manu wrote:
Nobody is volunteer for A 182, so I have made it. I had to break the three weeks rule; I hope no one will be hurted, but I think it's better than no Assassin.
Thanks manu for a challenging Assassin! I took a long time until I found the key breakthrough which gave my first placement. After I made that breakthrough I removed my technically most difficult steps which I realised weren't necessary; there are comments about what they were.
Here is my walkthrough for A182.
Prelims
a) R1C34 = {29/38/47/56}, no 1
b) R2C23 = {69/78}
c) R2C67 = {14/23}
d) R34C3 = {18/27/36/45}, no 9
e) R34C4 = {49/58/67}, no 1,2,3
f) R45C7 = {19/28/37/46}, no 5
g) R56C2 = {39/48/57}, no 1,2,6
h) R5C34 = {14/23}
i) R56C5 = {14/23}
j) R78C6 = {29/38/47/56}, no 1
k) R7C78 = {49/58/67}, no 1,2,3
l) R8C78 = {39/48/57}, no 1,2,6
m) R9C67 = {19/28/37/46}, no 5
n) 19(3) cage in N3 = {289/379/469/478/568}, no 1
o) 11(3) cage in N6 = {128/137/146/236/245}, no 9
p) 10(3) cage in N9 = {127/136/145/235}, no 8,9
q) 13(4) cage in N1 = {1237/1246/1345}, no 8,9, 1 locked for N1, clean-up: no 8 in R4C3
1. 45 rule on C12 2 innies R27C2 = 9 = [63/72/81], clean-up: no 6 in R2C3
2. 45 rule on C789 2 outies R29C6 = 5 = {14/23}, clean-up: R9C7 = {6789}
3. 45 rule on C6789 2 innies R13C6 = 15 = {69/78}
4. 45 rule on N9 2 innies R7C9 + R9C6 = 10 = [19/28/37/46] -> R7C9 = {1234}
4a. Max R7C9 = 4 -> min R56C9 = 14, no 1,2,3,4 in R56C9
5. 45 rule on C9 1 innie R1C9 = 1 outie R9C8 + 1, no 9 in R1C9
6. 45 rule on R89 2 innies R8C16 = [19]/{28/37/46}, no 5, no 9 in R8C1, clean-up: no 6 in R7C6
7. 14(3) cage in N5 = {158/257/356} (cannot be {167} which clashes with R13C6, cannot be {248/347} which clash with R56C5, cannot be {149/239} which clash with R5C4 + R56C5, ALS block), no 4,9, 5 locked for C6 and N5, clean-up: no 8 in R3C4, no 6 in R8C6, no 4 in R8C1 (step 6)
7a. Killer quad 1,2,3,4 in 14(3) cage, R5C4 and R56C5, locked for N5, clean-up: no 9 in R3C4
7b. Min R3C6 + R4C5 = 13 -> max R3C5 = 5
8. 45 rule on N8 2 innies R9C46 = 1 outie R6C4 + 5
8a. Max R9C46 = 13 -> max R6C4 = 8
8b. Min R6C4 = 6 -> min R9C46 = 11, min R9C4 = 7, no 1 in R9C6, clean-up: no 4 in R2C6 (step 2), no 1 in R2C7, no 9 in R9C7, no 1 in R7C9 (step 4)
8c. 9 in N5 locked in R4C45, locked for R4, clean-up: no 1 in R5C7
8d. 4 in C6 locked in R789C6, locked for N8
9. 13(3) cage in N8 = {139/157/256} (cannot be {238} which clashes with R789C6, ALS killer block), no 8
10. 16(3) cage at R6C4 = {169/178/268/358/367} (cannot be {259} because R6C4 only contains 6,7,8)
10a. 13(3) cage in N8 (step 9) = {157/256} (cannot be {139} which clashes with R7C45 + R789C6, ALS killer block), no 3,9, 5 locked for N8
11. 9 in N9 locked in R78C78
11a. R7C78 = {49/58/67}, R8C78 = {39/48/57} -> combined cage R78C78 = {4957/5839/6739} -> R8C78 = {39/57}, no 4,8
12. R7C9 + R9C7 (step 4) = 10 = [28/46] (cannot be [37] which clashes with R8C78), clean-up: no 3 in R9C6, no 2 in R2C6 (step 2), no 3 in R2C7
13. 1 in R1 locked in R1C125
13a. 45 rule on R1 4 innies R1C1256 = 15 = {1239/1248/1257/1347/1356}
13b. R1C6 = {6789} -> no 6,7,8,9 in R1C125
14. 45 rule on C123 3 outies R159C4 = 15 = {159/168/249/258/267/348/357} (cannot be {456} because R9C4 only contains 7,8,9)
14a. R9C4 = {789} -> no 7,8,9 in R1C4, clean-up: no 2,3,4 in R1C3
15. 25(4) cage in N2 = {1789/2689/3589/3679/4579/4678}
15a. 1,2 of {1789/2689} must be in R1C5 -> no 1,2 in R2C45
16. 45 rule on C1234 2 innies R28C4 = 1 outie R7C5 + 1
16a. Min R28C4 = 4 -> min R7C5 = 3
16b. 16(3) cage at R6C4 (step 10) = {169/178/268/367}
16c. 1 of {169} must be in R7C4 -> no 9 in R7C4
[At this stage I originally used
R9C46 = R6C4 + 5 (step 8)
R9C6 = {24} -> R6C4 and R9C4 must be either odd/even or even/odd
Hidden killer pair 1,6 in R7C45 and 13(3) cage for N8, 13(3) cage contains one of 1,6 (step 10) -> R7C45 must contain one of 1,6
and then did permutation analysis on 16(3) cage at R6C4 including clashes with R9C4. I’ve now deleted that step and one later step but have left my other steps in their original order.]
