manu wrote:
On the other hand, the solving path is more narrow for this V2
It is. At least one of my key steps was also used by Afmob but our walkthroughs were still sufficiently different for me to post my one.
I'll rate A156 V2 at Easy 1.25 because I used 4(3+1) innies and because it needed more work than A156 before the first placement.
Here is my walkthrough.
Prelims
a) R23C1 = {19/28/37/46}, no 5
b) R23C9 = {16/25/34}, no 7,8,9
c) R34C2 = {29/38/47/56}, no 1
d) R34C8 = {69/78}
e) R45C1 = {16/25/34}, no 7,8,9
f) R45C3 = {29/38/47/56}, no1
g) R45C7 = {49/58/67}, no 1,2,3
h) R45C9 = {18/27/36/45}, no 9
i) 19(3) cage in N1 = {289/379/469/478/568}, no 1
j) R123C5 = {289/379/469/478/568}, no 1
k) R1C678 = {127/136/145/235}, no 8,9
l) 8(3) cage at R2C6 = {125/134}, CPE no 1 in R2C4
m) 19(3) cage in N3 = {289/379/469/478/568}, no 1
n) R678C1 = {489/579/678}, no 1,2,3
o) 9(3) cage in N7 = {126/135/234}, no 7,8,9
p) 19(3) cage at R7C4 = {289/379/469/478/568}, no 1
q) 19(3) cage in N9 = {289/379/469/478/568}, no 1
r) R9C234 = {126/135/234}, no 7,8,9
s) R9C678 = {389/479/569/578}, no 1,2
t) R6789C5 = {1236/1245}, no 7,8,9, 1,2 locked for C5
1. 45 rule on C1 2 innies R19C1 = 7 = {25/34}/[61], no 7,8,9, no 6 in R9C1
2. 45 rule on C9 2 innies R19C9 = 17 = {89}, locked for C9, clean-up: no 1 in R45C9
3. 45 rule on C5 2 innies R45C5 = 14 = {59/68}
3a. 7 in C5 locked in R123C5, locked for N2
3b. R123C5 = {379/478}, no 5,6
4. 45 rule on R1 3 innies R1C159 = 21 = {489/579/678}, no 2,3, clean-up: no 4,5 in R9C1 (step 1)
4a. R1C1 = {456} -> no 4 in R1C5
4b. Killer triple 4,5,6 in R1C1, R45C1 and R678C1, locked for C1
5. Killer triple 1,2,3 in R9C1 and R9C234, locked for R9
5a. R6789C5 = {1236/1245}
5b. 6 of {1236} must be in R9C5 -> no 6 in R678C5
6. 19(3) cage in N1 = {469/478/568} (cannot be {289/379} because R1C1 only contains 4,5,6), no 2,3
7. 45 rule on R123 2 outies R4C28 = 15 = {69/78}, clean-up: no 6,7,8,9 in R3C2
8. 45 rule on R6789 3 outies R5C258 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R5C5), no 7,8,9, clean-up: no 5,6 in R4C5 (step 3)
8a. R5C5 = {56} -> no 5,6 in R5C28
8b. Killer pair 8,9 in R4C28 and R4C5, locked for R4, clean-up: no 2,3 in R5C3, no 4,5 in R5C7
8c. Max R5C8 = 4 -> min R67C8 = 11, no 1
9. 45 rule on N69 3 outies R789C6 = 2 innies R4C8 + R6C7 + 16
9a. Min R4C8 + R6C7 = 7 -> min R789C6 = 23 -> R789C6 = {689/789}, 8,9 locked for C6 and N8
9b. Max R789C6 = 24 -> max R4C8 + R6C7 = 8, no 8,9 in R4C8, R6C7 = {12}, clean-up: no 6,7 in R3C8, no 6,7 in R4C2 (step 7), no 4,5 in R3C2
9c. R45C7 = [49/58] (cannot be {67} which clashes with R4C8
9d. R45C9 = {27/36} (cannot be {45} which clashes with R4C7)
9e. Killer pair 6,7 in R4C8 and R45C9, locked for N6
10. R5C7 + R6C8 = {89} (hidden pair in N6)
10a. Naked pair {89} in R36C8, locked for C8
10b. Naked pair {89} in R1C9 and R3C8, locked for N3
10c. 19(3) cage in N3 = {379/469/478/568} (cannot be {289} which clashes with R3C8), no 2
10d. Min R56C8 = 9 -> max R7C8 = 6
11. 45 rule on N3 1 innie R3C8 = 3 outies R123C6 + 1
11a. R3C8 = {89} -> R123C6 = 7,8 = {124/125} (cannot be {134} which clashes with R123C5) , no 3,6, 1,2 locked for C6 and N2
11b. 6 in N2 locked in R123C4, locked for C4
11c. 3 in C6 locked in R456C6, locked for N5
12. Max R78C4 = {57} = 12 -> min R8C3 = 8 (19(3) cage cannot be {577})
[Afmob used 19(3) cage at R7C4 must contain one of 8,9 -> R8C3 = {89}, a more direct way to look at this step.]
