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Afmob Expert
Joined: 22 Sep 2007 Posts: 103 Location: MV, Germany

Posted: Fri Feb 22, 2008 5:47 pm Post subject: Assassin 91 


This was a fun assassin since I got to use Killer triples and Killer quads. It took me more time than it should have to solve it since I didn't see step 7a which is a basic move.
A91 Walkthrough:
1. R123
a) 16(2) = {79} locked for C6+N2
b) 9(2) @ N2 <> 2
c) Innies N2 = 6(2) = {15/24}
d) Killer pair (45) locked in 14(3) + Innies N2 for N2
e) Innies N3 = 27(4) <> 1,2
f) 9(2) @ N3 <> 3,6 since (36) is a Killer pair of 9(3)
2. C789
a) 23(3) = {689} locked for R5, 9 locked for N6
b) 27(4) = 9{378/468/567} > 9 locked for N3
c) Innies C89 = 13(3): R28C8 <> 6,7,8,9 because R5C8 = (689)
d) Outies C789 = 14(3) must have 6 xor 8 and R5C6 = (68) > R7C6 <> 6,8
e) 1 locked in R9C789 for N9
f) Outies N9 = 9(2+1) <> 8
3. R6789
a) Innies R9 = 6(2) = [42/51]
b) Innies R89 = 5(2) = [14/23/32]
c) 9(2) <> {45} since it's blocked by R9C3 = (45)
d) 20(3) = {479/569/578} because R9C3 = (45) > R8C23 <> 3,4,5
e) 12(3) <> {345} because R9C7 = (12)
f) 12(3) must have 6,7,8 xor 9 and it's only possible @ R8C7 > R8C7 = (6789)
g) Innies N7 = 14(4) <> 9
h) Outies N7 = 19(2+1) > R7C4 <> 1
i) Innies = 10(2) <> 5; R6C1 <> 1
j) 19(3): R9C45 <> 3 because R9C6 <> 7,9
4. C123
a) Innies C12 = 19(3) <> 1; R2C2 <> 2 because R5C2 <> 8,9
b) Outies C123 = 12(3) <> 8 because {138} blocked by Killer pair (13) of 9(2) @ C4
c) Innies+Outies N1: 3 = R4C2  R3C3 > R4C2 <> 7,8,9; R3C3 <> 1,2,3
d) Innies+Outies N7: 4 = R6C2  R7C3 > R6C2 = (56789); R7C3 <> 6,7,8
5. N9 !
a) Innies+Outies: 5 = R6C8  R7C7 > R6C8 = (1234); R7C7 = (6789)
b) 19(4) must have 2 of (56789) and they are only possible @ R7C89 > R7C89 <> 2,3,4
c) 4 locked in R8C89 for R8
d) ! 19(4) can only have one of (6789) because of Killer quad (6789) in R78C7 and 9(2)
> 19(4) = 5{149/239/248/347} > 5 locked R7+N9
6. R789
a) 5 locked in 14(3) @ N8 = 5{18/27/36} for N8
b) 15(3): R6C3 <> 1 because R7C34 <= 13
c) Innies+Outies N7: 4 = R6C2  R7C3 > R6C2 <> 9
7. N58 !
a) Innies+Outies N5: 8 = R7C5  R5C46 > R7C5 <> 8,9 because R5C46 <= 15
