} must be in R8C3, no 1 in R8C3
11b. 9 in N7 locked in R8C12, locked for R8, clean-up: no 1 in R9C8

12. 22(5) cage at R5C6 = {12568/13459/23458}
12a. R7C6 = {46} -> no 4,6 in R56C6
12b. 2,8 of {12568/23458} must be in R56C6, 9 of {13459} must be in R6C6, no 1 in R6C6
12c. Killer pair 8,9 in R1C6 and R56C6, locked for C6

13. 45 rule on R123 3 innies R3C456 = 12 = {129/156/237/246} (cannot be {138/147/345} because R3C4 only contains 2,6), no 8
13a. 7 of {237} must be in R3C5 -> no 3 in R3C5

14. R6C78 = {46} (cannot be {28} which clashes with R6C23), locked for R6 and N6, clean-up: no 9 in R4C78, no 1 in R45C9
14a. Naked pair {78} in R4C78, locked for R4 and N6 -> R67C9 = [97], R9C7 = 3 (step 5), R9C6 = 5, R7C6 = 6 (step 8), clean-up: no 1 in R3C6, no 1,2 in R4C23, no 1,2 in R4C6, no 1 in R5C1, no 7 in R8C2, no 2 in R8C9
14b. R2C23 = [45], R45C1 = [18], R34C6 = [43], R45C9 = [23], R34C4 = [26], R4C5 = 9, clean-up: no 7 in R89C1, no 5 in R8C9
14c. R89C1 = [96], R8C2 = 3, R7C23 = [51], R8C3 = 8, R9C2 = 7, R89C9 = [61], R9C5 = 2, R9C8 = 8
14d. Naked pair {49} in R7C78, locked for R7 and N9 -> R7C5 = 3, R8C78 = [52]

15. R5C78 = [15], R5C56 = [42], R6C56 = [18], R8C456 = [471]

16. R2C34 = [31], R2C67 = [72] -> R12C5 = 13 = {58}, locked for N2 -> R3C5 = 6, R1C46 = [39], clean-up: no 8 in R2C2 (step 6)

17. R3C8 = 3 (hidden single in C8) -> 27(4) cage = {3789}, R3C9 = 8, R2C8 = 9, R3C7 = 7

and the rest is naked singles.

3x3::k:6144:6144:6144:6144:10500:6405:6405:6405:6405:6144:5386:10500:10500:10500:10500:10500:6928:6405:5386:5386:5386:3349:10500:3863:6928:6928:6928:3611:10012:3349:3349:10500:3863:3863:7458:5411:3611:10012:10012:10012:1320:7458:7458:7458:5411:3611:2350:2350:10012:1320:7458:2611:2611:5411:3611:3639:3639:10012:4410:7458:4668:4668:5411:6463:6463:3639:4410:4410:4410:4668:4422:4422:6463:6463:3402:3402:4410:2125:2125:4422:4422

There were lots of little eliminations you could make but after going through my wt again, I noticed that a lot of those moves were unnecessary which helped me to shorten my walkthrough quite a bit.

A143 V2 Walkthrough

1. R123
a) Innies+Outies N1: R2C3 = R1C4 <> 4
b) Innies+Outies N3: 7 = R1C6 - R2C7 -> R1C6 = (89), R2C7 = (12)
c) 4 locked in R3C46 @ N2 for R3
d) Innies+Outies R123: 3 = R4C5 - R3C46: R3C46 = 4{1/2} -> R4C5 = (89)

2. C1234
a) Outies N47 = 37(6) -> Innies C4 = 8(3) = 1{25/34} -> 1 locked for C4
b) Killer pair (24) locked in Innies C4 + R3C4 for C4
c) 39(6) = {456789} -> 4 locked for N4
d) Innies N7 = 6(2) = [15/24]
e) 14(4) = 12{38/56} -> 1,2 locked for C1
f) 9(2) = {18/27} since (36) is a Killer pair of 14(4)
g) Killer pair (12) locked in 14(4) + 9(2) for N4
h) 13(3) <> 9
i) 9 locked in 39(6) @ N4 for 39(6)

3. C1234
a) Hidden Single: R9C4 = 9 @ C4 -> R9C3 = 4
b) Innie N7 = R7C1 = 2
c) 14(4) = 12{38/56} -> 1 locked for N4
d) 9(2) = {27} locked for R6+N4
e) 17(5) = 123{47/56} -> 1,2,3 locked for N8
f) 25(4) = 9{178/358/367} -> 9 locked for R8+N7

4. R789
a) 8 locked in R7C46 @ N8 for R7
b) 8(2): R9C7 = (123)
c) Innies N9 = 10(2) = [73/91]
d) 8(2) <> 6
e) Killer pair (57) locked in 17(5) + R9C6 for N8
f) Hidden Single: R5C4 = 7 @ 39(6)

5. R456 !
a) 10(2) <> 3,8
b) 15(3): R4C67 <> 1 since R3C6 <= 4
c) 1 locked in Innies R1234 @ R1 = 14(4) = 12{38/47/56} <> 9 because {1346} blocked by Killer pair (36) of 13(3)
-> 2 locked for R4+N6
d) ! Innies R1234 = 14(4): R4C89 <> {12} because R4C12 = 11(2) clashes with 14(4) @ C1 = 12{38/56} = {12} + 11(2) (IOU @ N4)
-> R4C89 <> 1
e) Hidden Single: R4C1 = 1 @ R4
f) Innies R1234 = 14(4): R4C89 <> 4,8 since R4C2 <> 2,3,7
g) 39(6) = {456789} -> 9 locked for R5
h) 13(3): R4C3 <> 8 because [283] blocked by Killer pair (23) of Innies C4

6. R456 !
a) ! R4C2 <> 6,8 because it sees all 6,8 of C4
b) Innies R1234 = 14(4) = 12{47/56} and R4C89 <> 5 because R4C2 = (45)
c) 15(3) <> 7 since R3C6 = (124) and {267} blocked by R4C89 = (267)
d) 7 locked in Innies R1234 @ R4 = {1247} -> R4C2 = 4
e) ! 21(4) = 2{379/469/478} <> 1,5 because R47C9 = (279) and {1479} blocked by Killer pair (14) of 10(2)
-> R4C9 = 2
f) R4C8 = 7
g) R6C6 <> 1 since it sees all 1 of R5
h) Hidden Killer pair (12) in R5C6 for N5 since 5(2) can only have one of (12) -> R5C6 = (12)
i) Hidden Killer pair (49) in R56C9 for 21(4) since 7 of {379} must be in R6C9
j) Killer pair (49) locked in 10(2) + R56C9 for N6

7. R456
a) R6C1 <> 5 since it sees all 5 of 39(6)
b) 5 locked in R6C46 @ R6 for N5
c) 9 locked in R6C789 @ N6 for R6
d) 21(4): R6C9 <> 3 since R5C9 <> 7,9
e) 15(3): R4C7 <> 6 because {168} blocked by Killer pair (68) of 13(3) and R4C6 <> 4,5

8. C456 !
a) ! Consider placement of 4 in N2 -> 5(2) <> {23}
- i) R3C6 = 4 -> 4 locked in 5(2) @ N5
- ii) R3C4 = 4 -> Innies C4 = 8(3) = {125} locked for C4 -> R6C6 = 5 (HS @ N5) -> 29(6) = 2578{16/34} -> R5C6 = 2
b) 5(2) = {14} locked for C5+N5
c) R5C6 = 2

9. R456
a) Killer pair (14) locked in R6C5 + 10(2) for R6
b) 21(4) = 2{379/469/478} -> R5C9 = (34)
c) R6C6 <> 6 since it sees all 6 of N6
d) ! 29(6): R7C6 <> 8 because 4 only possible there and {125678} with R5C78 = {16} blocked by Killer pair (16) of 10(2)
e) Hidden Single: R7C4 = 8 @ N8
f) 8 locked in 14(4) @ N4 = {1238} -> 3,8 locked for C1+N4
g) Caged X-Wing: 8 locked in 14(4) + 29(5) for R56
h) Killer pair (69) locked in 10(2) + R6C9 for R6+N6
i) R6C4 = 5

10. C4567
a) Hidden Single: R4C3 = 5 @ N4, R4C4 = 6 @ C4 -> R3C4 = 2
b) 15(3) = {348} -> R3C6 = 4, {38} locked for R4
c) Naked pair (38) locked in R46C6 for C6
d) Outies N69 = 28(6) -> Innies C6 = 17(3) = {179} -> R1C6 = 9; {17} locked for C6
e) R9C6 = 5 -> R9C7 = 3
f) Innie N3 = R2C7 = 2

11. C789
a) Innie N9 = R7C9 = 7
b) 21(4) = {2379} -> R5C9 = 3, R6C9 = 9
c) R7C6 = 6, R7C5 = 3, R7C3 = 1, R7C2 = 5 -> R8C3 = 8

12. R123
a) Innies+Outies N1: R1C4 = R2C3 = 3
b) Hidden Single: R3C8 = 3 @ N3
c) 27(3) = {3789} -> R3C9 = 8, R2C8 = 9, R3C7 = 7
d) 21(4) = {1569} since (78) only possible @ R2C2 -> R3C1 = 5; {16} locked for N1

13. Rest is singles.

Rating: (Easy) 1.75. I used a forcing chain.

Nice work Afmob , the initial move that enables to crack V1 is not strong enough for this V2 ! Your wt is very clear and you have avoided a too much difficult forcing chain. A 144 is going to be posted, so I'd like to post an alternative end for solving V2. It uses a contradiction move less elegant than the chain Afmob used, but enables to crack the puzzle quite quickly. I start from step 6.f) from Afmob's WT (I have copied the beginning of his WT) because I have followed a similar path until this point.

I would be interested if someone sees a way of avoiding contradiction step 10.

Afmob's initial steps

1. R123
a) Innies+Outies N1: R2C3 = R1C4 <> 4
b) Innies+Outies N3: 7 = R1C6 - R2C7 -> R1C6 = (89), R2C7 = (12)
c) 4 locked in R3C46 @ N2 for N3
d) Innies+Outies R123: 3 = R4C5 - R3C46: R3C46 = 4{1/2} -> R4C5 = (89)

2. C1234
a) Outies N47 = 37(6) -> Innies C4 = 8(3) = 1{25/34} -> 1 locked for C4
b) Killer pair (24) locked in Innies C4 + R3C4 for C4
c) 39(6) = {456789} -> 4 locked for N4
d) Innies N7 = 6(2) = [15/24]
e) 14(4) = 12{38/56} -> 1,2 locked for C1
f) 9(2) = {18/27} since (36) is a Kiler pair of 14(4)
g) Killer pair (12) locked in 14(4) + 9(2) for N4
h) 13(3) <> 9
i) 9 locked in 39(6) @ N4 for 39(6)

3. C1234
a) Hidden Single: R9C4 = 9 @ C4 -> R9C3 = 4
b) Innie N7 = R7C1 = 2
c) 14(4) = 12{38/56} -> 1 locked for N4
d) 9(2) = {27} locked for R6+N4
e) 17(5) = 123{48/56} -> 1,2,3 locked for N8
f) 25(4) = 9{178/358/367} -> 9 locked for R8+N7

4. R789
a) 8 locked in R7C46 @ N8 for R7
b) 8(2): R9C7 = (123)
c) Innies N9 = 10(2) = [73/91]
d) 8(2) <> 6
e) Killer pair (57) locked in 17(5) + R9C6 for N8
f) Hidden Single: R5C4 = 7 @ 39(6)

5. R456 !
a) 10(2) <> 3,8
b) 15(3): R4C67 <> 1 since R3C6 <= 4
c) 1 locked in Innies R1234 @ R1 = 14(4) = 12{38/47/56} <> 9 because {1346} blocked by Killer pair (36) of 13(3)
-> 2 locked for R4+N6
d) ! Innies R1234 = 14(4): R4C89 <> {12} because R4C12 = 11(2) clashes with 14(4) = 12{38/56} = {12} + 11(2) (IOU @ N4)
-> R4C89 <> 1
e) Hidden Single: R4C1 = 1 @ R4
f) Innies R1234 = 14(4): R4C89 <> 4,8 since R4C2 <> 2,3,7
g) 39(6) = {456789} -> 9 locked for R5
h) 13(3): R4C3 <> 8 because {238} blocked by Killer pair (23) of Innies C4

6. R456 !
a) ! R4C2 <> 6,8 because it sees all 6,8 of C4
b) Innies R1234 = 14(4) = 12{47/56} and R4C89 <> 5 because R4C2 = (45)
c) 15(3) <> 7 since R3C6 = (124) and {267} blocked by R4C89 = (267)
d) 7 locked in Innies R1234 @ R4 = {1247} -> R4C2 = 4
e) ! 21(4) = 2{379/2469/2478} <> 1,5 because R47C9 = (279) and {1479} blocked by Killer pair (14) of 10(2)
-> R4C9 = 2
f) R4C8 = 7

Alternative end :

7. Digit in r1c4 = digit in r2c3 is locked for r3 in cage 27(3) : cannot be 1 or 2.
→ r1c4=r2c3={35}

8.r128c4 totals 8 : [314] or 5{12} → r2c4={12} r8c4={124} : naked pair {12} for r2 at c47

9.Innies in c6789 : r2c67+r8c6=10

10.!!!!! Contradiction move : suppose r9c7=1
→ r9c6=7 and cage 17(5) at n8 = { 12356} : no 4
→ 4 locked for c5 in cage 5(2) ={14}
→ r2c7=2 (naked single) r2c4=1 r8c6=1 (hidden single in cage 17(5))
→ step 9 implies r2c6=7 : contradiction with r9c6=7

11.Cage 8(2) at r9 =[5 3]
Cage 17(5) at n8 = {12347}
{68} locked for r7 at c46

12.Digit 5 locked for c5 in cage 41(8)
→ r1c4=r2c3=3 r2c4=1 r8c4=4 r2c7=2 r1c6=9 r4c5=9 (hidden single in cage 41(8)) r3c4=2 (naked single) r3c6=4.

13.Digit 3 is locked for r3 in cage 27(4) : Combination = {3789}

14.Digit 4 is locked for c5 in cage 5(2) = {14}
→ r8c6=1 (hidden single in cage 17(5)) r2c6 = 7 (Step 9)

15.Cage 15(3) at n256 : r4c67 = [38] or [65]

16.Cage 18(3) at n9 : 4 is locked for r7 in 18(3) cage. Combintion for cage 18(3) : {468} or {459}. Combination {468} blocked by r7c46={68} .
→ r8c7=5 (naked single : 9 is locked at r8c12 for r8, Afmob's step 3.f)) r7c78 = {49}
→ r4c7=8 r4c6=3.

17.C6 : r5c6=2 (hidden single) r67c6 ={68}
→ r5c78=[15] (combination of cage 29(6))

Rest is naked singles or pairs ({56} in r3).

That's certainly true. I also had a lot of little eliminations but since I didn't know which ones were necessary I've left them in.

IMHO it would have been better to wait a few more days. It's normal to wait a week unless there have been at least two walkthroughs posted or there is something that requires earlier comment. That should apply particularly for the harder puzzles which take longer to solve; I only finished v2 yesterday evening. It's only 4 days since V2 was posted.

I'll agree with Afmob's rating of Easy 1.75 because of my forcing chains and contradiction move.

Here is my walkthrough for A143 V2. I started by using any steps from my A143 walkthrough that still worked for this variant. I tried to find a forcing chain for step 34 but could only see it as a contradiction move.

