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(Unofficial) Assassin 99.5

 
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frank
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Joined: 07 Oct 2006
Posts: 10
Location: Victoria, B.C., Canada

PostPosted: Tue Apr 22, 2008 1:32 pm    Post subject: (Unofficial) Assassin 99.5 Reply with quote

A midweek Assassin to keep you going until sudokuEd's
UA100.

Don't be fooled by the equatorial nonets. They are designed
to lull you into a sense of false security. The Assassin
shows its true colours when you venture forth to the poles.
SS rating 1.29. Enjoy Smile



Text: http://members.shaw.ca/fdkr2/fdkr064.txt

Soln: http://members.shaw.ca/fdkr2/fdkr064.soln.png
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gary w
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Joined: 07 Sep 2007
Posts: 84
Location: south wales

PostPosted: Tue Apr 22, 2008 10:48 pm    Post subject: Reply with quote

Enjoyed this one..many thanks.Took me just under the hour..no really difficult moves so I'ld rate it about 1.0.

Regards

Gary

P.S. Looking forward to seeing no.100 even though it sounds fearsome!!
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Andrew
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Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

PostPosted: Fri May 02, 2008 5:57 am    Post subject: Reply with quote

frank wrote:
Don't be fooled by the equatorial nonets. They are designed to lull you into a sense of false security. The Assassin shows its true colours when you venture forth to the poles.

That's certainly true. Easy progress in the middle three rows with several cells fixed and the remaining cages and hidden cages down to 1 or 2 combinations. Then apart from one cell in row 9, it was a very long time before this puzzle finally crumbled. In some ways it felt a bit like a mini version of the Brick Wall.

Thanks Frank for a challenging puzzle!

One general comment, which I've already made to Frank off forum. Additional midweek puzzles shouldn't be called Assassins unless they are variants of the current week's Assassin. They should either be added to the Maverick series or be given a name appropriate to the puzzle.

Franks's puzzle is clearly an Assassin level puzzle but it's a new cage pattern, not a variant of uA99.


Although most of my moves weren't difficult ones, some of them were hard to find and it's a very long solving path so I'll rate uA99.5 at 1.5.

Here is my walkthrough. Typos corrected in step 54.

Prelims

a) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
b) 19(3) cage in N3 = {289/379/469/478/568}, no 1
c) R234C5 = {127/136/145/235}, no 8,9
d) R5C456 = {589/679}, 9 locked for R5 and N5
e) R456C9 = {126/135/234}, no 7,8,9
f) 22(3) cage in N9 = {589/679}, 9 locked for N9

1. 45 rule on N1 1 outie R2C4 = 1 innie R3C3 + 1, no 9 in R3C3

2. 45 rule on N3 1 outie R2C6 = 1 innie R3C7 + 3, no 1,2,3 in R2C6, no 7,8,9 in R3C7

3. 45 rule on N7 1 outie R8C4 = 1 innie R7C3 (no eliminations yet)

4. 45 rule on N9 1 outie R8C6 = 1 innie R7C7 + 6, R8C6 = {789}, R7C7 = {123}

5. 45 rule on R12 3 innies R2C258 = 9 = {126/135/234}, no 7,8,9

6. 45 rule on C12 3 innies R456C2 = 19 = {289/379/469/478/568}, no 1

7. 45 rule on C89 3 innies R456C8 = 13
7a. 45 rule on N6 3 remaining innies R456C7 = 23 = {689}, locked for C7 and N6, clean-up: no 9 in R2C6 (step 2)

8. R456C9 = {135/234}, 3 locked for C9 and N6

9. 7 in N6 locked in R456C8, locked for C8

10. 22(3) cage in N9 = {589/679}
10a. 7 of {679} must be in R7C9 -> no 6 in R7C9

11. 45 rule on C5 3 innies R159C5 = 22 = {589/679}, 9 locked for C5

12. 45 rule on C1234 3 innies R159C4 = 19 = {289/379/469/478/568}, no 1

13. 45 rule on R6789 2 innies R6C19 = 13 = [85/94]

14. R456C9 (step 8) = {135/234}
14a. R6C9 = {45} -> no 4,5 in R45C9

15. R456C1 = {149/158/239/248} (only combinations containing 8 or 9), no 6,7
15a. R6C1 = {89} -> no 8,9 in R45C1

16. R456C2 (step 6) = {379/469/478/568} (cannot be {289} which clashes with R6C1), no 2
16a. Killer pair 8,9 in R456C2 and R6C1, locked for N4