b) ! 14(3) @ N8 <> 2,7 since {257} is a Killer triple of Innies N8
8. R789
a) Killer pair (13) locked in 14(3) + Innies R89 for R8
b) 12(3) = {129/147/246} <> 8
c) 9(2) <> 2,7 since (27) is a Killer pair of 12(3)
d) Killer pair (16) locked in 9(2) + 12(3) for N9
e) 11(2) <> {38} because it's a Killer pair of 9(2)
f) 3 locked in Innies N7 = 14(4) = 13{28/46} <> 7
g) Innies+Outies N9: 5 = R6C8  R7C7 > R6C8 <> 1
9. C789 !
a) ! Killer quad (6789) locked in 14(3) @ N3 + R578C7 for C7
b) 9(3) = 3{15/24} > 3 locked for N3
c) 9(2) <> 4,5 since (45) is a Killer pair of 9(3)
d) Innies+Outies N3: R3C7 = R4C8 <> 3
e) R6C8 <> 4 since it sees all 4 of N9
f) Innies+Outies N9: 5 = R6C8  R7C7 > R7C7 <> 9
10. C789
a) Innies C89 = 13(3) <> 9 because R8C8 = (24)
b) Hidden Single: R5C7 = 9 @ N6
c) 12(3) = 4{17/26} > R8C8 = 4
d) 19(4) = {2359} > 9 locked for R7; {23} locked between N6 and C9 > 13(3) <> 2,3
e) 13(3) = 1{48/57} > 1 locked for C9+N6
f) Both 9(2): R19C8 <> 8
11. R789
a) Innies R89 = 5(4) = {23} locked for R8
b) 14(3) @ R8 = {158} locked for R8+N8
c) 19(3) = 9{37/46} > 9 locked for R9
d) 11(2) <> 2
e) Killer pair (45) locked in 11(2) + R9C3 for R9+N7
f) 2 locked in Innies N7 = 14(4) = {1238}
h) 19(3) = {379} > R9C6 = 3; 7 locked for R9+N8
i) Hidden Single: R9C9 = 8 @ R9 > R9C8 = 1
j) 14(3) @ N9 = 7{25/34} > R7C7 = 7; R6C7 = (35)
12. C456
a) Outies C789 = 14(3) = {248} because R7C6 = (24) > R5C6 = 8; {24} locked for C6
b) Innies N2 = 6(2) = {24} locked for R3+N2
c) Outies C123 = 12(3) = {246} > R7C4 = 6; {24} locked for C4
d) 9(2) = {18} locked for C4+N2
e) 12(3) must have 2 xor 4 because R5C4 = (24) > R5C23 <> 2,4
13. R123
a) 9(2) @ N3 = {27} locked for R1+N3
b) 9(3) = {135} locked for N3
c) 1 locked in R3C12 for N1
d) 10(2) = {46} locked for R1+N2
e) 14(3) @ N1 = 2{39/57} > R2C3 = 2
f) R1C6 = 9, R2C6 = 7
g) 14(3) @ N1 = {239} > R1C3 = 3, R2C2 = 9
14. N45
a) 15(3) @ N7 = {168} > R6C3 = 8, R7C3 = 1
b) 15(3) @ N1 = 6{27/45} because R3C3 = (57) > R4C3 = 6
c) 18(4) @ N5 = {1359} because 24{39/57} blocked by R5C4 = (24)
15. Rest is singles.
Rating: Hard 1.25. I used some Killer triples and Killer quads.
Last edited by Afmob on Thu Feb 28, 2008 7:58 am; edited 1 time in total 