Prelims

a) R56C5 = {14/23}
b) R6C23 = {18/27/36/45}, no 9
c) R6C78 = {19/28/37/46}, no 5
d) R9C34 = {49/58/67}, no 1,2,3
e) R9C67 = {17/26/35}, no 4,8,9
f) 27(4) cage in N3 = {3789/4689/5679}, no 1,2, 9 locked for N3
g) R4567C1 = {1238/1247/1256/1346/2345}, no 9
h) 17(5) cage in N8 = {12347/12356}, no 8,9, 1,2,3 locked for N8, clean-up: no 5,6,7 in R9C7
i) 39(6) cage at R4C2 = {456789}
j) 41(8) cage at R1C5 = {12356789}

1. 8,9 in C5 locked in R1234C5, locked for 41(8) cage at R1C5

2. 45 rule on N3 1 outie R1C6 = 1 innie R2C7 + 7, R1C6 = {89}, R2C7 = {12}

3. 45 rule on N1 1 outie R1C4 = 1 innie R2C3, no 4,8,9 in R1C4
3a. 4 in N2 locked in R3C46, locked for R3

4. 45 rule on N7 2 innies R7C1 + R9C3 = 6 = [15/24], clean-up: R9C4 = {89}

5. 45 rule on N9 2 innies R7C9 + R9C7 = 10 = [73/82/91]

6. 45 rule on R123 1 outie R4C5 = 2 innies R3C46 + 3
6a. Max R3C46 = 6 and must contain 4 -> R3C46 = {14/24}
6b. R3C46 = 5,6 -> R4C5 = {89}

7. 45 rule on C1234 3(2+1) innies R2C34 + R8C4 = 8, R1C4 = R2C3 (step 3) -> R128C4 = 8 = {125/134}, no 6,7, 1 locked for C4, clean-up: no 6,7 in R2C3 (step 3)
7a. 4 of {134} must be in R8C4 -> no 3 in R8C4
7b. Killer pair 2,4 in R128C4 and R3C4, locked for C4

8. 4 in 39(6) cage at R4C2 locked in R4C2 + R5C23, locked for N4, clean-up: no 5 in R6C23
8a. R4567C1 = {1238/1256}, no 7, 1,2 locked for C1
8b. R6C23 = {18/27} (cannot be {36} which clashes with R456C1), no 3,6
8c. Killer pair 1,2 in R456C1 and R6C23, locked for N4

9. 45 rule on C5 4 innies R1234C5 = 2 outies R8C46 + 23
9a. Max R1234C5 = 30 -> max R8C46 = 7, no 7 in R8C6
9b. Min R8C46 = 3 -> min R1234C5 = 26, no 1
9c. 1 in 41(8) cage locked in R2C3467, locked for R2

10. 45 rule on R1234 4 innies R4C1289 = 14 = {1238/1247/1256/1346/2345}, no 9
10a. 8 of {1238} must be in R4C2 -> no 8 in R4C189

11. 45 rule on C6789 3(2+1) innies R2C67 + R8C6 = 10
11a. Max R2C7 + R8C6 = 8 -> no 1 in R2C6
11b. R2C67 + R8C6 cannot be [226] -> no 2 in R2C6

12. 45 rule on R89 2 innies R8C37 = 1 outie R7C5 + 10
12a. Min R8C37 = 11, no 1

13. 13(3) cage at R3C4 = {238/256/346} (cannot be {247} because 2,4 only in R3C4), no 7,9
13a. R4C1289 (step 10) = {1238/1247/1256} (cannot be {1346/2345} which clash with R4C34), 1,2 locked for R4

14. 9 in N4 locked in R5C23, locked for R5 and 39(6) cage at R4C2
14a. R9C4 = 9 (hidden single in C4), R9C3 = 4, R7C1 = 2 (step 4)
14b. 1 in C1 locked in R456C1, locked for N4, clean-up: no 8 in R6C23
14c. 4 in N4 locked in R45C2, locked for C2
14d. 2 in R4 locked in R4C89, locked for N6, clean-up: no 8 in R6C78
14e. 8 in N8 locked in R7C46, locked for R7, clean-up: no 2 in R9C7 (step 5), no 6 in R9C6

15. Naked pair {27} in R6C23, locked for R6 and N4, clean-up: no 3 in R5C5, no 3 in R6C78

16. 45 rule on N8 4 innies R7C46 = 28 = {4789/5689}
16a. R9C6 = {57} -> no 5,7 in R7C46
16b. R5C4 = 7 (hidden single in C4)
16c. 5 in 39(6) cage at R4C2 locked in R4C2 + R5C23 + R6C4, CPE no 5 in R6C1

17. 45 rule on N4 2 remaining outies R67C4 = 1 innie R4C3 + 8
17a. Max R67C4 = 14 -> max R4C3 = 6

18. 14(3) cage in N7 = {158/167/356}, no 9
18a. 9 in N7 locked in R8C12, locked for R8

19. R8C37 = R7C5 + 10 (step 12)
19. Max R8C37 = 15 -> max R7C5 = 5
19b. Min R8C37 = 11, no 2 in R8C7

20. R4567C9 = {1389/1578/2379/2469/2478/3459/3567} (cannot be {1479/1569} which clash with R6C78, cannot be {2568/3468} because R7C9 only contains 7,9)
20a. 2 of {2379/2478} must be in R4C9, 7 of {1578/3567} must be in R7C9 -> no 7 in R4C9
20b. R4C1289 (step 13a) = {1238/1247/1256}
20c. 4 of {1247} must be in R4C2, no 4 in R4C89

21. 18(3) cage in N9 = {189/378/459/567} (cannot be {369} which clashes with R7C9 + R9C7, cannot be {468} which clashes with R7C46)
21a. 8 in {378} must be in R8C7 -> no 3 in R8C7
21b. Killer pair 7,9 in 18(3) cage and R7C9, locked for N9

22. 14(3) cage in N7 (step 18) = {158/167/356} -> 25(4) cage = {1789/3589/3679}
22a. 6 of {3679} must be in R9C12 (R9C12 cannot be {37} which clashes with R9C67), no 6 in R8C12
22b. 5 of {3589} must be in R8C2 + R9C12 (R89C1 cannot be {35/58} which clash with R456C1 and 9 of {59} must be in R8C1), no 5 in R8C1

23. R4C1289 (step 13a) = {1238/1247/1256}
23a. Hidden killer pair 4,7 in R4C28 and R4C67 for R4 -> R4C28 must have both or neither of 4,7
23b. R4C67 cannot be {47} because 15(3) cage at R3C6 cannot be 4{47} -> R4C28 must contain both of 4,7 -> R4C1289 = {1247} = [1472]
23c. 2 in N9 locked in R89C8, locked for C8
[In hindsight most of this step could have been done immediately after step 13a but I don’t think it made much difference that I didn’t see it then.]

24. R4567C9 (step 20) = {2379/2469/2478}, no 1,5
24a. 3 of {2379} must be in R5C9 -> no 3 in R6C9
24b. 5 in R6 locked in R6C46, locked for N5
24c. R4567C1 (step 8a) = {1238/1256}
24d. R56C1 = {38}/[56], no 6 in R5C1
24e. 18(3) cage in N9 (step 21) = {189/378/459/567}
24f. 7 of {378} must be in R7C7 -> no 3 in R7C7

25. 5 in N6 locked in R4C7 + R5C78
25a. 45 rule on N6 3 remaining innies R4C7 + R5C78 = 1 outie R7C9 + 7
25b. R7C9 = {79} -> R4C7 + R5C78 = 14,16 = {158/356/358}, no 4,9
25c. 9 in N6 locked in R6C789, locked for R6

26. 29(6) cage at R4C8 = {125678/134678/234578}
26a. Hidden killer pair 1,2 in R56C5 and R56C6 for N5 -> R56C6 must contain one of 1,2
26b. R5C6 must contain 2 or R567C6 must contain 1,4 -> 2 locked in R3C6 + R5C6, locked for C6
26c. Hidden killer triple 1,2,4 in R56C5 and R56C6 for N5 -> either R56C6 = {14} or R5C6 = 2 -> R5C6 = {124}
26d. Hidden killer triple 1,2,4 in R5C56 and R5C789 for R5 -> R5C789 must contain one of 1,4
26e. Killer pair 1,4 in R5C789 and R6C78, locked for N6

27. R4567C9 (step 24) = {2379/2469/2478}
27a. 4 of {2469/2478} must be in R5C9 -> no 6,8 in R5C9

28. 15(3) cage at R3C6 = {159/258/348/456} (cannot be {168} which clashes with R4C34, cannot be {249} because 2,4 only in R3C6)
28a. 5 of {456} must be in R4C7 -> no 6 in R4C7

29. 1,3,5 in R7 locked in R7C23578
29a. 45 rule on R789 5 innies R7C23578 = 22 = {13459/13567}
29b. 5,9 of {13459} cannot both be in R7C78 (because R7C23 = {13} clashes with 14(3) cage in N7) -> no 4 in R8C7 (step 21)

30. 1,2 in N3 locked in R1C789 + R2C7
30a. R2C7 = 1, R1C7 = 2 -> no 2 in R1C4 -> no 1,2 in R2C3 (also using step 3)
R2C7 = 2, 1 in N3 locked in R1C789 -> no 1 in R1C4 -> no 1,2 in R2C3 (also using step 3)
-> R2C3 = {35}, R1C4 = {35} (step 3)
30b. R128C4 (step 7) = {125/134}
30c. R1C4 = {35} -> no 3,5 in R28C4
[Alternatively for step 30a, R1C4 = R2C3 (step 3), R1C4 + R2C3 “see” all of R1C789 + R2C7 -> no 1,2 in R1C4 + R2C3, a CPE “clone” step. However although it looks a simpler move, IMHO it's a technically harder one.]

31. Naked pair {12} in R2C47, locked for R2 and 41(8) cage at R1C5

32. 21(4) cage in N1 = {1389/1569/1578/2379/2568} (cannot be {3567} which clashes with R2C3)
32a. Killer pair 3,5 in 21(4) cage and R2C3 for N1

33. 45 rule on N3 5 innies R1C789 + R2C79 = 18 = {12348/12357/12456}
33a. 7 of {12357} must be in R1C79 (R1C789 cannot be {135/235} which clash with R1C4), no 7 in R2C9

34. R4C3 cannot be 3, here’s how
R4C3 = 3 => R2C3 = 5 => R1C4 = 5 (step 3) => R467C4 are all {68}
34a. 3 in N4 locked in R56C1 = {38} (step 24d), locked for C1 and N4
34b. 8 in 39(6) cage at R4C2 locked in R67C4, locked for C4

35. 13(3) cage at R3C4 (step 13) = {256/346}, 6 locked in R4C34, locked for R4

36. 5 in N6 must be in R4C7 or R5C78
36a. R4C7 = 5 => no 5 in R4C3 => 5 in R5C23 => no 5 in R6C4 => R6C6 = 5 => 5 in 29(6) cage at R4C8
5 in R5C67 => 5 in 29(6) cage at R4C8
-> 29(6) cage at R4C8 must contain 5
36b. 29(6) cage (step 26) = {125678/234578} (cannot be {134678} which doesn’t contain 5) -> R5C6 = 2, clean-up: no 3 in R6C5

37. Naked pair {14} in R56C5, locked for C5 and N5
37a. 2 in C5 locked in R89C5, locked for N8
37b. 1 in N8 locked in R8C46, locked for R8

38. 29(6) cage (step 36b) = {125678/234578}
38a. 6 of {125678} must be in R67C6 (R5C78 cannot be {16} which clashes with R4C7 + R5C78, step 25b), no 6 in R5C78

39. R5C23 = {69} (hidden pair in R5), locked for N4 and 39(6) cage at R4C2 -> R4C3 = 5, R2C3 = 3, R1C4 = 3 (step 3), R4C4 = 6, R67C4 = [58], R3C4 = 2 (step 35), R2C47 = [12], R3C6 = 4, R7C6 = 6, R8C4 = 4, R9C6 = 5 (step 16), R9C7 = 3, R7C9 = 7 (step 5), R7C5 = 3, R8C6 = 1, R4C7 = 8, R4C56 = [93], R16C6 = [98], R56C1 = [83], R2C6 = 7, R7C23 = [51], R8C3 = 8 (step 22), R8C7 = 5 (step 21), R8C89 = [26], R89C5 = [72], R8C12 = [93], R5C7 = 1, R56C5 = [41], R56C9 = [39], R5C8 = 5
39a. 4 in C9 locked in R12C9, locked for N3

40. 27(4) cage in N3 = {3789/5679} -> R3C7 = 7, R1C7 = 6, R6C78 = [46], R7C78 = [94], clean-up: no 5 in 27(4) cage

41. R3C1 = 5 (hidden single in C1), R3C9 = 8, R3C5 = 6, R3C23 = [19], R2C2 = 6 (step 32)

and the rest is naked singles.

3x3::k:1793:4866:4866:4866:7171:4100:8197:3078:3078:1793:4866:7171:7171:7171:4100:8197:8197:8197:7175:5384:7945:7945:7171:4100:2826:2826:8197:7175:5384:5384:7945:7945:7945:8971:2826:8197:7175:7175:7175:2316:6413:7945:8971:8971:8971:8206:2831:7175:2316:6413:6413:3088:3088:8971:8206:2831:2831:3089:7442:6413:6413:3088:8971:8206:8206:8206:3089:7442:7442:7442:3859:2068:3093:3093:8206:3089:7442:3859:3859:3859:2068:

Thanks Ed! Lots of nonets you had to combine to find the hidden cages, but it was fun to solve nonetheless.

A144 Walkthrough:

1. C6789
a) 35(6) = 89{1467/2367/2457/3456} -> CPE: R4C9 <> 8,9
b) Outies N3 = 10(2) <> 1,5; R4C8 <> 2
c) Outies N36 = 12(2) <> 1,2,6
d) 12(3): R6C78 <> 9 since R7C8 >= 3
e) 9 locked in 35(6) @ N6 for 35(6)
f) Outies N36 = 12(2): R7C8 <> 3
g) 11(3): R3C78 <> 8 since R4C8 >= 3
h) 12(3): R6C78 <> 8 since R7C8 >= 4

2. C1234 !
a) Outies N7 = 10(2) <> 5; R6C1 <> 1
b) Outies N47 = 14(2) = {59/68}
c) ! 28(6) = 3{12589/12679/14569/24568} because 47{1259/1268/1358} blocked by Killer pair (47) of 21(3)
-> 3 locked for N4
d) Outies N7 = 10(2) <> 7

3. N35689
a) Innies N3689 = 14(2) = {59/68}
b) Outies N35689 = 6(2) = {15/24}
c) 11(3) <> 8 since {12}8 blocked by Killer pair (12) of Outies N35689
d) Outies N3 = 10(2) <> 2
e) 8 locked in 35(6) @ N6 for 35(6)
f) Outies N36 = 12(2): R7C8 <> 4
g) 12(3) @ N6: R6C78 <> 5,7 because R7C8 >= 5 and R7C8 <> 6
h) 5 locked in 35(6) @ N6 for 35(6) -> 35(6) = 4589{27/36} -> CPE: R4C9 <> 4
i) 1 locked in 12(3) @ N6 for R6

4. R456 !
a) Outies N7 = 10(2) <> 9
b) 1 locked in 28(6) @ N4 = 139{258/267/456}
c) ! Killer pair (24) locked in 28(6) + Outies N7 for N4
d) 21(3) = 7{59/68} -> 7 locked for R4+N4
e) Outies N3 = 10(2) = {46} -> R4C9 = 6, R4C8 = 4
f) 35(6) = {245789} -> R7C9 = 4; 2 locked for N6
g) 12(3) = {138} -> R7C8 = 8; 1,3 locked for R6

5. C789
a) 6 locked in 11(3) @ N3 = {146} -> 1,6 locked for R3+N6
b) 1 locked in 8(2) @ C9 = {17} locked for C9+N9
c) 35(6) = {245789} -> 7 locked for R5

6. R3456
a) Outies N47 = 14(2) = {59} locked for R3+N1
b) 31(6) = {234589} since R3C34 = (24) -> 2,4 locked for R3+31(6); {3589} locked for N5
c) 9(2) = {27} -> R5C4 = 2, R6C4 = 7
d) 25(5) = {14569} -> R5C5 = 1; {46} locked for R6+25(5); {59} locked for R7
e) R3C4 = 4, R3C3 = 2

7. R789
a) 12(3) = 1{38/56} -> 1 locked for C4+N8
b) 15(4) = {2346} -> R9C6 = 4; {236} locked for N9
c) 12(2) <> 8
d) 8 locked in 32(6) @ N7 for 32(6)
e) R6C1 = 2, R6C2 = 8
f) 11(3) = {128} -> R7C3 = 1, R7C2 = 2

8. C123
a) Hidden Single: R4C1 = 1 @ R4
b) 7(2) = {34} locked for C1+N1
c) 28(5) = 268{39/57} -> 2 locked for C5+N2

9. C456
a) R6C6 = 6
b) 16(3) = 8{17/35} -> 8 locked for C6+N2
c) 28(5) = 268{39/57} -> R2C3 = 8
d) Innie N2 = R1C4 = 5
e) 12(3) = {138} -> R7C4 = 3; 8 locked for C4+N8

10. Rest is singles.

Rating: 1.0 - Hard 1.0. I used Killer pairs.