17. 45 rule on N4 2 innies R6C23 = 8 = {35}/[62/71], no 4,8,9, no 6,7 in R6C3

18. 45 rule on N6 2 innies R6C78 = 16 = [97] -> R6C1 = 8, R6C9 = 5 (step 13), clean-up: no 3 in R6C23, no 1 in R6C3 (both step 17)
18a. R6C23 = [62], clean-up: no 3 in R2C4 (step 1), no 2,6 in R8C4 (step 3)
18b. R6C9 = 5 -> R45C9 = 4 = {13}, locked for C9 and N6
18c. Naked pair {24} in R45C8, locked for C8
18d. R6C1 = 8 -> R45C1 = 6 = {15}, locked for C1 and N4
18e. R4C2 = 9 (hidden single in R4), R5C2 = 4 (step 6), R45C8 = [42]
18f. Naked pair {37} in R45C3, locked for C3, clean-up: no 4,8 in R2C4 (step 1), no 3,7 in R8C4 (step 3)
18g. Naked triple {134} in R6C456, locked for N5

19. 18(3) cage at R8C6 = {279/378/459} (cannot be {189} because 8,9 only in R8C6), no 1
19a. 8,9 must be in R8C6 -> R8C6 = {89}, clean-up: no 1 in R7C7 (step 4)

20. R9C8 = 1 (hidden single in N9), R89C9 = 10 = {28/46}, no 7

21. 1 in C7 locked in R123C7
21a. 45 rule in N3 3 innies R123C7 = 10 = {127/145}, no 3, clean-up: no 6 in R2C6 (step 2)

22. R6C78 = 16 (step 18) -> R6C6 + R7C67 = 6 = {123}, 1 locked in R67C6, locked for C6, 2 locked in R7C67, locked for R7

23. 20(5) cage at R6C2 = {12368/12467/23456}, no 9, clean-up: no 9 in R8C4 (step 3)

24. 16(3) cage in N3 = {259/268/349/358/367} (cannot be {457} because 4,7 only in R3C9)
24a. 2,4 of {259/349} must be in R3C9 -> no 9 in R3C9
24b. 2,7 of {268/367} must be in R3C9 -> no 6 in R3C9

25. 13(3) cage in N7 = {238/247/256/346}, no 9

26. R234C5 = {127/136/145/235}
26a. 6 of {136} must be in R4C5 -> no 6 in R23C5

27. 45 rule on C6789 3 innies R159C6 = 15 = {249/258/267/348/357/456}
27a. 9 of {249} must be in R5C6 -> no 9 in R19C6

28. 45 rule on N3 3 outies R234C6 = 18 = {279/378/459/468/567} (cannot be {369} because R2C6 only contains 4,5,7,8)
28a. 9 of {279} must be in R3C6 -> no 2 in R3C6

29. 45 rule on N1 3 innies R123C3 = 18 = {189/459/468}

30. 12(3) cage in N1 = {129/237/246/345} (cannot be {138} because 1,8 only in R1C2, cannot be {147/156} which clash with R123C3), no 8

31. 15(3) cage in N1 = {159/168/267/357} (cannot be {249/258/348} which clash with R123C3, cannot be {456} because 4,6 only in R3C1), no 4
31a. 2 of {267} must be in R2C2 -> no 2 in R3C12

32. 17(3) cage in N7 = {179/278/359/368} (cannot be {269/458} which clash with 13(3) cage, cannot be {467} because 4,6 only in R7C1}, no 4
32a. 6,9 of {359/368} must be in R7C1 -> no 3 in R7C1

33. 45 rule on N7 3 innies R789C3 = 15 = {159/168/456}
33a. 13(3) cage in N7 (step 25) = {238/247/346} (cannot be {256} which clashes with R789C3), no 5

34. 12(3) cage in N1 = {129/237/246} (cannot be {345} which clashes with R89C1 because 13(3) cage must have 3 or 4 in R89C1), no 5, 2 locked for N1

35. R678C5 = {148/238/247/346} (cannot be {157/256} which clash with R159C5), no 5
35a. 2 of {247} must be in R8C5 -> no 7 in R8C5

36. 45 rule on N1 3 outies R234C4 = 14 = {158/167/239/248/257/356} (cannot be {149/347} because 1,3,4 only in R3C4)
36a. 1,3,4 of {158/167/239/248/356} must be in R3C4 -> no 6,8,9 in R3C4

37. 19(3) cage at R1C3 = {289/469/478/568}
37a. 5 of {568} must be in R2C4 (R12C3 cannot be {58} because R123C3 cannot be {58}5), no 5 in R12C3