17. 45 rule on R1234 2 outies R5C17 = 1 innie R4C6 + 11
17a. Min R5C17 = 12, no 1,2, clean-up: no 8 in R4C7
17b. Max R5C17 = 17 -> max R4C6 = 6
18. 18(3) cage at R5C9 = {279/459/468}
18a. 16(3) cage at R2C9 = {178/259/268/358/367} (cannot be {169/349/457} which clash with 18(3) cage at R5C9), no 4
[Here I originally did combination analysis on 45 rule on N6 4 innies R4C89 + R56C9 = 24, excluding the ones which weren’t compatible with the remaining combinations for R56C9.]
19. 45 rule on C9 3 innies R189C9 = 11 = {128/137/146/236} (cannot be {245} which clashes with R7C9), no 5, clean-up: no 4 in R9C8 (step 5)
20. 45 rule on R12 2 innies R2C89 = 1 outie R3C1 + 2
20a. Max R3C1 = 7 -> max R2C89 = 9, no 9
20b. Min R2C89 = 5 (cannot be {12} which clashes with R2C67, cannot be {13} which clashes with R2C6), min R3C1 = 3
21. 45 rule on R1234 1 outie R5C1 = 2 innies R4C67 + 1
21a. Min R4C67 = 3 -> min R5C1 = 4
22. 45 rule on N2 3 (2+1) outies R2C7 + R4C45 = 1 innie R1C4 + 16
22a. Max R2C7 + R4C45 = 4 + 17 = 21 -> max R1C4 = 5, clean-up: no 5 in R1C3
[Having found several 45s which only gave minor eliminations, I then found this one. I’m sure I must have seen it earlier but it’s only really useful after R9C6 has been reduced to two candidates and 13(3) cage in N9 to two combinations.]
23. 45 rule on N8 4 innies R7C45 + R9C46 = 21 = {1479/2469/3468} (cannot be {1389} because R9C6 only contains 2,4, cannot be {2379/2478} which clash with 13(3) cage) -> R9C6 = 4, R9C7 = 6, R2C6 = 1 (step 2), R2C7 = 4, R7C9 = 4 (step 4), clean-up: no 7 in R1C9 (step 5), no 8 in R56C6 (step 7), no 7 in R78C6, no 7,9 in R7C78, no 3,6 in R8C1 (step 6), no 3 in R9C8 (step 5)
23a. Naked pair {58} in R7C78, locked for R7 and N9, clean-up: no 6 in R1C9 (step 5), no 3 in R8C6, no 7 in R8C1 (step 6), no 7 in R8C78
23b. Naked pair {39} in R8C78, locked for R8 and N9, clean-up: no 2 in R7C6, no 1 in R8C1 (step 6)
23c. Naked pair {28} in R8C16, locked for R8
24. R189C9 (step 19) = {128/137}, 1 locked in R89C9 for C9 and N9, clean-up: no 2 in R1C9 (step 5)
25. 9 in R4 locked in R4C45
25a. 45 rule on N2 2 remaining outies R4C45 = 1 innie R1C4 + 12
25b. R4C45 = {69/79/89} = 15,16,17 -> R1C4 = {345}, no 2, clean-up: no 9 in R1C3
26. 2 in N2 locked in R13C5, locked for C5, clean-up: no 3 in R56C5
26a. Naked pair {14} in R56C5, locked for C5 and N5, clean-up: no 1,4 in R5C3
26b. Naked pair {23} in R5C34, locked for R5, clean-up: no 7 in R4C7, no 9 in R6C2
27. 13(3) cage in N8 (step 10a) = {157} (only remaining combination), no 6 -> R8C4 = 1, R8C9 = 7, R89C5 = [57], R9C89 = [21], R1C9 = 3 (step 24), R1C5 = 2, R3C5 = 3, clean-up: no 8 in R1C3, no 6 in R4C3
28. R1C9 = 3 -> R1C78 = 16 = {79}, locked for R1 and N3 -> R1C3 = 6, R1C4 = 5, R1C6 = 8, R8C6 = 2, R7C6 = 9, R7C45 = [36], R6C4 = 7 (step 16b), R9C4 = 8, R2C45 = [69], R34C4 = [49], R3C6 = 7, R4C5 = 8, R3C1 = 5, R5C34 = [32], R8C3 = 4, R9C3 = 5 (cage sum), R8C12 = [86], clean-up: no 2 in R4C3, no 5,9 in R5C2
29. Naked pair {78} in R2C23, locked for R2 and N1 -> R3C3 = 2, R4C3 = 7, R2C8 = 5, R2C9 = 2, R34C9 = 14 = [86], R3C78 = [16], R4C8 = 4 (cage sum), clean-up: no 9 in R5C7, no 5 in R6C2
30. R2C23 = [78], R7C23 = [21], R6C3 = 9, R7C1 = 7, R6C1 = 2 (cage sum), R4C12 = [15], R4C6 = 3, R4C7 = 2, R5C7 = 8
and the rest is naked singles.