After a longer period of no-sudoku this was a good puzzle to find the way back. Hopefully I'll find the time to contribute a new puzzle in a couple of weeks (after I've solved some older ones).

Here's my walkthrough, the way I did it, so it's not very orderly.

Walkthrough Assassin 144

0. Preleminaries
0a. 7(2) @ r1c1 = {16|25|34} -> no 7,8,9
0b. 12(2) @ r1c8 = {39|48|57} -> no 1,2,6
0c. 12(2) @ r9c1 = {39|48|57} -> no 1,2,6
0d. 21(3) @ r3c2 = {489|579|678} -> no 1,2,3
0e. 11(3) @ r3c7 = {128|137|146|236|245} -> no 9
0f. 11(3) @ r6c2 = {128|137|146|236|245} -> no 9
0g. 9(2) @ r5c4 = {18|27|36|45} -> no 9
0h. 8(2) @ r8c9 = {17|26|35} -> no 4,8,9

1. 8,9 locked in 35(6) @ r4c7 -> no 8,9 in r4c9

2. 45 on n7: r6c12 = h10(2) = {28|37|46}|[91] -> no 5, no 1 in r6c1

3. 45 on n47: r3c12 = h14(2) = {59|68} -> no 1,2,3,4,7

4. 45 on n3: r4c89 = h10(2) = {37|46}|[82] -> no 1,5, no 2 in r4c8
4a. 11(3) @ r3c7: no 8 in r3c78

5. 45 on n36: r7c89 = h12(2) = {39|48|57} -> no 1,2,6

6. 45 on c4: r1234c4 = h24(4)

7. 45 on c789 (2 innies, 1 outie): r78c7 = r9c6 + 10 -> no 8,9 in r9c6, no 1 in r78c7

8. 45 on n2 (1 outie, 2 innies): r2c3 = r13c4 + 1 -> no 1 in r2c3

9. 45 on n3689: r7c67 = h14(2) = {59|68} -> no 1,2,3,4,7
9a. -> r5c5 r6c56 = h11(3) = {128|137|146|236|245} -> no 9
9b. r7: 8 locked in h14(2) and h12(2) for r7

10. 45 on n1247: r3c34 = h6(2) = {15|24} -> no 3,6,7,8,9
10a. -> 9 locked in h25(4) = 9{178|268|358|367} -> no 4

11. 11(3) @ r3c7: {128|245} removed, blocked by h6(2) @ r3c3 -> no 8 in r4c8, no 4,5 in r3c78
11a. -> h10(2) @ r4c8: no 2 in r4c9
11b. r3: 1,2 locked in h6(2) and r3c78 for r3

12. 32(6) @ r1c7: {125789 removed, blocked by 11(3)

13. r4: 4,7 locked in r4c23 and h10(2) for r4

14. 12(3) @ r6c7: no 9 in r6c78
14a. -> 9 locked in n6 for 35(6) -> no 9 in r7c9
14b. -> h12(2) @ r7c8: no 3 in r7c8
14c. -> 12(3) @ r6c7: no 8 in r6c78
14d. -> 8 locked in n6 for 35(6) -> no 8 in r7c9
14e. -> h12(2) @ r7c8: no 4 in r7c8
14f. -> 12(3) @ r6c7: no 5,7 in r6c78
14g. -> 12(3) @ r6c7: {345} removed, blocked by h10(2) @ r4c8
14h. 5 locked in n6 for 35(6) -> 35(6) = 4589{27|36} -> no 1, no 5 in r7c9, no 4 in r4c9
14i. -> no 6 in r4c8, no 7 in r7c8
14j. -> 12(3) @ r6c7: no 4 in r6c78, 1 locked in r6c78 for r6
14k. -> no 9 in r6c1, no 8 in r5c4

15. 1 locked in n4 for 28(6) -> {234568} removed

16. 11(3) @ r3c7: {236} removed -> 1 locked in r3c78 for r3 and n3

17. h6(2) @ r3c3 = {24} -> 2,4 locked for r3 and 31(6)
17a. -> h25(5) @ r4c4: {2689} removed
17b. -> h11(3) @ r5c5: {137} removed, blocked by h25(4) -> no 7

18. 12(3) @ r7c4: {246} removed blocked by r3c3

19. c9: 1 locked in 8(2) @ r8c9 -> 8(2) = {17} -> 1,7 locked for c9
19a. -> h12(2) @ r7c8: no 5
19b. -> 12(3) @ r6c7: no 6 in r6c78
19c. -> r7: 8,9 locked in h14(2) and r7c8 for r7
19d. -> h10(2) @ r4c8: no 3 in r4c8
19e. -> 11(3) @ r3c7: no 7 in r3c78
19f. -> 12(2) @ r1c8: no 5 in r1c8

20. 15(4) @ r8c8: 17{25|34} removed, blocked by r9c9 -> no 7

21. h24(4) @ r1c4: no 1

22. 45 on n2 (2 innies, 1 outie): no 2,3 in r2c3, no 9 in r1c4

23. 45 on c1234 (3 innies r2c34 r4c4): h23(2+1) = [959]|[878]|{689}
-> no 4,5,7 in r2c3, no 3,5 in r4c4, no 2,3,4 in r2c4
23a. -> 9 locked in h14(2) @ r3c1 and r2c3 for n1 (-> no 9 in r3c5)
23b. -> no 9 in 19(4) @ r1c2, 7 locked in 19(4) for n1
23c. -> from step 22: no 2,4 in r1c4

24. 19(4) @ r1c2: {2467} removed, blocked by r3c3 -> no 2

25. h10(2) @ r4c8: [73] removed, blocked by 35(6) -> h10(2) = [46]
25a. -> r3c78 = {16} -> 1,6 locked for r3 and n3
25b. -> h14(2) @ r3c1 = {59} -> 5,9 locked for r3 and n1
25c. -> r7c89 = [84]
25d. -> r6c78 = {13} -> 1,3 locked for r6 and n6
25e. -> h14(2) @ r7c6 = {59} -> 5,9 locked for r7 and 25(5)
25f. -> h11(3) @ r5c5: no 2,4,6,8 in r5c5
25g. -> no 2 in r12c1
25h. -> 10(2) @ r6c1 = {28|46} -> no 3,7
25i. -> 21(3) @ r3c2 = {579} -> 7 locked in r4c23 for r4 and n4
25j. -> 11(3) @ r6c2: {245|137} removed -> no 7
25k. -> {2468} locked in r6c1256 for r6
25l. -> r56c4 = [27], r3c34 = [24]
25m. -> no 8 in r1c9

26. 7 locked in r3c56 for r3 and n2

27. {59} locked in r3c1 r6c3 for 28(6)

28. 12(3) @ r7c4 = 1{38|56} -> 1 locked for c4 and n8, no 9
28a. -> 15(4) @ r8c8 = {2346} -> r9c6 = 4, r8c8 r9c78 = {236} -> 2,3,6 locked for n9
28b. -> {59} locked in r78c7 for c7
28c. -> r4c7 = 2, r2c9 = 2
28d. -> h10(2) @ r6c1 = {28}
28e. -> r6c56 = [46], r5c5 = 1
28f. -> r4c1 = 1, r12c1 = {34}, r5c1 = 6
28g. -> 12(2) @ r9c1 = {57}|[93]

29. 16(3) @ r1c6 = {178} -> r3c6 = 7, r12c6 = {18} -> 1,8 locked for c6
29a. -> r3c5 = 3, r3c9 = 8

30. {1236} locked in r3689c8 for c8
30a. -> {59} locked in r56c9 for c9 and n6
30b. -> r5c78 = [87], r1c89 = [93], r2c8 = 5, r12c1 = [43], r12c7 = [74]
30c. -> r2c45 = {69} -> r2c3 = 8, r1c45 = [52], r12c6 = [81], r2c2 = 7

Rating: I'm a little rusty, so no rating from me.

This puzzle seems to bring about much activity ! Very enjoyable puzzle Ed ! I like all these hidden cages !
I think this killer seems quite difficult to solve for a human because the path is not direct, but I did not have to use technical moves (which explains may be SSscore) : locked candidates, combinations, naked subsets and simple cage blockers.

EDIT : I have made further explanations for step 2

ASSASSIN 144 WALKTHROUGH

1.Hidden cages
a. Outies at n7 : r6c12 total 10 no 5
b. Innies at n1247 : r3c34 total 6 no 36789
c. Outies at n5 : r7c67 total 14 no 12347
d. Outies at n3 : r4c89 total 10 no 5
e. Outies n36 : r7c89 total 12 no 126
f. Outies at n47 : r3c12 total 14 no 12347
g. Innies at c1234 using hidden cage 6(2) at r3c34 : r2c34 + r4c4 total 23 : combinations :
6{89} / [797] / 8{69} / [878] / [959] / 9{68}

2.C789
a. IO for n36 : r7c9 = r6c7+r6c8 → r7c9 different of both r6c7 and r6c8 → r7c9=r4c8
b. r4c8<>9, and r4c8<>8 since r3c78 ={12} blocks combinations of hidden cage 6(2) at r3c23.
c.We have r7c9=r4c8=(347) : r4c89 r7c89 = [3793] / [4684] / [7357]
d. r4c89 r7c89 = [3793] → r6c78 = {12}
r4c89 r7c89 = [4684] → r6c78= {13}
r4c89 r7c89 = [7357] → r6c78= {16} ({25} impossible since r7c8 would be 5 and {34} is blocked by combinations of r4c89)
→ 1 locked for n6 and r6
e. If r4c9=6, r3c78 must contain 6 (nowhere else at n3). Let us see combinations of r3c78
r3c78 = {17} / {26} if r4c89 r7c89 = [3793] (no {35} since r4c8=3)
r3c78={16} if r4c89 r7c89 = [4684] (no {25} which would block cage 6(2) at r3)
r3c78={13} if r4c89 r7c89 = [7357].
But {26} is impossible it would block both hidden cages 14(2) and 6(2) of r3 → 1 is locked for n3 and r3 at r3c78.
f. 1 is locked for c9 at cage 8(2) : r89c9={17} locked for c9/n9 and r4c8<>7
→ r3c34 ={24} locked for r3 and the rest of cage 31(6)
r4c89r7c89=[4684] (since there is no 7 at cells r4c89 and r7c9)
r6c78={13} locked for r6 and n6
- r3c78={16} locked for r3 and n3
r3c12={59} locked for r3 and n1
r7c67={59} locked for r7 and the rest of cage 25(5)

3. N12
a. Cage 21(3)={579} (last combination)
b. 7 locked for r4 and n4 at r4c23 → r4c4<>7 → r2c3<>7 (step 1.g)
c. 7 locked for n1 in cage 19(4) → r1c4<>7
d. IO for n1 : r1c4 +5 = r2c3+r3c3. r2c3={68} and r3c3={24} → r1c4={35} (no 7 (step 3.c))
e. R23c3 cannot be [84] because r1c4<>7 and r23c3 cannot be {64} because it would block combinations of cage 7(2) = {16} {34} → r3c3=2 r3c4=4.

4.N5
a. No 5 in n5 in cages 9(2) (r3c3=4) and in cage 25(5) (r7c67 contain 5) → digit 5 locked for n5 in cage 31(6).
b. Cage 31(6) contains all of {245} → cage 31(6) = {234589} → r4c56={3589} and r5c6 = {3589}
c. Naked subset of size 5 {35789} locked for r4 at r4c23456 → {38} locked for r4 and n5 at r4c456 → No 3/8 at r5c6. r5c6={59}
d. Naked singles for r4 : r4c7=2 r4c1=1
e. Cage 7(2) at c1 = {34} → 3 4 locked for c1 and n1
f. Cage 9(2) at n5 ={27} → 2 7 locked for c4 and n5.
g. Cage 25(5) at n5 = {146}{59} → r5c5=1 and r6c56={46} locked for r6

5.C456 N4
a. Hidden cage 10(2) at r6c12={28} (last combination) locked for r6/n4 → r56c4=[27]
b. Naked pair {59} for r6 locked at r6c39 and naked triple {579} locked for n4 at r4c23 and r6c3
c. r5c1 =6 (naked single) r5c23={34}
d. Digit 1 locked for n2 in cage 16(3). Combination {196} for cage 16(3) blocked by the naked pair {59} locked at r57c6 → r123c6={178} locked for c6 and n2.
e. R4c6=3 (naked single) Naked triple {246} locked for c6 at r689c6.

6.C6789
a. Digit 2 locked for n9 and c8 at r89c8
→ r9c6<>2 r2c9=2 (hidden single for n3) r1c5=2 (hidden single for n2)
b. r9c6<>6 since {14} at r79c9 would block all combinations for cage 15(4) → r9c6=4
r8c6=2 r6c6=6 (all naked singles)
c. Hidden single for r3 : r3c6=7 (I should have seen it earlier) → r12c6={18}
d. Last combination for cage 15(4) at n89 :{2346} with r9c6=4 (step 6b.) and {236} locked for n9.

7.a. Naked singles : r3c5=3 r3c9=8 r1c4=5
b. R2c3=8 (IO for n1 :step 3d)
c. Step 1.g → r24c4 cannot be [78] (r6c4=7) so r24c4 =[69]
d. Last combination : Cage 12(2) in n3-> r1c89={39} locked for n3/r1
e.r12c1=[43] r123c6=[817]
f. r5c7=8 (hidden single in n6) r5c8=7 (hidden single in n6) r56c9={59} locked for c9
g. Cage 12(2) at r1 : r1c89=[93]
h. naked pair {57} at r4c23 locked for r4/r3c2 → r3c2=9=r6c3.
i. NS : r5c6=5, r4c5=8, r7c67=[95], r8c7=9
j. Hidden singles for r9 : r9c1=9 (→ r9c2=3), r9c4=8


Rest is singles.


Edit : It was lacking steps 7h and 7i for stating step 7j; thanks Andrew !]

Thanks Ed for an interesting puzzle.

Three very different walkthroughs already posted but I think my one is different enough to post it as well.

I'll rate A144 at Easy 1.25 because I used a killer triple and some split cages.

Here is my walkthrough. After an easy start I slowed right down until I decided in step 18 to look at the 28(6) cage at R3C1 which didn't seem promising even though 1 was locked in it. After that it was easy although my mop-up took a lot of steps.