38. 45 rule on R89 3 innies R8C258 = 17 = {179/269/278/359/368/458/467}
38a. 1 of {179} must be in R8C5 -> no 1 in R8C2

39. 17(3) cage in N7 (step 32) = {179/278/359/368}
39a. 1 of {179} must be in R7C2, 7 of {278} must be in R7C1 -> no 7 in R7C2

40. R2C258 (step 5) = {126/135} (cannot be {234} because 2,4 only in R2C5), no 4, 1 locked for R2

41. 13(3) cage at R1C7 = {148/157/247}
41a. 1 of {157} must be in R1C7 -> no 5 in R1C7
41b. 1 of {148} must be in R1C7, 4 of {247} must be in R2C6 (cannot be in R1C7 because R123C7 cannot be [424]) -> no 4 in R1C7

42. 19(3) cage in N3 = {289/379/469/478} (cannot be {568} which clashes with R89C9), no 5

43. 16(3) cage in N3 (step 24) = {259/268/358/367} (cannot be {349} which clashes with 19(3) cage), no 4

44. 6 in N3 must be in 16(3) cage or in 19(3) cage
44a. 16(3) cage in N3 (step 43) = {268/358/367} (cannot be {259} which clashes with the only combination in 19(3) cage that contains 6), no 9
44b. Killer pair 5,6 in R23C8 and R78C8, locked for C8

45. 45 rule on N7 3 remaining outies R678C4 = 12 = {138/147/345}
45a. R159C4 (step 12) = {289/469/568} (cannot be {379/478} which clash with R678C4), no 3,7
45b. R234C4 (step 36) = {167/239/257/356} (cannot be {158/248} which clash with R678C4), no 4,8

46. 45 rule on N9 3 remaining outies R678C6 = 12 = {129/138}
46a. R159C6 (step 27) = {249/267/348/357/456} (cannot be {258} which clashes with R678C6)
46b. 8 of {348} must be in R5C6 -> no 8 in R19C6

47. 9 in N3 locked in 19(3) cage = {289/379/469}
47a. R123C7 (step 21a) = {127/145}-> combined cage R123C89 = {236789} (cannot be {345689} because R123C9 = {46}8 clashes with R89C8), no 4,5, clean-up: no 6 in 19(3) cage (step 47)
[I originally had
47a. If {469} => 16(3) cage in N3 = {358} (step 44a) => R123C9 = {46}8 which clashes with R89C8
47b. -> 19(3) cage in N3 = {289/379), no 4,6
but have replaced it with the step using the combined cage which is better because itís a normal move rather than a contradiction move.]

48. R89C9 = {46} (hidden pair in C9), locked for N9, clean-up: no 7 in R7C9 (step 10)

49. 22(3) cage in N9 = {589}, locked for N9
49a. Naked triple {237} in R789C7, locked for C7 -> R1C7 = 1, clean-up: no 9 in R12C1 (step 34), no 4,5 in R2C6 (step 2)
49b. R2C67 = [75/84]

50. 16(3) cage in N3 (step 44a) = {268/367}
50a. 2 of {268} must be in R3C9 -> no 8 in R3C9

51. R234C6 (step 28) = {279/378/468/567} (cannot be {459} because R2C6 only contains 7,8)
51a. 7,8 of {279/468/567} must be in R2C6
51b. 3 of {378} must be in R3C6
51c. -> no 7,8 in R3C6
51d. R159C6 (step 46a) = {249/348/357/456} (cannot be {267} which clashes with R234C6)

52. R2C258 (step 40) = {126/135}
52a. 3 of {135} must be in R2C8 -> no 3 in R2C25

53. R234C5 = {127/136/145/235}
53a. 3,4 of {145/235} must be in R3C5 -> no 5 in R3C5

54. 9 in C1 locked in R37C1
54a. 45 rule on C1 2 innies R37C1 = 2 outies R19C2 + 6
54b. R19C2 cannot total 6 -> R37C1 cannot total 12 -> no 3 in R3C1

55. 15(3) cage in N1 (step 31) = {159/168/357}
55a. 3 of {357} must be in R3C2 -> no 7 in R3C2

56. R123C3 (step 29) = {189/459/468}
56a. 6 of {468} must be in R12C3 (R12C3 cannot be [48] because R2C34 = [87] clashes with R2C6, R12C3 cannot be [84] because R2C34 = [47] clashes with R2C67) -> no 6 in R3C3, clean-up: no 7 in R2C4 (step 1)