13. R789C6 = {689/789}
13a. Min R78C6 = {68} = 14 -> max R8C7 = 4
14. R678C9 = {147/156/345} (cannot be {237/246} which clash with R45C9), no 2
15. R567C2 = {148/157/247/256/346} (cannot be {139/238} which clash with R34C2), no 9
16. R567C8 = {159/249/258/348} (cannot be {168/267} which clash with R34C8, cannot be {357/456} because R6C8 only contains 8,9), no 6
17. 3 in C6 locked in R456C6
17a. 45 rule on C6789 4(3+1) innies R456C6 + R6C7 = 15 = {347}1/{346}2 (cannot be {356}2 which clashes with R4C5), no 5, 4 locked in R456C6, locked for C6 and N5
18. Naked triple {125} in R123C6, locked for N2
18a. R123C6 = 8 -> R3C8 = 9 (step 11), R4C8 = 6, R4C2 = 9 (step 7), R3C2 = 2, R1C9 = 8, R9C9 = 9, R4C5 = 8, R5C5 = 6 (step 3), R6C8 = 8, R5C7 = 9, R4C7 = 4, clean-up: no 1,8 in R2C1, no 4 in R23C5 (step 3b), no 3 in R2C7 (prelim l), no 5 in R2C9, no 8 in R3C1, no 1 in R4C1, no 2,5 in R4C3, no 3 in R45C9, no 1,3 in R5C1, no 5,7 in R5C3
18b. Naked triple {379} in R123C5, locked for C5 and N2
19. Naked triple {347} in R456C6, locked for C6 and N5, R6C7 = 1 (step 17a)
20. Naked pair {27} in R45C9, locked for C9 and N6 -> R5C8 = 3, R7C8 = 4 (step 16), R6C9 = 5, R6C45 = [92], R5C2 = 1 (step 8; also hidden single in N4), R45C4 = [15], clean-up: no 2 in R4C1
21. Naked pair {37} in R4C36, locked for R4 -> R4C1 = 5, R5C1 = 2, R45C9 = [27], R5C6 = 4, R5C3 = 8, R5C3 = 3, R4C6 = 7, R6C6 = 3, R8C3 = 9, clean-up: no 4 in R68C1 (prelim n)
22. Naked pair {57} in R29C8, locked for C8 -> R8C8 = 2, R1C8 = 1, R8C7 = 3, R7C7 = 8 (prelim q), clean-up: no 6 in R23C9
23. R1C9 = 8 -> R2C8 + R3C7 = 11 = [56], R12C7 = [72], R123C6 = [215], R1C5 = 9, R9C78 = [57], R9C6 = 8 (prelim s), R78C6 = [96], R9C5 = 4, R8C4 = 7, clean-up: no 3 in R9C234 (prelim r)
23a. R9C234 = [612], R1C9 = 3, clean-up: no 7 in R23C1
23b. R23C1 = [91]
and the rest is naked singles