Prelims

a) R12C1 = {16/25/34}, no 7,8,9
b) R1C89 = {39/48/57}, no 1,2,6
c) R56C4 = {18/27/36/45}, no 9
d) R89C9 = {17/26/35}, no 4,8,9
e) R9C12 = {39/48/57}, no 1,2,6
f) 21(3) cage at R3C2 = {489/579/678}, no 1,2,3
g) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
h) 11(3) cage at R6C2 = {128/137/146/236/245}, no 9
i) 35(6) cage at R4C7 = {146789/236789/245789/345689}, CPE no 8,9 in R4C9

1. 45 rule on N3 2 outies R4C89 = 10 = {37/46}/[82], no 1,5, no 2 in R4C8

2. 45 rule on N7 2 outies R6C12 = 10 = {28/37/46}/[91], no 5, no 1 in R6C1

3. 45 rule on N36 2 outies R7C89 = 12 = {39/48/57}, no 1,2,6
3a. 45 rule on N36 1 outie R7C9 = 2 innies R6C78
3b. Max R6C78 = 9, no 9

4. 45 rule on N47 2 outies R3C12 = 14 = {59/68}

5. 45 rule on N1247 2 innies R3C34 = 6 = {15/24}

6. 45 rule on N3689 2 innies R7C67 = 14 = {59/68}
6a. R7C67 = 14 -> R5C5 + R6C56 = 11 = {128/137/146/236/245}, no 9
6b. R3C34 = 6 (step 5) -> R4C456 + R5C6 = 25 and must contain 9 = {1789/2689/3589/3679} (cannot be {4579} which clashes with R3C34), no 4

7. 45 rule on N89 4 innies R7C6789 = 26 = {3689/4589/5678} (cannot be {4679} which clashes with R7C67), 8 locked for R7

8. 11(3) cage at R3C7 = {137/146/236} (cannot be {128/245} which clash with R3C34), no 5,8, clean-up: no 2 in R4C9 (step 1)
8a. 6 of {146} must be in R3C78 (R3C78 cannot be {14} which clashes with R3C34), no 4 in R3C78
8b. Killer pair 1,2 in R3C34 and R3C78, locked for R3

9. 9 in N6 locked in R4C7 + R5C789 + R6C9, locked for 35(6) cage, clean-up: no 3 in R7C8 (step 3)
9a. Max R7C9 = 8 -> max R6C78 (step 3a) = 8, no 8
9b. 8 in N6 locked in R4C7 + R5C789 + R6C9, locked for 35(6) cage, clean-up: no 4 in R7C8 (step 3)
9c. Max R7C9 = 7 -> max R6C78 (step 3a) = 7, no 7
[I originally started this as step 4 but it’s more interesting here when it can be used recursively]

10. 12(3) cage at R6C7 = {129/138/147/156/237} (cannot be {246} because 2,4,6 only in R6C78, cannot be {345} which clashes with R4C89)
10a. 5 of {156} must be in R7C8, no 5 in R6C78

11. 5 in N6 locked in R4C7 + R5C789 + R6C9, locked for 35(6) cage, clean-up: no 7 in R7C8 (step 3), clean-up: no 1 in 35(6) cage (prelim i, because 5 locked in cage)
11a. 1 in N6 locked in R6C78, locked for R6, clean-up: no 8 in R5C4, no 9 in R6C1 (step 2)

12. 12(3) cage at R6C7 (step 10) = {129/138/156}, no 4
12a. R5C5 + R6C56 (step 6a) = {128/137/146/236/245}
12b. 1 of {128/137} must be in R5C5 -> no 7,8 in R5C5

13. 35(6) cage at R4C7 = {245789/345689}, CPE no 4 in R4C9, clean-up: no 6 in R4C8 (step 1)
13a. 3 of {345689} must be in R7C9 (R4C7 + R5C789 + R6C9 cannot be {35689} which clashes with R4C89), no 3 in R4C7 + R5C789 + R6C9

14. 21(3) cage at R3C2 = {489/579/678}
14a. 6 of {678} must be in R3C2 (R4C23 cannot be {67} which clashes with R4C89), no 6 in R4C23

15. 45 rule on R1234 3(1+2) innies R3C1 + R4C17 = 1 outie R5C6 + 3
15a. Max R3C1 + R4C17 = 12, min R3C1 = 5 -> max R4C17 = 7, no 7,8,9, no 6 in R4C1
15b. Min R3C1 + R4C17 = 5 + 3 = 8 -> min R5C6 = 5

16. 45 rule on C789 2 innies R78C7 = 1 outie R9C6 + 10
16a. Min R78C7 = 11, no 1
16b. Max R78C7 = 17 -> max R9C6 = 7

17. 45 rule on C1234 5(2+3) innies R23C3 + R234C4 = 29
17a. R3C34 = 6 (step 5) -> R2C3 + R24C4 = 23
17b. Max R2C34 = 17 -> min R4C4 = 6
17c. Max R24C4 = 17 -> min R2C3 = 6
17d. Max R2C3 + R4C4 = 18 -> min R2C4 = 5

18. 1 in N4 locked in 28(6) cage at R3C1
18a. 28(6) cage at R3C1 = {123589/123679/124579/124678/134569/134578}
18b. Killer triple 2,3,4 in 28(6) cage and R6C12, locked for N4

19. 21(3) cage at R3C2 = {579/678}, 7 locked in R4C23, locked for R4 and N4, clean-up: no 3 in R4C89 (step 1), no 3 in R6C12 (step 2)
19a. R4C89 = [46], clean-up: no 8 in R1C9, no 2 in R89C9

20. R4C8 = 4 -> R3C78 = {16} (step 8), locked for R3 and N3, clean-up: no 8 in R3C12 (step 4), no 5 in R3C34 (step 5)
20a. Naked pair {59} in R3C12, locked for R3 and N1, clean-up: no 2 in R12C1
20b. Naked pair {24} in R3C34, locked for R3 and 31(6) cage at R3C3

21. 21(3) cage at R3C2 = {579} (only remaining combination), CPE no 5,9 in R5C2
[That CPE could have been given in step 20a]
21a. 8 in R4 locked in R4C456, locked for N5, clean-up: no 1 in R5C4
21b. R4C456 + R5C6 (step 6b) = {1789/3589}, no 6

22. 1 in C9 locked in R89C9 = {17}, locked for C9 and N9, clean-up: no 5 in R1C8, no 5 in R7C8 (step 3)

23. Hidden killer pair 1,3 in R4C1 and R4C56 for R4 -> R4C1 = {13}
23a. Killer pair 1,3 in R12C1 and R4C1, locked for C1, clean-up: no 9 in R9C2
23b. R4C7 = 2 (hidden single in R4)

24. 35(6) cage at R4C7 (step 13) = {245789} (only remaining combination) -> R7C9 = 4, R7C8 = 8 (step 3), clean-up: no 6 in R7C67 (step 6)
24a. Naked pair {13} in R6C78, locked for R6, clean-up: no 6 in R5C4
24b. Naked pair {59} in R7C67, locked for R7 and 25(5) cage at R5C5

25. R5C5 + R6C56 (step 6a) = {146/236} (cannot be {137} because 1,3 only in R5C5), no 7
25a. 1,3 only in R5C5 -> R5C5 = {13}, 6 locked in R6C56, locked for R6 and N5, clean-up: no 3 in R5C4, no 4 in R6C12 (step 2)
25b. Naked pair {28} in R6C12, locked for R6 and N4, clean-up: no 7 in R5C4
25c. Naked pair {46} in R6C56, locked for R6 and N5, clean-up: no 5 in R56C4
25d. R56C4 = [27], R3C34 = [24]
[In step 25b I missed CPE no 2,8 in R8C2; I don’t think this made much difference.]

26. R6C56 = {46} -> R5C5 = 1 (step 25)
26a. R4C1 = 1 (hidden single in N4), clean-up: no 6 in R12C1
26b. Naked pair {34} in R12C1, locked for C1 and N1, clean-up: no 8 in R9C2

27. Naked pair {59} in R3C1 + R6C3, locked for 28(6) cage at R3C1 -> R5C1 = 6

28. R2C9 = 2 (hidden single in C9)

29. Naked pair {59} in R57C6, locked for C6

30. 11(3) cage at R6C2 = [236/263/821], no 1,7 in R7C2, no 7 in R7C3

31. R789C4 = {138/156}, no 9, 1 locked for C4 and N8

32. 15(4) cage at R8C8 = {2346) (only remaining combination) -> R9C6 = 4, R6C56 = [46], 3,6 locked for N9, clean-up: no 8 in R9C1
32a. Naked pair {59} in R78C7, locked for C7
32a. Naked triple {136} in R369C7, locked for C7
32b. Hidden killer pair 5,9 in R1C89 and R2C8 for N3 -> R2C8 = {59}

33. 19(4) cage at R1C2 = {1378/1567} (cannot be {1369} because 3,9 only in R1C4), no 9
33a. 3,5 only in R1C4 -> R1C4 = {35}
33b. Killer pair 3,5 in R1C4 and R1C89, locked for R1 -> R12C1 = [43]
33c. Killer pair 3,5 in R1C4 and R789C4, locked for C4
33d. R2C7 = 4 (hidden single in C7)

34. 45 rule on N2 1 outie R2C3 = 1 remaining innie R1C4 + 3 -> R2C3 = {68}
34a. 6 in N2 locked in R1C5 + R2C45, locked for 28(5) cage at R1C5 -> R2C3 = 8, R1C4 = 5, clean-up: no 7 in R1C8, no 6 in R789C4 (step 31)

35. Naked pair {39} in R1C89, locked for N3 -> R2C8 = 5, R3C9 = 8, R1C7 = 7, R5C7 = 8
35a. Naked pair {59} in R56C9, locked for C9 and N6 -> R1C89 = [93], R5C8 = 7
35b. Naked pair {16} in R1C23, locked for R1 and N1 -> R1C56 = [28], R2C2 = 7, R2C6 = 1, R4C6 = 3, R3C56 = [37], R8C6 = 2, clean-up: no 5 in R9C1

36. Naked triple {138} in R789C4, locked for C4 and N8 -> R4C4 = 9, R2C45 = [69], R4C23 = [57], R3C12 = [59], R4C5 = 8, R5C6 = 5, R56C9 = [95], R6C3 = 9, R7C67 = [95], R8C7 = 9, R9C2 = 3, R9C1 = 9, R5C23 = [43], R9C78 = [62], R8C8 = 3, R3C78 = [16], R6C78 = [31]

37. 11(3) cage at R6C2 (step 30) = [821]

and the rest is naked singles.

3x3::k:2817:6658:6658:6658:6915:3076:8197:2054:2054:2817:6658:6915:6915:6915:3076:8197:8197:8197:6919:4360:7945:7945:6915:3076:4618:4618:8197:6919:4360:4360:7945:7945:7945:5899:4618:8197:6919:6919:6919:780:6413:7945:5899:5899:5899:6926:5135:6919:780:6413:6413:4880:4880:5899:6926:5135:5135:5393:5906:6413:6413:4880:5899:6926:6926:6926:5393:5906:5906:5906:4627:2068:2325:2325:6926:5393:5906:4627:4627:4627:2068:

I have to agree that the important move was hard to find (it took me some time) since you usually don't look for these things but the move itself wasn't particularly difficult so I agree with SudokuSolver's rating.

A144 V2 Walkthrough:

1. N5
a) 3(2) = {12} locked for C4+N5
b) Innies N1247 = 4(2) = {13} -> R3C4 = 3, R3C3 = 1
c) 31(6) = 1369{48/57} -> 6,9 locked for N5
d) Innies N5 = 15(3) = 3{48/57} -> 3 locked for 25(5)
e) Outies N5 = 10(2) <> 5,7

2. R123 !
a) Outies N47 = 10(2) = {28/46}
b) 26(4): R1C4 <> 5 because R1C23+R2C2 = 8{49/67} blocked by Killer pairs (48,68) of Outies N47
c) Innies C123 = 23(4) = {2579/3479/3569/3578} since 8{249/267/456} blocked by Killer pairs (24,68) of Outies N47
d) ! Innies C123 = 23(4): R2C3 <> 4,6 because R1C23+R2C2 @ 26(4) cannot be 39{5/7}
e) Innies+Outies C123: 3 = R1C4 - R2C3 -> R2C3 = (35), R1C4 = (68)
f) 27(5) = {14589/23589/23679/24579/34569/34578} because R2C3 = (35) and 168{39/57} blocked by R1C4 = (68)
g) 12(3) = 1{29/47/56} <> 8 since {246} blocked by Killer pair (24) of 27(5) -> 1 locked for C6+N2

3. C456
a) Innies C4 = 18(3) = 6{48/57} since R1C4 = (68) -> 6 locked for C4
b) 21(3) = 9{48/57} -> 9 locked for N8
c) Outies N5 = 10(2) = {28/46}
d) Innies N5 = 15(3) = {357} locked for N6 since {348} blocked by Killer pair (48) of Outies N5
e) Innies C4 = 18(3) = {468} locked for C4 because R14C4 = (468)
f) 21(3) = {579} locked for N8

4. R1234
a) Innies+Outies R1234: 2 = R5C6 - (R3C1+R4C17) -> R5C6 = (89); R3C1+R4C17 <> 5,6,7,8,9 since R3C1 >= 2
b) 31(6) = {134689} -> 4,6 locked for R4
c) Outies N3 = 13(2) = {58} locked for R4+N6
d) Hidden Single: R5C6 = 8 @ N5
e) 31(6) = {134689} -> 9 locked for R4
f) Outies N47 = 10(2) = [28/46]
g) 7 locked in 17(3) @ R4 = {278} -> R3C2 = 8; 2,7 locked for R4+N4
h) Outie N47 = R3C1 = 2

5. C789
a) 9 locked in R23C9 @ C9 for N3
b) 18(3) = 6{48/57} -> 6 locked for R3+N3
c) 32(6) = 1789{25/34} -> 1,7 locked for N3
d) 8(2) = {35} locked for R1+N3
e) 32(6) = {125789} -> R4C9 = 5
f) R4C8 = 8, R1C9 = 3, R1C8 = 5
g) 1 locked in 23(6) @ N6 for 23(6)
h) 19(3) = 9{37/46}
i) Outies N36 = 10(2) = [37/46/64]

6. R789
a) Killer pair (67) locked in Outies N36 + 8(2) for N9
b) 1,8 locked in 23(5) @ N8 for C5+23(5) -> 23(5) = 138{29/56} -> R8C7 = (59)
c) Outies N5 = 10(2) = [28/64]
d) Hidden Single: R9C6 = 4 @ N8
e) 18(4) = {2349} because 5,8 only possible @ R9C7; {239} locked for N9
f) Outies N36 = 10(2) = {46} locked for R7+N9
g) R7C7 = 8
h) 20(3) = 9{47/56}

7. C1234
a) Hidden Single: R2C9 = 8 @ C9, R1C4 = 8 @ N2
b) Outie N2 = R2C3 = 5
c) Outies N7 = 11(2) = {56} locked for R6+N4
d) 20(3) = {569} -> R7C3 = 9, R7C2 = 5, R6C2 = 6
e) 27(5) = {24579} -> R2C4 = 4; {279} locked for C5+N2
f) 26(4) = {3689} -> R1C3 = 6, R1C2 = 9, R2C2 = 3
g) R2C1 = 7, R1C1 = 4
h) 9(2) = {18} -> R9C2 = 1, R9C1 = 8

8. Rest is singles.

Rating: (Hard?) 1.25. I used combo analysis.

Here's how I solved v2.

The usual preliminary innies and outies include R4C89 = 13.

There are 3 possibilities:

1. R4C89 = {67}. By tracking along R4 this quickly leads to a contradiction with the 17(3) cage.
2. R4C89 = {49}. This leads to a contradiction but by a slightly longer path.
3. R4C89 = {58}. Actually [85].

From here the puzzle drops out. In fact, if you start SS from this point the score
drops from 1.25 to 0.76 - just a tad higher than a typical Times deadly killer.

I am not sure I have seen the important move since I had to use technical moves. Here is my wt, different from Afmob's who seems to have found a more direct path.

Edit : have changed slightly my wt : it might be easier to read and avoid some previous horrible combinations !
WALKTHROUGH A144 V2

1)Innies for n1247 : r3c34 totals 4 → r3c34={13}. Split cage 31(6) → hidden cage 27(4) at r3c4 and r4c456.

2){12} locked for c4 and n5 in cage 3(2) → r3c34=[13]

3)Outies for n47 : r3c12 totals 10 → combinations {28/46}

4)Outies n3 → r4c89 totals 13 : {49/58/67}

5)Innies for n3689 : r7c67 totals 10 → split cage 25(5) : hidden cage 15(3) at r5c5 and r6c56.

6)Hidden single 3 for hidden cage 15(3) at n5 : combinations {348/357} → hidden cage 27(4) at n5 admits combinations {4689/5679}

7)IO for r4 : r3c2+r5c6 =12+r4c1+r4c7 → r3c2+r5c6 >= 15 → r3c2={68}. We deduce from step 3) that r3c12=[28/46]

8)Combinations using steps 4) and 6) : r4c45689={567}{49} / {269}{58} / {469}{58} / {489}{67}
→ r4c1237 ={1238/1234/1237/1235}
(If r4c89= {49}, hcage 27(4) at n5 cannot be {4689} and if r4c89={67}, hcage 27(4) at n5 cannot be {5679}).

9)Since r3c2={68}, there is no valid combinations for cage 17(3) at n14 if r4c123={1234/1235} → r4c45689={567}{49} / {469}{58}. We deduce that cage 17(3) at n14 admits the following combinations : 6{38} or 8{27} and there is no {67} for r4c89.