57. R5C456 = {589/679} -> R4C456 = {258/267}
57a. 8 of {258} must be in R4C6 -> no 5 in R4C6

58. R234C6 (step 51) = {279/378/468/567}
58a. 5 of {567} must be in R3C6 -> no 6 in R3C6

59. 17(3) cage in N7 (step 32) = {179/278/359/368}
59a. 5 of {359} must be in R8C2 (R7C12 cannot be [95] which clashes with R7C89) -> no 5 in R7C2

60. 20(5) cage at R6C2 (step 23) = {12467/23456} (cannot be {12368} because R7C34 = {18/38} clashes with R7C2 + R7C67), no 8, clean-up: no 8 in R8C4 (step 3)

61. 8 in C4 locked in R159C4
61a. R159C4 (step 45a) = {289/568}, no 4

62. R678C4 (step 45) = {147/345}
62a. 7 of {147} must be in R7C4 -> no 1 in R7C4

63. R234C4 (step 45b) = {167/239/356} (cannot be {257} which clashes with R678C4)
63a. 1,3 of {167/356} must be in R3C4 -> no 5,7 in R3C4
63b. 2 of {239} must be in R4C4 -> no 2 in R23C4, clean-up: no 1 in R3C3 (step 1)
63c. 5 of {356} must be in R2C4 (R234 cannot be [635] because 13(3) at R3C3 cannot be [535]), no 5 in R4C4

64. R123C3 (step 29) = {459/468}, 4 locked for C3 and N1, clean-up: no 6 in R12C1 (step 34), no 4 in R8C4 (step 3)
64a. Naked triple {237} in 12(3) cage, locked for N1

65. 20(5) cage at R6C2 (step 60) = {12467/23456}
65a. R7C3 = {15} -> no 1 in R6C4, no 5 in R7C4

66. 4 in N7 locked in 13(3) cage (step 33a) = {247/346}, no 8
66a. 3 of {346} must be in R9C2 -> no 3 in R89C1
66b. 3 in C1 locked in R12C1, locked for N1

67. R1C456 = {369/459/468/567} (cannot be {279} which clashes with R1C2, cannot be {378} which clashes with R2C6), no 2

68. 2 in N2 locked in R23C5, locked for C5
68a. R234C5 = {127/235}, no 4,6
68b. 4 in N2 locked in R13C6, locked for C6

69. 1 in N1 locked in R23C2, locked for C2
69a. 17(3) cage in N7 (step 32) = {278/359/368}
69b. 2 of {278} must be in R8C2 -> no 7 in R8C2

70. R159C4 (step 61a) = {289/568}
70a. 2 of {289} must be in R9C4 -> no 9 in R9C4

71. 15(3) cage at R8C3 = {159/168}, 1 locked in R8C34, locked for R8

72. R678C5 (step 35) = {148/346}, no 7

73. R9C456 cannot contain both 8 and 9
73a. Hidden killer pair {89} in R9C3 and R9C456 -> R9C3 = {89}, R9C456 must contain 8 or 9
73b. R9C456 = {259/358} (cannot be {268} which clashes with R78C5, cannot be {367} which doesnít contain 8 or 9), no 6,7
73c. 5 locked in R9C456, locked for N8 -> R8C4 = 1, R3C4 = 3, R67C4 = [47], R7C3 = 1 (step 3)

74. Naked pair {23} in R7C67, locked for R7 -> R7C2 = 8, R7C89 = [59], R7C1 = 6, R7C5 = 4, R3C1 = 9, R6C6 = 1 (step 22), R6C5 = 3, R8C8 = 8, R8C56 = [69], R89C3 = [59], R89C9 = [46], R8C2 = 3 (step 32), R7C7 = 3 (step 4), R7C6 = 2

75. R9C1 = 4, R9C6 = 3 (hidden singles in R9)

76. Naked pair {45} in R3C67, locked for R3 -> R23C2 = [51], R3C3 = 8, R2C4 = 9 (step 1), R23C7 = [45], R3C6 = 4, R12C3 = [46], R4C4 = 2 (step 63), R2C6 = 8 (step 41), R4C6 = 6 (step 51)

77. Naked triple {567} in R1C456, locked for R1 and N2 -> R1C12 = [32], R2C1 = 7

78. R23C5 = [12] -> R4C5 = 7 (step 68a)

and the rest is naked singles

I've included the solution in case something goes wrong with Frank's link.