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gary w Addict
Joined: 07 Sep 2007 Posts: 84 Location: south wales

Posted: Tue Feb 26, 2008 12:17 am Post subject: 


Not many replies re this one.I think Afmob's rating is about right.I didn't use any really hard moves solving this killer combos in n9 and rows 89 together with r258c8=13 leading to some early placements after which it came out ok
Regards
Gary 

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Andrew Grandmaster
Joined: 11 Aug 2006 Posts: 300 Location: Lethbridge, Alberta

Posted: Thu Feb 28, 2008 11:21 pm Post subject: 


Assassin 91 took me a long time to solve. The killers and hidden killers were fairly easy to see but some of the other steps weren't. It took me several sessions to spot step 36a, my first key move.
Therefore although my steps weren't hard ones, I'll rate A91 as a lower range 1.5.
My other key moves were steps 46 and 49, the latter another killer after which the rest of the puzzle was straightforward. Maybe the later stages might have been a bit shorter if I'd thought to reapply step 21, which became R5C4 = R7C5, after step 37.
I missed Afmob's step 8a, which I felt I ought to have seen even though it involves a cage split between C1 and C9. I don't know how much difference it would have made to my solving path; it wasn't marked as a key move.
Here is my walkthrough. I've added the solution because Ruud hasn't updated the archive.
Prelims
a) R1C12 = {19/28/37/46}, no 5
b) R12C4 = {18/27/36/45}, no 9
c) R12C6 = {79}, locked for C6 and N2, cleanup: no 2 in R12C4
d) R1C89 = {18/27/36/45}, no 9
e) R9C12 = {29/38/47/56}, no 1
f) R9C89 = {18/27/36/45}, no 9
g) 9(3) cage in N3 = {126/135/234}, no 7,8,9
h) R5C678 = {689}, locked for R5, 9 locked in R5C78 for N6
i) 20(3) cage in N7 = {389/479/569/578}, no 1,2
j) R9C456 = {289/379/469/478/568}, no 1
k) 27(4) cage at R2C9 = {3789/4689/5679}, no 1,2, 9 locked in R2C9 + R3C89 for N3
1. 1 in R9 locked in R9C789, locked for N9
2. 45 rule on R89 2 innies R8C19 = 5 = [14]/{23}
3. 45 rule on R9 2 innies R9C37 = 6 = [42/51]
3a. R9C89 = {18/27/36} (cannot be {45} which clashes with R9C3), no 4,5
3b. 20(3) cage in N7 = {479/569/578} (cannot be {389} because R9C3 only contains 4,5), no 3
3c. R9C3 = {45} > no 4,5 in R8C23
4. 45 rule on C12 3 innies R258C2 = 19 = {289/379/469/478/568}, no 1
4a. 2 of {289} must be in R5C2 > no 2 in R2C2
4b. 5 of {568} must be in R5C2 > no 5 in R2C2
5. 45 rule on N1 1 innie R3C3 = 1 outie R4C2 + 3, no 1,2,3 in R3C3, no 7,8,9 in R4C2
6. 45 rule on N2 2 innies R3C46 = 6 = {15/24}
6a. R12C4 = {18/36} (cannot be {45} which clashes with R3C46), no 4,5
7. 45 rule on N3 1 innie R3C7 = 1 outie R4C8, no 1,2 in R3C7
8. R1C89 = {18/27/45} (cannot be {36} which clashes with 9(3) cage in N3), no 3,6
9. 45 rule on N7 1 outie R6C2 = 1 innie R7C3 + 4, R6C2 = {56789}, R7C3 = {12345}
10. 45 rule on N9 1 innie R7C7 = 1 outie R6C8 + 5, R6C8 = {1234}, R7C7 = {6789}
11. 19(4) cage at R6C8 = {1279/1369/1378/1459/1468/2359/2368/2458/2467/3457} (cannot be {1567} because R6C8 and R8C9 only contain 1,2,3,4)
11a. 1,2,3,4 must be in R6C8 + R8C9 > no 2,3,4 in R7C89
11b. 4 in N9 locked in R8C789, locked for R8
12. 45 rule on R6789 2 innies R6C19 = 10 = {28/37/46}/[91], no 5, no 1 in R6C1
13. 45 rule on C789 3 outies R357C6 = 14 = {158/248/356}
13a. R5C6 = {68} > no 6,8 in R7C6
13b. Min R7C67 = 7 > max R6C7 = 7
14. 45 rule on C123 3 outies R357C4 = 12 = {129/147/156/237/246/345} (cannot be {138} which clashes with R12C4), no 8
14a. 2 of {237} must be in R3C4
14b. 6,9 of {129/246} must be in R7C4
14c. > no 2 in R7C4