10)Outies for n7 : r6c12 totals 12 → hidden cage 11(2) at r6c12

11)- If cage 17(3) at n14=6{38}, r3c1=4 (step 3) ) and 4 is locked for n4 at r6c2 → r6c12=[74]
-If cage 17(3) at n14=8{27} and r6c12={38/56} (no other combinations)
→ No {29} for r6c12

12)cage 23(6) at n69 must uses digit 4 → r4c9 <> 4

13) There is no 4 at r4c8 ! By contradiction, if r4c8=4, r7c9=4 since cage 23(6) must use digit 4, so r7c8=6, r6c78 totals 13 and cannot contain 4 or 6 → r6c78={58} and r6c12={47} (no 2,9 from
step 11) , and these two previous combinations block hcage 15(2) at n5 (step 6 : {348} / {357})
→ r4c89={58}

14)From step 9, we deduce that cage 17(3) at n14 = 8{27}, r3c1=2, r4c234={469}, r5c6=8, and hidden cage 15(3) at n5 is composed by {357}

15)No 8 at r3c78 since r4c8 ={58} (no valid combination) → digit 8 is locked for n3 in cage 32(6) → r4c9<>8.
We deduce from step 13) that r4c89=[85].

16)R3c78={46} (last combination for cage 18(3) ) and 5 is locked for n3 at r1c8 → r1c9=3

17)Digit 5 is locked for r3 at r3c56 → 5 is locked for c4 in cage 21(3) : r789c4 = {579}, 5 7 and 9 locked for c4 and n8. R4c4={46}, {468} locked at r124c4, 8 locked for n2

18)IO for n1 : r1c4 = r2c3+3 → from step 17, r1c4={68} r2c3= {35} (no 1 at r2c3)

19) r2c1<>6 since r1c1 cannot be 5 → digit 6 is locked for n1 at r1c123+r2c2 → r1c4 <>6, so r1c4=8 and r2c3=5 (step 18) ).

20)Cage 11(2) at c1={47}, cage 26(4) at n1 = {369} with r2c2=3

21) Combinations for hcage 11(2) at n4 : {38/56} : {38} blocked by r23c3=[38] → r6c12={56}

22)HS for n5: r5c5=5, r6c56={37}, HS for n4 : r6c3=8

23)Digit 8 at r4c8 sees all cells of cage 19(3) at n69 → no 1 2 → Hidden pair {12} for r6 locked at r6c49 → r6c78={49}, r7c8=6, r7c9=4
(HS for c9)

24)HS for nr3 : r3c6=5 → r12c6=[16]

25)8 locked for c1 at r789c1 → r6c2<>5 (no combination for cage 20(3) ) → r6c12=[56], r7c23=[59]

26)NS : r7c4=7, r7c67=[28] (last combination for hidden cage 10(2))

27)HS for r6 : r4c6=9, r6c6=7

28)Last combination for cage 8(2) at c9 : {17}

29)HS for c4 : r2c4=4, r4c4=6

30)NS : r89c6 = {34}.

31)HS : r3c78=[64], r7c78=[49]

32)IO for n9 : r8c7=1+r9c6 : r8c7<>4 → (step 30) ) r8c7=5, r89c6=[34]

33)The rest is naked singles

Congratulations to Afmob on finding the "easy" way to do this puzzle (A144V2) - which is the same way as SS does. No wonder I couldn't find it! Am very glad I ditched this one as the V1 as I dislike that sort of combo analysis and would rate it much higher than Afmob and SS have! But as I said, really well done to Afmob for finding it.

BTW - by altering the code to block Afmob's way to this,
3x3::k:2817:5890:5890:7683:7683:3076:8197:2054:2054:2817:5890:5890:7683:7683:3076:8197:8197:8197:6919:4360:7945:7945:7683:3076:4618:4618:8197:6919:4360:4360:7945:7945:7945:5899:4618:8197:6919:6919:6919:780:6413:7945:5899:5899:5899:6926:5135:6919:780:6413:6413:4880:4880:5899:6926:5135:5135:5393:5906:6413:6413:4880:5899:6926:6926:6926:5393:5906:5906:5906:4627:2068:2325:2325:6926:5393:5906:4627:4627:4627:2068:
..it now gets a score of 2.26. However, it appears that SudokuSolver is unable to do one key move (see my WT below step 20). If I give SS that move when it's first available, it does 18 fewer steps, so the score could come down below 2. Still very tough and very close to my original estimation of 2.0.

Short WT for A144 v2
Prelims
i. 11(2)n1: no 1
ii. 26(4)n1: no 1
iii. 8(2)n3: no 4,8,9
iv. 23(6)n6: no 9
v. 3(2)n5 = {12}
vi. 20(3)n4: no 1,2
vii. 19(3)n6: no 1
viii. 21(3)n8: no 1,2,3,
ix. 8(2)n9: no 4,8,9
x. 9(2)n7: no 9

1. 3(2)n5 = {12}: both locked for n5 & c4

2. "45" n1247: 2 innies r3c34 = 4 = [13]
2a. split cage 27(4)n5 = {4689/5679}
2b. 6 & 9 locked for n5

3. 3 remaining innies n5 = 15 and must have 3 for n5
3a. = 3{48/57}
3b. 3 locked for 25(5)n5

4. "45" r1234: 1 outie r5c6 - 2 = 3 innies r3c1 + r4c17
4a. min. 3 innies = [2][12] = 5 -> min r5c6 = 7
4b. max. 3 innies = 7 -> max. r4c17 = 5 (no 5..9)
4c. max. 3 innies = 7 and min. r4c17 = 3 -> max. r3c1 = 4

5. "45" n47: 2 outies r3c12 = 10 = [28/46]

6. 6 in n5 only in r4: locked for r4

7. 23(6)n6 = 1234{58/67}
7a. r4c9 "sees" all of the 23(6) -> no 1,2,3,4 in r4c9 (CPE)

8. "45" n3: 2 outies r4c89 = 13 (no 1,2,3)
8a. = [49]{58}(no 7)

Now time for a new move, IOE (see image below) [edit: Changed wording for clarity, Thanks Afmob and Andrew!]
When the Outies "see" all of a candidate for a house except for the Innies, the 3rd cell must Equal the in/out difference (IOD).
i. For example, "45" n3: 2 innies r3c78 - 5 = 1 outie (r4c9)
ii. the 1 outie (r4c9) sees all of 4, 8 & 9 for n3 (they can't be in the 8(2)n3), except for the innies r3c78.
iii. so, when 8 is in r4c9, 8 must be in the innies, r3c78. Since 1 innie = 1 outie -> the 3rd cell (in this case, one of r3c78) must equal the IOD for n3 = 5
iv. same thing for 9 since it sees all 9s in n3 except r3c78. So, 9 in r4c9 -> r3c78 = {59}(IOE)
v. of course, this doesn't work for the 5 in r4c9 because it doesn't see all 5s in n3 apart from the innies. One 5 can hide from r4c9 in r1c8.

9. So, "45" n3: 1 outie + 5 = r3c78
9a. r4c9 = (589). If not 5, it must be 8 or 9 -> 5 locked in r3c78 (IOE).
9b. -> 5 locked in innies of n3 OR r4c9
9c. -> no 5 in common peers in r4c8, r1c7, r2c789, r3c9 & r1c9.



NOTE: IOE is not enough on its own to make eliminations in this case. Only if r4c9 = (89) would we have been able to lock 5 in r3c78 for n3 & r3 using IOE only.
9e. no 8 in r4c9 (h13(2))

10. 18(3)n3 must have 4/8 = {459/468}(no 2,7)
10a. {68}[4] blocked by r3c2 -> no 8 r3c78
10b. note: 4 locked in 18(3). Important for later.

11. 1 in n6 only in 23(6) -> no 1 in r7c9

12. "45" n36: 2 outies r7c89 = 10 (no 5)
12a. = {28/37/46}(No 9)

This move took a long time to spot.
13. 19(3)n6, {289} blocked since the 8 & 9 sees both 8 & 9 in h13(2)n6 = [49/85]
13a. 19(3) = {379/469/568}(no 2) ({478} blocked by r4c8)
13b. = [8/9..]

14. 2 in n6 only in 23(6) -> no 2 in r7c9
14a. h10(2)r7c89 = {37/46}(no 8)

15. Killer pair {89} in h13(2)n6 & r6c78 (step 13b): 8 locked for n6

16. 23(6)n6 = {123467}(no 5)

17. split cage 27(4)n5 = {4689/5679}
17a. {4689} must have 8 in r5c6 because r4c8 = (48) NOTE: r4c8 = r5c6
17b. {5679} must have 9 in r5c6 because r4c9 = (59) NOTE: r4c9 = r5c6
17c. r5c6 = (89)
17d. r4c456 = {469/567}(no 8)

Another one that took a long time to get since it meant seeing the cell cloning in steps 17a & b
18. since r5c6 = one of r4c89 (steps 17a & b) = (89) -> implied killer pair on (89) with r6c78 = [8/9..](step 13b) -> no 8 in r6c56
18a. 8 in n5 only in r5: locked for r5

19. h15(3)n5 = {348/357}
19a. 8 in {348} must be in r5c5 -> no 4 in r5c5

Now time for the final puzzle breaker.
20. no 4 in r3c1 because of 4s in r5 & 18(3)n3: Grouped Turbot Fish. Like this.
20a. 4 in r5 is in n4 or n6.
20b. If in n4 it must be in the 27(6)n1 -> no 4 in r3c1
20c. If in n6 -> 4 locked in 18(3)n3 must be in r3 -> no 4 in r3c1.
20d. r3c1 = 2

Puzzle is cracked. Very satisfying solution.

Another puzzle from my Unfinished folder "bites the dust"; I finished this one about a week ago but only later found time to go through the posted WTs.

Thanks Ed for a challenging V2 and also for your interesting post about IOE; I think I now understand that technique although I haven't yet been able to apply it to any puzzles.

I seem to have found another way for the key breakthrough, possibly not as technically simple as the way used by Afmob and SS but I feel more elegant, to use udosuk's word.

I took a long time to find the breakthrough but when it came I enjoyed it and felt that it was worth the effort.

Rating Comment. I’ll rate my walkthrough for A144 V2 at Easy 1.5 for the rewritten version of step 15 and because of the clashes in step 20. The latter may not have been needed but omitting it wouldn’t change my rating. If I hadn't seen the rewritten version of step 15, I was going to rate my walkthrough at 1.5 to Hard 1.5 for my original step 15.

Here is my walkthrough for A144 V2.

Prelims

a) R12C1 = {29/38/47/56}, no 1
b) R1C89 = {17/26/35}, no 4,8,9
c) R56C4 = {12}
d) R89C9 = {17/26/35}, no 4,8,9
e) R9C12 = {18/27/36/45}, no 9
f) 20(3) cage at R6C2 = {389/479/569/578}, no 1,2
g) 19(3) cage at R6C7 = {289/379/469/478/568}, no 1
h) 21(3) cage at R7C4 = {489/579/678}, no 1,2,3
i) 26(4) cage at R2C1 = {2789/3689/4589/4679/5678}, no 1
j) 23(6) cage at R4C7 = {123458/123467}, no 9, CPE no 1,2,3,4 in R4C9

Steps resulting from Prelims
1a. Naked pair {12} in R56C4, locked for C4 and N5
1b. 23(6) cage at R4C7 = {123458/123467}, CPE no 1,2,3,4 in R4C9

2. 9 in C9 only in R234C9, locked for 32(6) cage at R1C7, no 9 in R1C7 + R2C78

3. 45 rule on N3 2 outies R4C89 = 13 = [49]/{58/67}, no 1,2,3,9 in R4C8

4. 45 rule on N7 2 outies R6C12 = 11 = [29]/{38/47/56}, no 1,9 in R6C1

5. 45 rule on N36 2 outies R7C89 = 10 = {28/37/46}/[91], no 5

6. 45 rule on N47 2 outies R3C12 = 10 = {19/28/37/46}, no 5

7. 45 rule on N1247 2 innies R3C34 = 4 = [13], clean-up: no 7,9 in R3C12 (step 6)
7a. R3C34 = 4 -> R4C456 + R5C6 = 27 = {4689/5679}, 6,9 locked for N5

8. 3 in N5 only in R5C5 + R6C56, locked for 25(5) cage at R5C5, no 3 in R7C67
8a. R5C5 + R6C56 = {348/357}
8b. 45 rule on N5 2 remaining outies R7C67 = 10 = {19/28/46}, no 5,7

9. 45 rule on N2 1 remaining innie R1C4 = 1 outie R2C3 + 3, no 4 in R1C4, no 7,8,9 in R2C3

10. 1 in N6 only in R4C7 + R5C789 + R6C9, locked for 23(6) cage, no 1 in R7C9, clean-up: no 9 in R7C8 (step 5)

11. 17(3) cage at R3C2 = {269/278/368/458/467} (cannot be {179/359} because R3C2 only contains 2,4,6,8), no 1

12. 18(3) cage at R3C7 = {279/459/468/567}
12a. 8 of {468} must be in R4C8 (R3C78 cannot be {48/68} which clash with R3C12), no 8 in R3C78

13. 45 rule on C789 2 innies R78C7 = 1 outie R9C6 + 9
13a. Max R78C7 = 17 -> max R9C6 = 8

14. R123C6 = {129/147/156/246}, no 8

[This was how far I managed to get when this puzzle first appeared. When I came back to it, I still took some time to find my next step

9 in C9 only in R234C9, R4C89 = 13 (step 3) -> 18(3) cage at R3C7 (step 12) can only contain 9 if it also contains 4 in R4C8 (otherwise cannot place 9 in C9) -> 18(3) cage at R3C7= {459/468/567}, no 2
I’ve changed this to a comment because after the next step and then some more routine ones, the 18(3) cage is directly reduced to two combinations.

Next I studied the 27(6) cage at R3C1 and the 23(6) cage at R4C7 because R3C1 “sees” all of N4 except for R4C23 + R6C2, similarly for R7C9 and N6.
However this didn’t lead to anything. Then I spotted the next step which seems to be the key breakthrough.]

15. R1C4 = R2C3 + 3 (step 9)
15a. R2C3 cannot be 2, 4 or 6 because then 2,4,6,8 in R12C1, R2C3 and R3C12 form killer quad for N1, also if R2C3 is even then R1C4 is odd -> all numbers in 26(4) cage at R1C2 would be odd but this isn’t possible because {3579} only totals 24
15b. -> R2C3 = {35}, R1C4 = {68}
[Maybe step 15a seems to be a contradiction move but I prefer to consider it as creative analysis of even and odd numbers using an innie-outie difference for this purpose.

While checking my walkthrough I noticed a more direct way to write this step.
15. Hidden killer quad 2,4,6,8 in R12C1, R12C23 and R3C12 for N1, R12C1 contains one of 2,4,6,8, R3C12 contains two of 2,4,6,8 -> R12C23 must contain one of 2,4,6,8
15a. 26(4) cage at R1C2 must contain two even numbers (because {3579} only totals 24), R1C23 + R2C2 can only contain one even number -> R1C4 = {68}, R2C3 = {35} (step 9)]

16. 21(3) cage at R7C4 = {489/579} (cannot be {678} which clashes with R1C4), no 6, 9 locked for C4 and N8, clean-up: no 1 in R7C7 (step 8b)

17. 27(5) at R1C5 = {12789/14589/14679/23589/23679/24579/34569/34578} (cannot be {13689/15678/24678} which clash with R1C4
17a. R123C6 (step 14) = {129/147/156} (cannot be {246} which clashes with 27(5) cage), 1 locked for C6 and N2, clean-up: no 9 in R7C7 (step 8b)

18. R5C5 + R6C56 (step 8a) = {357} (only remaining combination, cannot be {348} which clashes with R7C67), 5,7 locked for N5

19. 21(3) cage at R7C4 (step 16) = {579} (only remaining combination, cannot be {489} which clashes with R14C4, ALS block), 5,7 locked for C4 and N8

20. R1C4 = R2C3 + 3 (step 9) -> R1C4 + R2C3 = [63/85]
20a. 27(5) at R1C5 (step 17) = {23589/24579/34578} (cannot be {23679/34569} which clash with R1C4 + R2C3), no 6, CPE no 5 in R2C6

21. R4C89 (step 3) = {58/67} (cannot be [49] which clashes with R4C456, ALS block), no 4,9
21a. Killer pair 6,8 in R4C456 and R4C89, locked for R4
21b. Hidden killer pair 6,8 in R4C456 and R4C89 for R4, R4C89 contains one of 6,8 -> R4C56 only contains one of 6,8 -> R5C6 = {68}
21c. 4,9 in N5 only in R4C456, locked for R4

22. 9 in C9 only in R23C9, locked for N3
22a. 18(3) cage at R3C7 (step 12) = {468/567}, no 2, CPE no 6 in R12C8, clean-up: no 2 in R1C9

23. 17(3) cage at R3C2 (step 11) = {278} (only remaining combination, cannot be {368/458/467} because 4,6,8 only in R3C2) -> R3C2 = 8, R4C23 = {27}, locked for R4 and N4, R3C1 = 2 (step 6), clean-up: no 3,9 in R12C1, no 6 in R4C89 (step 3), no 3,4 in R6C1 (step 4), no 4,9 in R6C2 (step 4), no 1 in R9C1, no 7 in R9C2

[It’s no longer relevant but earlier I’d written the note
1 in N4 only in 27(6) cage at R3C1
R4C23 must contain one odd and one even number, R6C12 must contain one odd and one even number, R3C1 only has even numbers -> 27(6) cage must contain three odd and three even numbers
27(6) cage = {123489/123678/124569/124578/134568} (cannot be {123579} which has four odd numbers).]

