SudokuSolver Forum

I have said that I was cooking it lovely.... Assassin 143 is now ready !

I would rate this puzzle at hard 1.25 but SudokuSolver does not agree with that score
Don't be afraid of SS score, there is nethertheless a straightforward logical path that does not use chains
or tedious brute eliminations : (the order of the steps seems actually to be very important to crack this puzzle)

ASSASSIN 143




PS Code : 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:

SS(V3.3.0)score : 2.37

Solution :


I will provide a "mind bending" V2 as soon as Assassin 144 is taken (est. rating 1.75, SS Score 3.36): !
Meanwhile I give you this lite version because V1
might get you lost in the solving path ...

ASSASSIN 143-Lite



PScode : 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:
SS(V3.3.0)score : 1.12

Solution :

PS : No internet access this week-end, so I won't be able to answer to messages until Sunday evening.

PPS: Note that my V1.5 V2 etc... will be generally the same puzzle with a slightly
different cage pattern (in fact, one of
the intermediate versions I have obtained trying to create V1 )

EDIT : PPPS I admit that I have broken the three weeks rule with my lite version, but I think that a lot of people
will find V1 too much hard whereas others will estimate the lite-version too easy ! None of these puzzles can satisfy everybody....
I tell you again :V2 will be posted only if A144 is claimed

You gave a good reason for posting V1 and V1-Lite at the same time while, at the same time, not posting V2 until there is a volunteer for A144.

Even though I do a lot of the harder puzzles, I'm also happy to solve the occasional much easier one. I still solve killers on the first sudoku site that I started using. All the ones there are easier than any that have been posted on this site.

There seem to be two basic ways to make variants, either to change the cage pattern slightly but keep the same final solution or to keep the same cage pattern and change the cage totals so that the solution is different. My personal preference is for those with different cage pattern but I'm happy to try both types.

Thanks Manu for giving the solution below both diagrams; IMHO that's better than saying that the solution is the same.

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

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

Thanks Ed for A144 : I am eager to try it.

Meanwhile, here is A143 V2 as promised :


ASSASSIN 143 V2








SS(V3.3.0)score : 3.36 (Est. : 1.5-1.75 ?)

PS code : 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:

Solution :

Not more difficult than V1 concerning the opening part, but be carefull for the other steps !!!

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.

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