15. 45 rule on C89 3 innies R258C8 = 13 = {139/148/238/256/346} (cannot be {157/247} because R5C8 only contains 6,8,9), no 7
15a. R5C8 = {689} > no 6,8,9 in R28C8
16. 12(3) cage in N9 = {129/138/147/156/237/246} (cannot be {345} because R9C7 only contains 1,2)
16a. 6,7,8,9 must be in R8C7 > R8C7 = {6789}
17. Killer quint 5,6,7,8,9 in R7C7, R7C89, R8C7 and R9C89, locked for N9
17a. 5 in N9 locked in R7C89, locked for R7, cleanup: no 9 in R6C2 (step 9)
18. 5 locked in R7C89
18a. 19(4) cage at R6C8 (step 11) = {1459/2359/2458/3457}, no 6
18b. CPE no 4 in R6C8, cleanup: no 9 in R7C7 (step 10)
19. 5 in R8 locked in R8C456, locked for N8
19a. R8C456 = 5{18/27/36}, no 9
20. 15(3) cage at R6C3 = {159/168/249/267/348/357} (cannot be {258} because no 2,5,8 in R7C4, cannot be {456} which clashes with R9C3)
20a. 1 of {159/168} must be in R7C3 > no 1 in R6C3 + R7C4
20b. 5,8 of {348/357} must be in R6C3 > no 3 in R6C3
21. 45 rule on N5 2 innies R5C46 = 1 outie R7C5 + 8
21a. Max R5C46 = 15 > max R7C5 = 7
21b. R5C46 cannot total 14 > no 6 in R7C5
22. 45 rule on N8 3 innies R7C456 = 12 = {129/147/237/246}
23. 15(3) cage at R6C3 (step 20) = {159/168/249/267/348/357}
23a. 5 of {357} must be in R6C3
23b. 6 of {267} must be in R6C3 (cannot be 7[26] which clashes with R7C456 = 6{24})
23c. > no 7 in R6C3
23d. 2,9 of {249} must be in R6C3 (cannot be 4[29] which clashes with R7C456 = 9{12})
23e. 8 of {348} must be in R6C3
23f. > no 4 in R6C3
24. 14(3) at R3C6 = {158/248/257/347/356} (cannot be {167} which clashes with R5C7, R7C7 and R8C7)
24a. Killer quad 6,7,8,9 in R34C7, R5C7, R7C7 and R8C7, locked for C7
25. 9(3) cage in N3 = {135/234}, 3 locked for N3, cleanup: no 3 in R4C8 (step 7)
25a. R1C89 (step 8) = {18/27} (cannot be {45} which clashes with 9(3) cage), no 4,5
25b. R1C12 = {19/37/46} (cannot be {28} which clashes with R1C89), no 2,8
26. 14(3) cage at R6C7 = {158/248/257/347/356} (cannot be {167} because 6,7 only in R7C7)
26a. 5 of {158} must be in R6C7 > no 1 in R6C7
27. 14(3) at R3C6 (step 24) = {158/248/257/347/356}
27a. 3 of {356} must be in R4C7 > no 6 in R4C7
27b. 8 of {158/248} must be in R3C7 (R3C67 cannot be {15/24} which clash with R3C46, overlapping cages) > no 8 in R4C7
27c. 4 of {347} must be in R3C6, 8 of {248} must be in R3C7 (step 27b) > no 4 in R3C7, cleanup: no 4 in R4C8 (step 7)
28. 15(3) cage at R3C3 = {159/168/249/258/267/348/357/456}
28a. 9 of {159/249} must be in R3C3 (R3C34 cannot be {15/24} which clash with R3C46, overlapping cages) > no 9 in R4C3
29. Hidden killer quad 6,7,8,9 in R7C12, R8C23 and R9C12 for N7 > R7C12 must contain one of 6,7,8,9
29a. 18(4) cage at R6C2 = {1269/1278/1359/1368/1458/1467/2358/2367/2457/3456} (cannot be {2349} because R6C2 only contains 5,6,7,8)
29b. R6C2 = R7C3 + 4 (step 9)
29c. 18(4) cage at R6C2 cannot be {1269/1359/1458/2367} which clash with R7C3)
> 18(4) cage = {1278/1368/1467/2358/2457/3456}, no 9
[I then realised that 45 rule on N7 4 innies = 14 eliminates 9 from R7C12 but it doesn’t give the permutations for the 18(4) cage which were used later.]
30. R6C2 = R7C3 + 4 (step 9)
30a. 15(3) cage at R6C3 (step 20) = {168/249/348/357} (cannot be {159/267} which clash with R6C2)
30b. 8 of {168} must be in R6C3 > no 6 in R6C3
30c. 3 of {348} must be in R7C3 (cannot be [843] which clashes with R6C2), 3 of {357} must be in R7C3 > no 3 in R7C4
31. R6C2 = R7C3 + 4 (step 9)
31a. 18(4) cage at R6C2 (step 29c) = {1278/1368/1467/2358/2457} (cannot be {3456} which clashes with 15(3) cage at R6C3)
32. 45 rule on N2369 2 outies R57C6 = 1 innie R3C4 + 8, max R57C6 = 12 > max R3C4 = 4, cleanup: no 1 in R3C6 (step 6)