24. Naked pair {58} in R4C89, locked for R4 and N6, CPE no 5,8 in R2C8
24a. R5C6 = 8 (hidden single in N5), clean-up: no 2 in R7C7 (step 8b)
24b. 8 in C4 only in R12C4, locked for N2

25. 18(3) cage at R3C7 (step 22a) = {468/567}, 6 locked for R3 and N3, clean-up: no 2 in R1C8

26. Killer pair 3,5 in R6C12 and R6C56, locked for R6
26a. 7 in R5C5 + R6C56 must be in R6C56 (R6C56 cannot be {35} which clashes with R6C12), 7 locked for R6 and N5
26b. 7 in N6 only in R5C789, locked for 23(6) cage at R4C7, no 7 in R7C9, clean-up: no 3 in R7C8 (step 5)

27. 9 in N6 only in R6C78, locked for R6
27a. 19(3) cage at R6C7 = {289/469}, no 7, clean-up: no 3 in R7C9 (step 5)
27b. 8 of {289} must be in R7C8 -> no 2 in R7C8, clean-up: no 8 in R7C9 (step 5)

28. Naked quad {2468} in R7C6789, locked for R7

29. 20(3) cage at R6C2 = {569} (only remaining combination) -> R6C2 = 6, R7C23 = {59}, locked for R7 and N7 -> R7C4 = 7, R6C1 = 5 (step 4), clean-up: no 6 in R12C1, no 3,4 in R9C1, no 4 in R9C2
[At first I spotted that R7C23 are both odd -> R6C2 must be even -> R6C2 = 6 ...]

30. Naked pair {47} in R12C1, locked for C1 and N1, clean-up: no 2 in R9C2

31. R1C3 = 6 (hidden single in N1), R1C4 = 8, R2C4 = 4, R4C4 = 6, R2C3 = 5 (step 9)

32. Naked triple {279} in R123C5, locked for C5 and N2 -> R3C6 = 5, R12C6 = [16], R4C56 = [49], R6C56 = [37], R5C5 = 5, R7C5 = 1, clean-up: no 7 in R1C89, no 4 in R7C7 (step 8b)

33. Naked pair {68} in R89C5, locked for 23(5) cage at R7C5, no 6,8 in R8C7
33a. R789C5 = 1{86} = 15 -> R8C67 = 8 = [35], clean-up: no 3 in R9C9

34. Naked pair {35} in R1C89, locked for R1 and N3 -> R12C2 = [93], R9C2 = 1, R9C1 = 8, R78C1 = [36], R89C5 = [86], R45C1 = [19], R5C23 = [43], R6C3 = 8, R4C7 = 3

36. R89C7 = {17} (only remaining combination) -> [17]

37. Naked pair {24} in R9C36, locked for R9 -> R9C78 = [93]

38. Naked pair {24} in R6C79, locked for R6 and N6 -> R5C9 = 6

39. Naked pair {24} in R67C9, locked for C9 -> R3C9 = 9

and the rest is naked singles.

3x3::k:5377:5377:5377:4866:7184:7184:7184:3606:3606:3843:3843:5377:4866:4111:7184:3603:4375:3606:3843:3076:4866:4866:4111:4111:3603:3603:4375:3076:3076:3590:3083:3083:4111:4120:5401:4375:2821:2821:3590:2573:2573:2573:4120:5401:5401:4359:4359:3590:2828:2828:4622:4120:5401:2581:4361:4359:6920:6920:4622:4622:2834:2834:2581:4361:4361:4362:6920:4622:4369:2834:2581:5140:4362:4362:4362:6920:4369:4369:4369:5140:5140:

Thanks Afmob. I enjoyed that this one. I hope we'll see some walkthroughs from solvers who don't usually post them.

I'll rate A145 at 1.0. I hope that step 9c, which made things a bit quicker but wasn't a key breakthrough, counts within this rating. Edit. Ed's message below suggests that my walkthrough should be rated 1.25; he's probably right. However Ed also shows an alternative step at this stage so a rating of 1.0 is valid for A145.

Here is my walkthrough. I've simplified steps 19 and 25.

Prelims

a) R4C45 = {39/48/57}, no 1,2,6
b) R5C12 = {29/38/47/56}, no 1
c) R6C45 = {29/38/47/56}, no 1
d) R5C456 = {127/136/145/235}, no 8,9
e) 10(3) cage at R6C9 = {127/136/145/235}, no 8,9
f) 11(3) cage in N9 = {128/137/146/236/245}, no 9
g) 20(3) cage in N9 = {389/479/569/578}, no 1,2
h) 28(4) cage at R1C5 = {4789/5689}, no 1,2,3
i) 27(4) cage at R7C3 = {3789/4689/5679}, no 1,2

1. 45 rule on N1 2 innies R3C23 = 9 = {18/27/36/45}, no 9

2. 45 rule on N4 2 outies R37C2 = 9 = {18/27/36/45}, no 9

3. 45 rule on N5 2 innies R46C6 = 12 = {39/48/57}, no 1,2,6
3a. 1 in N5 locked in R5C456, locked for R5

4. 45 rule on N6 2 innies R46C9 = 8 = {17/26/35}, no 4,8,9

5. 45 rule on N7 2 innies R7C23 = 11 = [29]/{38/47/56}, no 1, clean-up: no 8 in R3C2 (step 2), no 1 in R3C3 (step 1)

6. 45 rule on N3 1 innie R1C7 = 1 outie R4C9, no 4,8,9 in R1C7, no 1,2,3 in R4C9, no 5,6,7 in R6C9 (step 4)
6a. 8,9 in 28(4) cage locked in R1C56 + R2C6, locked for N2

7. 45 rule on C789 = R19C7 = 12 = {57}, locked for C7, clean-up: no 6 in R4C9 (step 6), no 2 in R6C9 (step 4)
7a. 28(4) cage at R1C5 = {4789/5689}
7b. R1C7 = {57}, no 5,7 in R1C56 + R2C6

8. R4C45 = {39/48} (cannot be {57} which clashes with R4C9), no 5,7
8a. R6C45 = {29/47/56} (cannot be {38} which clashes with R4C45), no 3,8

9. 45 rule on C1234 3 innies R456C4 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R4C4), no 7,8,9, clean-up: no 3,4 in R4C5, no 2,4 in R6C5
9a. R4C4 = {34} -> no 3,4 in R56C4, clean-up: no 7 in R6C5
9b. 1 of {136} must be in R5C4, no 6 in R5C4
9c. 2 of {235} must be in R5C4 (R456C4 cannot be [352] because R46C5 would both be 9), no 2 in R6C4, clean-up: no 9 in R6C5

10. Naked pair {56} in R6C56, locked for R6 and N5, clean-up: no 7 in R46C6 (step 3)
10a. R5C456 = {127} (hidden triple in N5), locked for R5, clean-up: no 4,9 in R5C12

11. 28(4) cage at R1C5 = {4789/5689}
11a. R1C5 = {89} (R12C6 cannot be {89} which clashes with R46C6)
11b. Naked pair {89} in R14C5, locked for C5
12. 45 rule on C89 2 innies R37C8 = 8 = {17/26/35}, no 4,8,9

13. 45 rule on N9 3 innies R7C9 + R8C8 + R9C7 = 14 = {167/257/356} (cannot be {347} because 10(3) cage at R6C9 cannot contain both of 3,4), no 4

14. 9 in N9 locked in 20(3) cage = {389/479} (cannot be {569} which clashes with R7C9 + R8C8 + R9C7), no 5,6
14a. 11(3) cage in N9 = {128/146/245} (cannot be {137/236} which clash with R7C9 + R8C8 + R9C7), no 3,7

15. 17(3) cage at R2C8 = {179/278/359/458/467} (cannot be {269/368} because R4C9 only contains 5,7)
15a. R4C9 = {57} -> no 5,7 in R2C8 + R3C9

16. 45 rule on R6789 3 innies R6C378 = 15 = {249/348}, no 1,7, 4 locked for R6, clean-up: no 8 in R4C6 (step 3)
16a. 7 in R6 locked in R6C12, locked for N4 and 17(3) cage at R6C1, clean-up: no 2 in R3C2 (step 2), no 7 in R3C3 (step 1), no 4 in R7C3 (step 5)
16b. 17(3) cage at R6C1 = {278} (only remaining combination, cannot be {179} because 1,7,9 only in R6C12, cannot be {467} because 4,6 only in R7C2) -> R6C12 = {278}, R7C2 = {28}, CPE no 8 in R45C2, clean-up: R3C2 = {17} (step 2), R3C3 = {28} (step 1), no 3 in R5C1, R7C3 = {39} (step 5)

17. R6C9 = 1 (hidden single in R6), R4C9 = 7 (step 4), R1C7 = 7 (step 6), R9C7 = 5
17a. 10(3) cage at R6C9 = {127/136}
17b. 7 of {127} must be in R8C8 -> no 2 in R8C8

18. 28(4) cage at R1C5 = {4789}, no 6, 4 locked in R12C6, locked for C6 and N2, clean-up: no 8 in R6C6 (step 3)
18a. Naked pair {39} in R46C6, locked for C6 and N5 -> R4C45 = [48], R1C5 = 9

19. 45 rule on R1234 3 innies R4C378 = 12 = {129/156} -> R4C3 = 1, R4C78 = [29/65/92], no 6 in R4C8

20. 4 in N4 locked in R56C3
20a. R4C3 = 1 -> R56C3 = {49}, locked for C3 and N4 -> R7C3 = 3, R7C2 = 8 (step 4), R3C2 = 1 (step 2), R3C3 = 8 (step 1)

21. Naked pair {27} in R6C12, locked for R6 and N4
21a. R5C1 = 8 (hidden single in N4), R5C2 = 3
21b. Naked pair {56} in R4C12, locked for R4
21c. Naked pair {29} in R4C78, locked for R4 and N6 -> R4C6 = 3, R6C6 = 9, R56C3 = [94]

22. R7C3 = 3 -> R789C4 = 24 = {789}, locked for C4 and N8

23. 17(4) cage at R8C5 = {2456} (only remaining combination) -> R9C5 = 4, R89C6 = {26}, locked for C6 and N8
23a. Naked pair {15} in R7C56, locked for R7 and N8 -> R8C5 = 3

24. Naked pair {26} in R7C89, locked for R7 and N9 -> R7C7 = 4, R5C7 = 6, R8C8 = 7
24a. R5C7 = 6 -> R46C7 = 10 = [28], R46C8 = [93], R8C7 = 1, R7C8 = 6 (step 14a), R7C9 = 2, R9C8 = 8, R89C9 = [93], R8C4 = 8
24b. R23C7 = {39} -> R3C8 = 2 (cage sum)

25. 8 in N3 locked in 14(3) cage = {158} (only remaining combination) -> R1C8 = 1, R2C8 = 4, R3C9 = 6, R5C89 = [54], R12C6 = [48], R12C9 = [85]

26. 19(4) cage at R1C4 = {2368} (only remaining combination) -> R3C4 = 3, R12C4 = {26}, locked for C4 and N2 -> R5C4 = 1, R5C56 = [27], R6C45 = [56], R3C56 = [75], R2C5 = 1, R7C56 = [51], R23C7 = [39], R3C1 = 4

27. 9 in N1 locked in 15(3) cage = {249} (only remaining combination) -> R2C12 = {29}, locked for R2 and N1 -> R12C4 = [26], R2C3 = 7

28. R1C1 = 3, R9C1 = 1 (hidden singles in C1), R8C2 = 4 (hidden single in C2)
28a. R8C2 = 4 -> R78C1 = 13 = [76]

and the rest is naked singles.

There certainly are. Ed's A144 V2 and Frank's A142 V2 are two that I haven't yet finished but hope to do so.

Afmob suggested to me that there's an easier way than my step 9c so I had another look and found

9. 45 rule on C1234 3 innies R456C4 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R4C4), no 7,8,9, clean-up: no 3,4 in R4C5, no 2,4 in R6C5
9a. R4C4 = {34} -> no 3,4 in R56C4, clean-up: no 7 in R6C5
9b. Hidden killer pair 2,6 in R5C456 and R6C45 for N5 -> R5C456 and R6C45 must each contain one of 2,6
9c. 1 locked in R5C456 (step 3a) = {127} (only remaining combination, cannot be {136} because R456C4 cannot contain both of 2,4), locked for R5 and N5, clean-up: no 5 in R46C6 (step 3), no 9 in R6C5

It's a more interesting way but I'm not sure that it's really any simpler than my original step 9c. Maybe I'm still missing something?

Thanks Afmob for a fun puzzle. Lots of areas to explore with lots of eliminations! [edit: for some reason I can't see the puzzle image right now. Can't blame ImageShack this time!]Here's a simpler step 9

A145 Andrew's step 9 ALT 2

9. 45 rule on c1234: 1 innie r5c4 + 13 = 2 outies r46c5. Max. 2 outies = 17 -> max. r5c4 = 4
9a. 45 rule on C1234 3 innies R456C4 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R4C4), no 7,8,9, clean-up: no 3,4 in R4C5, no 2,4 in R6C5
9b. R4C4 = {34} -> no 3,4 in R56C4, clean-up: no 7 in R6C5
9c. 2 of {235} must be in R5C4, no 2 in R6C4, clean-up: no 9 in R6C5

Andrew's step 13 (& 14 which results) is the trickiest one which I'd rate at least 1.25. However, those steps are not essential to the solution (left them out while going through the WT) so no worries with a 1.0 rating.

I meandered around after the equivalent of Andrew's step 9 before getting to his step 16 so I found this one a 1.25 rating puzzle. Nice feeling being on time with you guys. Think I'll just skip some of the recent V1s I haven't been able to get to.

Nice solution path, Ed! Your way is easier than mine. I think the way I solved it also justifies a 1.0 rating. I'm glad that despite SudokuSolver's rating this one was easier to solve than recent Assassins.

A145 Walkthrough snippet

1. C789
a) Innies N6 = 8(2) <> 4,8,9
b) Innies+Outies N3: R1C7 = R4C9 = (567)
c) Innies C789 = 12(2) = {57} locked for C7
d) 28(4) = 89{47/56} -> 8,9 locked for N2; R1C56+R2C6 <> 5,7 since R1C7 = (57)
e) Innies N69 = 12(1+1) = {57} -> CPE: R789C9 <> 5,7
f) Innies N6 = 8(2) = [53/71]

2. C1234
a) 12(2) <> {57} since it's blocked by R4C9 = (57)
b) Innies C1234 = 10(3) = {136/145/235} <> 7,8,9 because R4C4 = (3489); R56C4 <> 3,4
c) 8,9 locked in 27(4) @ C4 for N8+27(4) -> 27(4) = 89{37/46}
d) Innies C123 = 11(2) = [47/56/74/83]
e) Innies N7 = 11(2) = [47/56/74/83]
f) 11(2) = [29/56/65]

3. N235
a) ! Outies N23 = 18(2+1): R4C6 <> 5,7 because R4C9 = (57) and R3C3 <> 6
b) Innies N5 = 12(2) = {39/48}
c) 7 locked in 10(3) @ N5 = {127} locked for R5+N5
d) 11(2) = {56} locked for R6

3x3::k:5377:5377:1282:1282:4099:4099:8964:8964:8964:5377:5377:4357:5894:3335:4099:2568:8964:8964:2825:4357:4357:5894:3335:4362:2568:2568:8964:2825:5894:5894:5894:5899:4362:4362:2572:2572:4109:1806:1806:5899:5899:5899:2831:2831:2572:4109:4109:5648:5648:5899:5649:5649:5649:2322:7187:4372:4372:5648:3349:5649:3606:3606:2322:7187:7187:4372:3863:3349:5649:3606:6168:6168:7187:7187:7187:3863:3863:1561:1561:6168:6168:
and in 81 character JSudoku format
L<5<G<Z<<^^HND^A^^B>^^^H^<^^>>^N^<A<G7<>^<B<^^<M<^M<<9SH<^D^E<^^<^F^^^O<^^<^<6<^^

V2:
3x3::k:3585:3585:2050:2050:4611:4611:6148:6148:6148:3585:3585:5381:6918:1543:4611:5384:6148:6148:3081:5381:5381:6918:1543:3594:5384:5384:6148:3081:6918:6918:6918:6923:3594:3594:2828:2828:4877:2830:2830:6923:6923:6923:2319:2319:2828:4877:4877:2576:2576:6923:6417:6417:6417:3858:8211:3348:3348:2576:2325:6417:4118:4118:3858:8211:8211:3348:4119:2325:6417:4118:4632:4632:8211:8211:8211:4119:4119:2329:2329:4632:4632:
SSS=2.56 **** Uses Extended Trial and Error Steps ****

V3:
3x3::k:5377:5377:3586:3586:3587:3587:8708:8708:8708:5377:5377:3589:5382:1799:3587:2824:8708:8708:2569:3589:3589:5382:1799:4618:2824:2824:8708:2569:5382:5382:5382:7947:4618:4618:3596:3596:2061:3342:3342:7947:7947:7947:1807:1807:3596:2061:2061:4112:4112:7947:6417:6417:6417:2322:7955:3604:3604:4112:2581:6417:3862:3862:2322:7955:7955:3604:4375:2581:6417:3862:4888:4888:7955:7955:7955:4375:4375:3097:3097:4888:4888:
SSS=2.68 **** Uses Extended Trial and Error Steps ****

V4:
3x3::k:5377:5377:2818:2818:3075:3075:7172:7172:7172:5377:5377:4101:4614:2823:3075:4360:7172:7172:2313:4101:4101:4614:2823:4106:4360:4360:7172:2313:4614:4614:4614:6667:4106:4106:4620:4620:4877:2830:2830:6667:6667:6667:3087:3087:4620:4877:4877:2832:2832:6667:5649:5649:5649:3346:6931:4628:4628:2832:2069:5649:5142:5142:3346:6931:6931:4628:4887:2069:5649:5142:3608:3608:6931:6931:6931:4887:4887:2073:2073:3608:3608:
SSS=3.21 **** Uses Extended Trial and Error Steps ****

3x3::k:7168:7168:4866:4866:4866:6149:6149:6149:5128:4873:7168:7168:7168:4866:4866:6149:5128:5128:4873:4873:5908:5908:5908:5908:4888:5128:6682:4873:7196:5908:6174:4888:4888:4888:5128:6682:7196:7196:8230:6174:6174:6174:4888:6682:6682:7196:6190:8230:8230:8230:6174:7475:6682:4917:7196:6190:8230:7475:7475:7475:7475:4917:4917:6190:6190:5697:5442:5442:7236:7236:7236:4917:6190:5697:5697:5697:5442:5442:5442:7236:7236:

Unsolvable #41 is the one in blue
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A<H<MA<A<^P<<^N<<^E^E<^L<^E^^^^^^^^^M<<9<K<<<G^N<^F<SB^<^^L^^^^I<E>^>>^D^^^<^F<>^
E<8<ID<E<^N<<^L<<^A^Q<^K<^D^^^^^^^^^L<<G<I<<<K^C<^O<FB^<^^N^^^^M<C>^>>^K^^^<^B<>^
F<9<IF<K<^L<<^I<<^C^N<^N<^6^^^^^^^^^H<<I<I<<<9^K<^O<OA^<^^L^^^^R<F>^>>^G^^^<^6<>^
F<B<HB<K<^U<<^I<<^C^E<^I<^E^^^^^^^^^H<<G<M<<<C^R<^O<L6^<^^O^^^^K<A>^>>^F^^^<^B<>^
C<5<KD<I<^O<<^P<<^F^R<^C<^9^^^^^^^^^K<<H<I<<<A^X<^Q<IB^>^^I^^^^I<^>^>>^J^^6<^B<>^
C<9<L8<I<^P<<^L<<^C^J<^L<^E^^^^^^^^^N<<H<H<<<7^S<^J<PC^>^^G^^^^Q<^>^>>^G^^A<^9<>^
C<A<O7<G<^K<<^R<<^C^O<^G<^C^^^^^^^^^P<<B<M<<<B^V<^N<M8^>^^J^^^^J<^>^>>^F^^7<^C<>^
D<6<KH<C<^Q<<^P<<^E^M<^G<^9^^^^^^^^^H<<E<J<<<7^U<^Q<V8^>^^N^^^^K<^>^>>^C^^D<^5<>^
E<8<KF<F<^T<<^J<<^6^O<^F<^F^^^^^^^^^D<<E<R<<<A^W<^J<P9^>^^N^^^^N<^>^>>^E^^9<^7<>^
E<D<KA<H<^J<<^O<<^E^I<^J<^C^^^^^^^^^F<<K<M<<<B^X<^I<R9^>^^I^^^^K<^>^>>^F^^A<^7<>^
G<A<G6<M<^S<<^L<<^7^Q<^L<^7^^^^^^^^^J<<E<M<<<9^S<^J<T7^>^^J^^^^O<^>^>>^E^^9<^C<>^
I<A<E9<H<^Q<<^U<<^9^H<^F<^F^^^^^^^^^L<<I<G<<<9^S<^I<WC^>^^M^^^^O<^>^>>^9^^9<^7<>^
J<B<G9<G<^R<<^H<<^6^J<^R<^D^^^^^^^^^G<<E<O<<<9^T<^J<L9^>^^O^^^^N<^>^>>^F^^C<^A<>^
B<7<JF<B<^T<<^V<<^A^L<^R<^8^^^^^^^^^G<<M0^C<<AS>^OF<SB^^^^^^^^^H^<<^>>^E^<9<^8<>^
D<5<JE<H<^S<<^L<<^A^J<^M<^D^^^^^^^^^H<<N0^C<<CS>^KN<QD^^^^^^^^^9^<<^>>^A^<G<^9<>^
D<C<OF<C<^K<<^R<<^7^P<^N<^A^^^^^^^^^C<<N0^C<<DV>^EI<NF^^^^^^^^^E^<<^>>^I^<A<^7<>^
D<D<IB<9<^N<<^R<<^D^K<^S<^D^^^^^^^^^E<<N0^C<<6R>^KN<MD^^^^^^^^^F^<<^>>^G^<D<^6<>^
H<B<J8<C<^K<<^U<<^7^K<^Q<^G^^^^^^^^^K<<N0^C<<6P>^OM<PB^^^^^^^^^M^<<^>>^9^<9<^9<>^
D<A<GD<I<^S<<^H<<^B^P<^D<^B^^^^^^^F^E<N<<<<^<7^O<KO<NB^F^^^^^^^G^<<^>>^F^<D<^A<>^
D<A<MC<D<^N<<^M<<^A^N<^F<^E^^^^^^^C^G<N<<<<^<7^K<MR<LA^F^^^^^^^L^<<^>>^E^<B<^9<>^
G<9<M9<I<^T<<^J<<^A^G<^G<^9^^^^^^^E^E<T<<<<^<A^M<JK<OD^H^^^^^^^G^<<^>>^E^<9<^B<>^
K<B<GA<A<^Q<<^M<<^8^G<^L<^B^^^^^^^G^E<P<<<<^<7^K<PO<I8^M^^^^^^^E^<<^>>^K^<A<^B<>^
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3x3::k:2304:2304:2304:6147:6147:6147:6147:7431:5128:3337:3337:4363:6147:5133:5133:5133:7431:5128:3602:2579:4363:4629:4629:4629:4629:7431:5128:3602:2579:4363:6430:6430:9504:9504:7431:5128:5412:5412:7718:6430:6430:9504:7431:7431:7468:5412:7718:7718:7718:6430:9504:2867:7468:7468:5412:4663:4663:2617:2617:9504:2867:7468:7468:5412:4663:4663:5186:9504:9504:2867:4678:4678:5186:5186:5186:5186:9504:3149:3149:3149:4678:

Thanks Manu. Just like JFFK2 this one lived up to its name. I particularly enjoyed using the 37(8) cage.

I'll rate JFFK3 at Hard 1.0.

Here is my walkthrough.

Prelims

a) R2C12 = {49/58/67}, no 1,2,3
b) R34C1 = {59/68}
c) R34C2 = {19/28/37/46}, no 5
d) R7C45 = {19/28/37/46}, no 5
e) R1C123 = {126/135/234}, no 7,8,9
f) R2C567 = {389/479/569/578}, no 1,2
g) R678C7 = {128/137/146/236/245}, no 9
h) 30(4) cage at R5C3 = {6789}, CPE no 6,7,8,9 in R6C1
i) 37(8) cage at R4C6 = {12345679}, no 8

1. 45 rule on R1 2 innies R1C89 = 1 outie R2C4 + 12
1a. Max R1C89 = 17 -> max R2C4 = 5
1b. Min R1C89 = 13, no 1,2,3

2. 45 rule on R9 2 innies R9C59 = 1 outie R8C4 + 13
2a. Max R9C59 = 17 -> max R8C4 = 4
2b. Min R9C59 = 14, no 1,2,3,4

3. 45 rule on N14 1 outie R6C4 = 3 innies R5C12 + R6C1 + 3
3a. Min R5C12 + R6C1 = 6 -> R6C4 = 9, R5C12 + R6C1 = 6 = {123}, locked for N4 and 21(5) cage at R5C1, clean-up: no 7,8,9 in R3C2, no 1 in R7C5
3b. R5C3 + R6C23 = {678}, locked for N4, clean-up: no 6,8 in R3C1, no 2,3,4 in R3C2

4. Naked pair {59} in R34C1, locked for C1, clean-up: no 4,8 in R2C2
4a. Naked triple {459} in R4C123, locked for R4
4b. 9 in 37(8) cage at R4C6 locked in R7C6 + R8C56 + R9C5, locked for N8, clean-up: no 1 in R7C4
4c. 4 in 37(8) cage at R4C6 locked in R5678C6 + R8C5, CPE no 4 in R9C6

5. R5C12 + R6C1 = 6 -> R78C1 = 15 = {78}, locked for C1 and N7, clean-up: no 5,6 in R2C2

6. 45 rule on C123 2 remaining outies R89C4 = 8 = [17/26/35]

7. R1C123 = {135/234} (cannot be {126} which clashes with R3C2), no 6, 3 locked for R1 and N1

8. R2C567 = {389/578} (cannot be {479} which clashes with R2C2, cannot be {569} which clashes with R2C12), no 4,6, 8 locked for R2
8a. Killer pair 7,9 in R2C2 and R2C567, locked for R2

9. R234C3 = {179/269/458} (cannot be {278/467} which clash with R56C3)
9a. 9 of {179/269} must be in R4C3 -> no 9 in R3C3
9b. 7,8 of {179/458} must be in R3C3 -> no 1,4,5 in R3C3

10. 45 rule on C89 1 outie R5C7 = 1 innie R9C8 + 6, R5C7 = {789}, R9C8 = {123}

11. 45 rule on N58 1 remaining innie R9C6 = 1 outie R4C7 + 1, no 3 in R4C7, no 1,5,6 in R9C6
11a. 3 in 37(8) cage at R4C6 locked in R5678C6 + R8C5, CPE no 3 in R9C6, clean-up: no 2 in R4C7
11b. 2 in 37(8) cage at R4C6 locked in R45678C6 + R8C5, CPE no 2 in R9C6, clean-up: no 1 in R4C7

12. R9C678 = {138/147/237} (cannot be {129/156/246/345} because R9C6 only contains 7,8), no 5,6,9
12a. R9C6 = {78} -> no 7,8 in R9C7

13. Hidden killer pair 1,2 in R9C123 and R9C78 for R9 -> R9C123 must contain one of 1,2
13a. R89C4 = 8 (step 6) -> R9C123 = 12 = {156/246} (cannot be {129} which clashes with R9C678, cannot be {345} which doesn’t contain 1 or 2), no 3,9, 6 locked for R9 and N7, clean-up: no 2 in R8C4 (step 6)

14. 3 in R9 locked in R9C78, locked for N9
14a. R9C678 (step 12) = {138/237}, no 4
14b. 4 in R9 locked in R9C123 (step 13a) = {246} (only remaining combination), locked for R9 and N7, clean-up: no 8 in R5C7 (step 10)
14c. Naked pair {13} in R9C78, locked for N9, R9C6 = 8 (step 14a), R4C7 = 7 (step 11), clean-up: no 2 in R7C45
14d. R5C7 = 9, R9C8 = 3 (step 10), R9C7 = 1
14e. 2 in N8 locked in R7C6 + R8C56, locked for 37(8) cage at R4C6

15. R7C45 = {46} (cannot be {37} which clashes with R89C4), locked for R7 and N8
15a. 4,6 in 37(8) cage at R4C6 locked in R456C6, locked for C6 and N5

16. 45 rule on N5 3 remaining innies R456C6 = 11 = {146} (only remaining combination), locked for C6, N5 and 37(8) cage at R4C6

17. R8C4 = 1 (hidden single in N8), R9C4 = 7 (step 6)

18. R678C7 = {236/245}, no 8, 2 locked for C7
18a. 3 of {236} must be in R6C7 -> no 6 in R6C7
18b. 8 in C7 locked in R123C7, locked for N3

19. 18(3) cage in N9 = {279/459/567} (cannot be {468} because R9C9 only contains 5,9), no 8

20. 8 in N9 locked in R7C89, locked for R7 and 29(5) cage at R5C9 -> R78C1 = [78]

21. 9 in N3 locked in R13C9, locked for C9 -> R9C9 = 5, R7C7 = 2, R7C89 = [98], R9C5 = 9, clean-up: no 4 in R8C89 (step 19)
[9 in N3 locked in R13C9 has been there since step 14d but I’ve only just spotted it]
21a. R8C7 = 4 (hidden single in N9), R6C7 = 5 (step 18)
21b. Naked triple {368} in R123C7, locked for N3

22. R7C89 = [98] = 17 -> R5C9 + R6C89 = 12 = {246} (only remaining combination), locked for N6
22a. Naked pair {18} in R45C8, locked for C8 and N6 -> R4C9 = 3
22b. Naked pair {28} in R4C45, locked for R4 and N5 -> R45C8 = [18], R4C6 = 6

23. 7 in N5 locked in R56C5, locked for C5
23a. R2C26 = {79} (hidden pair in R2)

24. R4C9 = 3 -> R123C9 = 17 = {179} (only remaining combination) -> R2C9 = 1, R13C9 = {79}, locked for C9 and N3 -> R8C89 = [76]
24a. R6C8 = 6 (hidden single in N6)

25. Naked pair {78} in R6C23, locked for R6 and N4 -> R5C3 = 6, R6C5 = 3, R5C45 = [57]

26. Killer pair 4,5 in R1C123 and R1C8, locked for R1

27. R1C89 (step 1) = R2C4 + 12
27a. Max R1C89 = 14 -> R2C4 = 2, R1C89 = 14 = [59], R3C9 = 7, R12C6 = [79], R4C45 = [82], R1C4 = 6, R1C57 = [18], R23C7 = [36], R3C2 = 1, R4C2 = 9 , R34C1 = [95], R4C3 = 4, R2C2 = 7, R2C1 = 6

and the rest is naked singles.

You make great puzzles manu! Here is a slightly different way to do this one without any killer pairs. Just to the cracked stage. I have NOT used a trick that could get a placement in step 1 since that would rate much higher than this puzzle needs (see JFFK 1 for details of the trick, My WT step 1 & 2 for a harder way, manu's ALT step 1 for the simplest way) Still, I'll give this WT way a 1.25 rating for step 9b and it takes 25 steps to crack it, even though the other 24 steps are all "easy" ones. Too much work for an optimized 1.0 WT!