33. 15(3) cage at R3C3 (step 28) = {159/168/249/258/267/348/456} (cannot be {357} because R3C4 only contains 1,2,4)
33a. 1 of {159/168} must be in R3C3 > no 1 in R4C3
33b. 9 of {249} must be in R3C3, 4 of {348/456} must be in R3C4 > no 4 in R3C3, cleanup: no 1 in R4C2 (step 5)
34. 45 rule on C1234 4 innies R4689C4 = 24 = {2589/2679/3579/4569/4578} (cannot be {1689/3489/3678} which clash with R12C4), no 1
35. R357C4 (step 14) = {129/147/237/246} (cannot be {156} which clashes with R4689C4, cannot be {345} because 3,5 only in R5C4), no 5
35a. R4689C4 (step 34) = {2589/3579/4569/4578} (cannot be {2679} which clashes with R357C4)
[Alternatively 5 in C4 locked in R4689C4 = {2589/3579/4569/4578}]
36. 15(3) cage at R6C3 (step 30a) = {168/249/348/357}
36a. R7C456 (step 22) = {129/147/246} (cannot be {237} which clashes with 15(3) cage), no 3 in R7C56
37. R357C6 (step 13) = {158/248} > R5C6 = 8
37a. Naked pair {69} in R5C78, locked for N6, cleanup: no 6 in R3C7 (step 7)
38. R8C456 = 5{18/36} (cannot be {257} which clashes with R7C456), no 2,7
39. 14(3) cage at R6C7 (step 26) = {158/248/257/347} (cannot be {356} because 3,5 only in R6C7), no 6, cleanup: no 1 in R6C8 (step 10)
40. Hidden pair {69} in R58C7 for C7 > R8C7 = {69}
41. 12(3) cage in N9 (step 16) = {129/246}, no 3, 2 locked for N9, cleanup: no 7 in R9C89
41a. 7 in N9 locked in R7C789, locked for R7
42. R7C456 (step 36a) = {129/246}, 2 locked for R7 and N8, cleanup: no 6 in R6C2 (step 9)
42a. 6,9 must be in R7C4 > R7C4 = {69}
43. 7 in N8 locked in R9C456, locked for R9, cleanup: no 4 in R9C12
43a. R9C456 = {379/478}, no 6
43b. R9C6 = {34} > no 3,4 in R9C45
44. 15(3) cage at R6C3 (step 30a) = {168/249} (cannot be {348} because R7C4 only contains 6,9), no 3,5, cleanup: no 7 in R6C2 (step 9)
44a. 2 of {249} must be in R6C3 > no 9 in R6C3
45. 18(4) cage at R6C2 (step 31a) = {1368/2358}, no 4
45a. 3 locked in R7C12, locked for N7, cleanup: no 8 in R9C12
45b. CPE no 8 in R8C2
45c. 4 in N7 locked in R79C3, locked for C3
46. Either R6C2 = 5 or R7C12 must contain 6 (step 45) > no 5 in R9C2, cleanup: no 6 in R9C1
47. 20(3) cage in N7 (step 3b) = {479/578} (cannot be {569} which clashes with R8C7), no 6
[This also comes from 7 locked in R8C23]
48. 9 in N4 locked in R46C1, locked for C1, cleanup: no 1 in R1C2, no 2 in R9C2
48a. R456C1 = {149/239}, no 5,6,7,8
49. Killer pair 1,2 in R456C1 and R8C1, locked for C1 > R9C1 = 5, R9C2 = 6, R9C3 = 4, R7C3 = 1, R6C2 = 5 (step 9), R8C1 = 2, R8C89 = [43], R9C6 = 3, R6C8 = 2, R7C7 = 7 (step 10), R6C3 = 8, R7C4 = 6 (step 44), cleanup: no 4 in R1C1, no 9 in R1C2, no 3 in R12C4, no 3 in R456C1 (step 48a), no 7 in R4C8 (step 7)
50. R89C7 = [62] (hidden singles in N9) > R5C78 = [96]
51. Naked pair {18} in R9C89, locked for R9 and N9
52. R1C9 = 2 (hidden single in C9), R1C8 = 7, R12C6 = [97], cleanup: no 3 in R1C12
52a. R1C12 = [64]
53. 9(3) cage in N3 = {135} (only remaining combination), locked for N3 > R3C7 = 8, R4C8 = 8 (step 7), R3C8 = 9, R7C89 = [59], R9C89 = [18], R2C8 = 3, R2C12 = [89], R7C12 = [38], R8C23 = [79], R3C1 = 7, R3C3 = 5, R12C3 = [32], R2C3 = 1, R45C3 = [67], R12C4 = [81], R12C7 = [15], R1C5 = 5, R8C456 = [581], R4C2 = 2 (step 5), R5C2 = 3
54. R3C4 = 4 (step 33), R3C6 = 2, R23C5 = [63], R23C9 = [46], R7C56 = [24], R46C6 = [56], R46C7 = [43], R5C4 = 2
55. R6C6 + R7C5 = 8 > R6C45 = 11 = [74]
and the rest is naked singles
6 4 3 8 5 9 1 7 2
8 9 2 1 6 7 5 3 4
7 1 5 4 3 2 8 9 6
1 2 6 3 9 5 4 8 7
4 3 7 2 1 8 9 6 5
9 5 8 7 4 6 3 2 1
3 8 1 6 2 4 7 5 9
2 7 9 5 8 1 6 4 3
5 6 4 9 7 3 2 1 8 

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