Off Topic: I'll be quietening down on the forum for a little while with a busy patch coming up. Great that Tarek can take up some slack.

JFFK 3 WT (25 steps to crack)
[edit after Andrew's next two post: Thanks to Andrew for some typos and optimising ( ) step 22]
Prelims

i. 9(3)n1: no 7,8,9
ii. 13(2)n1: no 1,2,3
iii. 20(3)n2: no 1,2
iv. 14(2)n1 = {59/68}
v. 10(2)n1: no 5
vi. 37(8)n5: no 8, note: all other candidates are required.
vii. 30(4)n4 = {6789}
viii. 11(3)n6: no 9
ix. 10(2)n8: no 5

1. "45" n14: 1 outie r6c4 - 3 = 3 innies r5c12, r6c1
1a. min. 3 innies = {123} = 6 -> r6c4 = 9
1b. no 1 in r7c5
1c. 3 innies = {123}: all locked for n4 & 21(5)n4
1d. no 7,8,9 in r3c2

2. naked triple {678} in n4: all locked for n4
2a. r3c2 = (16)

3. 14(2)n1 = {59} (only valid combination): both locked for c1
3a. no 4,8 in r2c2

4. naked triple {459} in r4c123: all locked for r4

5. "45" n14: 2 remaining outies r78c1 = 15 = {78}: both locked for c1 & n7
5a. r2c2 = (79)

6. 4,5 & 9 which must be in the 37(8)n5 are all in c6 or n8 -> no 4,5,9 in r9c6 (Common Peer Elimination CPE)

7. "45" n2369: 1 innie r4c7 + 1 = r9c6
7a. no 3 in r4c7
7b. no 1,6 in r9c6

8. keep doing steps 6 & 7 recursively (thanks for that verb Andrew!): locked candidate 3 in 37(8)n5 -> no 3 in r9c6 -> no 2 in r4c7 -> no 2 in r9c6 -> no 1 in r4c7

9. So finally, we have r4c7 = (67) & r9c6 = (78)
9a. from step 7, the permutations are [67/78]
9b. -> 7 locked in the innie or outie -> no 7 in common peers r45678c6 & r89c5

10. 7 in 37(8)n5 now only in r4c7 = 7
10a. -> r9c6 = 8 (step 7)
10b. no 2 in 10(2)n8

11. r9c78 = 4 (cage sum) = {13}: both locked for r9 & n9

12. "45" c89: 1 outie r5c7 - 6 = r9c8
12a. -> r5c7 = 9
12b. r9c8 = 3, r9c7 = 1

13. "45" n147: 3 remaining innies r9c123 = 12 = {246}
13a. all locked for n7 & r9 & 20(5)n8

14. "45" c9: 3 outies r678c8 = 22 = {589/679}(no 1,2,4)
14a. 9 locked for c8 & n9

15. r9c5 = 9 (hidden single r9)
15a. no 1 in r7c4

16. split cage (from step 13) r89c4 = 8 = [17/35]
16a. = [3/7..]

17. 10(2)n8 = {46} ({37} blocked by r89c4 (step 16a)
17a. 4 & 6 locked for n8 & r7

18. 4 & 6 required in the 37(8)n5 now only in n5: both locked for n5 & c6

19. "45" n5: 3 remaining innies r456c6 = 11 and must have 4 & 6 -> 1 remaining innie = 1
19a. naked triple {146} in r456c6: 1 locked for c6, n5 & 37(8)n5

20. naked triple {235} in n8: locked for n8
20a. r89c4 = [17]
20b. r9c9 = 5

21. better get this hidden single: r6c2 = 8 (hidden for c2)
21a. r56c3 = {67}: both locked for c3

22. Naked triple {278} in r7c179: locked for r7 -> r7c8 = 9. [simpler than the naked quad I saw]

23. h22(3) r678c8 = {589/679}
23a. r6c8 = (56) -> no 6 in r8c8

24. r8c89 = 13 (cage sum)
24a. = [76] (last permutation)
24b. r6c8 = 6 (h22(3)r678c8)

25. 17(3)n1 must have 8 for c3 = {458}: all locked for c3

Now its smooth.

manu

I would like to explain a particular technic that can be used fruitfully for this puzzleposted one week ago. It had be mentionned by Ed in his previous post. It consists in using both CPE and IO difference.
I think everyone who have tried this puzzle has noticed the role of cage 37(8) : the particular cell R9C6 sees almost all cells of that cage. If it had seen all cells of cage 37(8), one could have deduced R9C6=8 since 37(8)={12345679} (Isn't the technic called CPE ?). Here, I have made the cage pattern in order to enable the solver to deduce R9C6 <> R4C7 using IO for N2369 : R9C6 = R4C7+1 -> R9C6 <> R4C7 (Ed would say IOI : Innies Outies Inequality )

That enables to prove that R4C9 is different of all cells of 37(8) : R9C6=8, BTW R4C7=7.

One could use a similar technic for JFFK1 (I have posted sth about that in JFFK1 topic). I would be interested if someone could point out a previous Assassin for which that kind of technic can be used, because I have made the cage pattern of JFFK1/3 intentionally for using such a step.


Andrew

This is of course referring to the technique discussed in manu's message; I'll say a bit more about that in my next message.

Having gone through my WT again and then Ed's one, I think Ed's step 9b is harder than any of my moves. It's a neat move of a type that we don't often see. From memory the first time I saw such a move was in a WT by either Mike or Para on Ruud's site, before we moved here. Ed's step 9b is a very powerful one because it makes so many eliminations.

I've now done some minor editing to my WT and changed my rating from 1.0 to Hard 1.0. It might be argued that my step 9 should get a higher rating, because it uses a triple blocker, but it was such an obvious block that IMHO a Hard 1.0 rating is appropriate, just like I argue that rating is right for very simple (naked) killer triples; I always go to at least Easy 1.25 for hidden killer triples.

Ed has made an interesting point about giving a higher rating because of the number of steps. I give my ratings based on the types of steps and, where appropriate, increase the rating for difficulty of finding steps but I've never considered number of steps counting toward the rating; I think Ed and I will have to agree to disagree on that point.

I'm normally a fairly slow solver but I finished JFFK3 in one session; that's not something I would expect to do for a 1.25 rated puzzle so that's another reason why I didn't go for that rating.


Andrew

Thanks manu for the discussion about that technique that you intentionally designed the cage patterns of JFFK1 and JFFK3 for.

The WTs posted by Ed and myself for JFFK3 have shown that it wasn't necessary to use that technique to solve JFFK3. I must admit I didn't spot it as described by manu although I did manage to get quite a lot out of that particular cage using recursion in my step 11. Ed took it further with his clever step 9b.

Manu told me about the technique after I'd posted my WT. I immediately realised that it was probably what I'd been missing when I was stuck on JFFK1. It was! Now I know about that key breakthrough I'll have another try at that puzzle.

The technique was clearly necessary to solve JFFK1.

There is one that's not quite the same but very similar. The original steps 1e and 1f of Afmob's WT for Ed's A138 are also based on a cell seeing all except one cell of an 8-cell cage.

After A138, JFFK1 and JFFK3 we'll know to look out for this type of move. At the moment it's probably at least a 1.5 rated move and almost certainly not programmed into the current version of SS. I've no idea whether this type of move is going to be sufficiently common to be programmed into software solvers.

One final thought prompted by this type of move. What is an optimised WT? Is it the most direct solving path, which may use technically harder and therefore higher rated steps, or is it a longer path that uses the lowest possible rated steps? IMHO it's probably a question that's answered according to personal preference rather than having one answer.

I don't usually make significant changes to my walkthroughs, except when necessary because of errors, but Ed's comment about the rating made me think about omitting step 9, my technically hardest step, which only gave a few candidate eliminations.

I'll stick with my rating of Hard 1.0.

Here is my improved walkthrough. I also found step 13b which significantly shortened step 14, have moved step 15a into step 16 and shortened step 27a.

Prelims

a) R2C12 = {49/58/67}, no 1,2,3
b) R34C1 = {59/68}
c) R34C2 = {19/28/37/46}, no 5
d) R7C45 = {19/28/37/46}, no 5
e) R1C123 = {126/135/234}, no 7,8,9
f) R2C567 = {389/479/569/578}, no 1,2
g) R678C7 = {128/137/146/236/245}, no 9
h) 30(4) cage at R5C3 = {6789}, CPE no 6,7,8,9 in R6C1
i) 37(8) cage at R4C6 = {12345679}, no 8

1. 45 rule on R1 2 innies R1C89 = 1 outie R2C4 + 12
1a. Max R1C89 = 17 -> max R2C4 = 5
1b. Min R1C89 = 13, no 1,2,3

2. 45 rule on R9 2 innies R9C59 = 1 outie R8C4 + 13
2a. Max R9C59 = 17 -> max R8C4 = 4
2b. Min R9C59 = 14, no 1,2,3,4

3. 45 rule on N14 1 outie R6C4 = 3 innies R5C12 + R6C1 + 3
3a. Min R5C12 + R6C1 = 6 -> R6C4 = 9, R5C12 + R6C1 = 6 = {123}, locked for N4 and 21(5) cage at R5C1, clean-up: no 7,8,9 in R3C2, no 1 in R7C5
3b. R5C3 + R6C23 = {678}, locked for N4, clean-up: no 6,8 in R3C1, no 2,3,4 in R3C2

4. Naked pair {59} in R34C1, locked for C1, clean-up: no 4,8 in R2C2
4a. Naked triple {459} in R4C123, locked for R4
4b. 9 in 37(8) cage at R4C6 locked in R7C6 + R8C56 + R9C5, locked for N8, clean-up: no 1 in R7C4
4c. 4 in 37(8) cage at R4C6 locked in R5678C6 + R8C5, CPE no 4 in R9C6

5. R5C12 + R6C1 = 6 -> R78C1 = 15 = {78}, locked for C1 and N7, clean-up: no 5,6 in R2C2

6. 45 rule on C123 2 remaining outies R89C4 = 8 = [17/26/35]

7. R1C123 = {135/234} (cannot be {126} which clashes with R3C2), no 6, 3 locked for R1 and N1

8. R2C567 = {389/578} (cannot be {479} which clashes with R2C2, cannot be {569} which clashes with R2C12), no 4,6, 8 locked for R2
8a. Killer pair 7,9 in R2C2 and R2C567, locked for R2

9. Omitted

10. 45 rule on C89 1 outie R5C7 = 1 innie R9C8 + 6, R5C7 = {789}, R9C8 = {123}

11. 45 rule on N58 1 remaining innie R9C6 = 1 outie R4C7 + 1, no 3 in R4C7, no 1,5,6 in R9C6
11a. 3 in 37(8) cage at R4C6 locked in R5678C6 + R8C5, CPE no 3 in R9C6, clean-up: no 2 in R4C7
11b. 2 in 37(8) cage at R4C6 locked in R45678C6 + R8C5, CPE no 2 in R9C6, clean-up: no 1 in R4C7

12. R9C678 = {138/147/237} (cannot be {129/156/246/345} because R9C6 only contains 7,8), no 5,6,9
12a. R9C6 = {78} -> no 7,8 in R9C7

13. Hidden killer pair 1,2 in R9C123 and R9C78 for R9 -> R9C123 must contain one of 1,2
13a. R89C4 = 8 (step 6) -> R9C123 = 12 = {156/246} (cannot be {129} which clashes with R9C678, cannot be {345} which doesn’t contain 1 or 2), no 3,9, 6 locked for R9 and N7, clean-up: no 2 in R8C4 (step 6)
13b. R9C123 = {246} (only remaining combination, cannot be {156} which clashes with R89C4), locked for R9 and N7, clean-up: no 8 in R5C7 (step 10)

14. Naked pair {13} in R9C78, locked for N9, R9C6 = 8 (step 12), R4C7 = 7 (step11), clean-up: no 2 in R7C45
14a. R5C7 = 9, R9C8 = 3 (step 10), R9C7 = 1
14b. 2 in N8 locked in R7C6 + R8C56, locked for 37(8) cage at R4C6

15. R7C45 = {46} (cannot be {37} which clashes with R89C4), locked for R7 and N8

16. 4,6 in 37(8) cage at R4C6 locked in R456C6, locked for C6 and N5
16a. 45 rule on N5 3 remaining innies R456C6 = 11 = {146} (only remaining combination), locked for C6, N5 and 37(8) cage at R4C6

[Alternatively steps 15 and 16 can be replaced by
15. 45 rule on N5 3 remaining innies R456C6 = 11 = {146} (only remaining combination), locked for C6, N5 and 37(8) cage at R4C6
16. R7C45 = {46} (hidden pair in N8), locked for R7]

17. R8C4 = 1 (hidden single in N8), R9C4 = 7 (step 6)
[Or hidden pair in N8, if preferred]

18. R678C7 = {236/245}, no 8, 2 locked for C7
18a. 3 of {236} must be in R6C7 -> no 6 in R6C7
18b. 8 in C7 locked in R123C7, locked for N3

19. 18(3) cage in N9 = {279/459/567} (cannot be {468} because R9C9 only contains 5,9), no 8

20. 8 in N9 locked in R7C89, locked for R7 and 29(5) cage at R5C9 -> R78C1 = [78]

21. 9 in N3 locked in R13C9, locked for C9 -> R9C9 = 5, R7C7 = 2, R7C89 = [98], R9C5 = 9, clean-up: no 4 in R8C89 (step 19)
[9 in N3 locked in R13C9 has been there since step 14 but I’ve only just spotted it]
21a. R8C7 = 4 (hidden single in N9), R6C7 = 5 (step 18)
21b. Naked triple {368} in R123C7, locked for N3

22. R7C89 = [98] = 17 -> R5C9 + R6C89 = 12 = {246} (only remaining combination), locked for N6
22a. Naked pair {18} in R45C8, locked for C8 and N6 -> R4C9 = 3
22b. Naked pair {28} in R4C45, locked for R4 and N5 -> R45C8 = [18], R4C6 = 6

23. 7 in N5 locked in R56C5, locked for C5
23a. R2C26 = {79} (hidden pair in R2)

24. R4C9 = 3 -> R123C9 = 17 = {179} (only remaining combination) -> R2C9 = 1, R13C9 = {79}, locked for C9 and N3 -> R8C89 = [76]
24a. R6C8 = 6 (hidden single in N6)

25. Naked pair {78} in R6C23, locked for R6 and N4 -> R5C3 = 6, R6C5 = 3, R5C45 = [57]

26. Killer pair 4,5 in R1C123 and R1C8, locked for R1

27. R1C89 (step 1) = R2C4 + 12
27a. Max R1C89 = 14 -> R2C4 = 2, R1C89 = 14 = [59], R2C8 = 4, R2C1 = 6, R3C2 = 1, R4C2 = 9

and the rest is naked singles.

Probably more the second for me, though that may still use much harder steps than another walkthrough. In practice optimising my solution works like this.

1) Solve the puzzle once keeping rough notes

2) Think backwards from the first placement to guess which steps (in that area of the puzzle) were essential to achieve that first placement.

3) Solve it again, ticking those parts of the notes that help get to the first placement as directly as possible. Put brackets around the parts that don't appear to help.

4) While doing that, find simpler ways to do steps. Keep notes...possibly heading off into a completely new direction with something important missed the first time.

5) Work backwards from the second placement, then the 3rd etc.

6) Think about whether the 2nd placement could be more important than the 1st placement and can get to it straight away without the first placement. etc

7) Finally, get a clear picture in my mind of the whole solving path.

8) Type the WT. That can change the solution again if something new is found.

9) Check the WT

10) Triple check the WT and hope you don't find anything new!!

11) Decide how difficult that whole process was to keep "in the head". What rating does that feel like? 24 steps before I get to stop thinking feels like a 1.25 rating to me. Usually, 1.0 rated puzzles are around 5-15 with the remainder just getting it to singles.

Of course, deciding on the most difficult move also influences the rating. A very short WT with one difficult step still gets that steps rating. With JFFK3 I chose to go the longer route to get the lower rating.

12) Read other's WT to find what you missed.

Time consuming process but very satisfying when it's an interesting solution. But no wonder we don't get many new WT writers!