3 2 4 6 5 7 1 9 8
7 5 6 9 1 8 4 3 2
9 1 8 3 2 4 5 6 7
5 9 3 2 7 6 8 4 1
1 4 7 8 9 5 6 2 3
8 6 2 4 3 1 9 7 5
6 8 1 7 4 2 3 5 9
2 3 5 1 6 9 7 8 4
4 7 9 5 8 3 2 1 6
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Afmob
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Joined: 22 Sep 2007
Posts: 103
Location: MV, Germany

PostPosted: Sun May 04, 2008 9:12 am    Post subject: Reply with quote

Like Andrew, I think that this (fun and challenging) Killer shouldn't be called an Assassin since it's against our tradition and is in no relation to uA 99. So I was reluctant to post my wt, but Andrew convinced me to do so.
The most important move was step 5k which I don't look for too often but the candidate pattern at that stage led me to that move which is also the reason why I don't rate it 1.5.

Frank's 99.5 walkthrough:

1. C789
a) 22(3) = 9{58/67} -> 9 locked for N9
b) Innies N3 = 10(3) <> 8,9
c) 9 locked in R456C7 for N6
d) Innies N6 = 16(2) = [97] -> R6C7 = 9, R6C8 = 7
e) Outies C89 = 14(2) = {68} locked for C7+N6
f) 22(5) = {12379}
g) Innies+Outies N9: 6 = R8C7 - R7C7 -> R8C7 = (789)
h) 18(3) must have 8 or 9 and it's only possible @ R8C7 -> R8C7 <> 7
i) 18(3) <> 1 because (89) only possible @ R8C7
j) Innies+Outies N9: 6 = R8C7 - R7C7 -> R7C7 <> 1

2. R456
a) Innies R6789 = 13(2) = [85] -> R6C1 = 8, R6C9 = 5
b) 9(3) = {135} locked for C9+N6
c) Hidden Single: R9C8 = 1 @ N9 -> R89C9 = 10(2) = {28/46}
d) Innies N4 = 8(2) = {26} locked for R6+N4+20(5)
e) 14(3) = {158} locked for C1+N4
f) Hidden Single: R5C8 = 2 @ R5, R4C8 = 4
g) 22(3) = 9{58/67} -> 9 locked for R5+N5

3. C789 !
a) ! Innies+Outies C9: -7 = R1C8 - R37C9 -> R7C9 <> 7 (IOU)
b) 22(3) = {589} locked for N9, 5 locked for C8
c) 11(3) = {146} -> {46} locked for C9+N9
d) Naked triple (237) locked in R789C7 for C7
e) 19(3) = 9{28/37} -> 9 locked for N3
f) 13(3) = 1{48/57} because R12C7 = (145) -> 1 locked for N3 and R2C6 = (78)

4. C123+C5
a) Innies C12 = 19(3) = [946] -> R4C2 = 9, R5C2 = 4, R6C2 = 6
b) R6C3 = 2
c) Naked pair (37) locked in R45C3 for C3
d) 20(5) = 26{138/147/345} <> 9
e) Innies C5 = 22(3) = 9{58/67} -> 9 locked for C5
f) 13(3) @ C5 <> 5 because 5{17/26} blocked by Killer pairs (56,57) of Innies C5

5. R789 !
a) Innies+Outies N7: R7C3 = R8C4 = (1458)
b) 22(5) = {12379} -> 1 locked for C6, 2 locked for R7
c) 13(3) @ C5: R8C5 <> 7 because R67C5 <> 2
d) Innies R89 = 17(3) <> {467} because R8C9 = (46)
e) Killer pair (89) locked in Innies R89 + R8C6 for R8
f) Innies R89 = 17(3): R8C2 <> 1 because R8C58 <> 7
g) Innies N7 = 15(3) = {159/168/456}
h) 13(3) @ N7 = {238/247/346} <> 5,9 because {256} blocked by Killer pair (56) of Innies N7
i) Innies+Outies N7: R7C3 = R8C4 = (145)
j) 17(3): R7C2 <> 7 because 1 only possible there, R7C1 <> 2,8 and R8C2 <> 4,6
k) ! Outies R9 = 28(6): R8C1 <> 4,6 because:
- R8C1349 would be {1456} which forces R8C67 = {39} -> no combo for 18(3)

6. N78
a) 13(3) @ N7 = 2{38/47} because (46) only possible @ R9C1 -> 2 locked for N9
b) 17(3): R7C1 <> 7 because (69) only possible there
c) 7 locked in R7C45 for N8
d) Killer pair (89) locked in R8C6+16(3) for N8
e) 13(3) @ C5 = 4{27/36} -> 4 locked for C5
f) 1 locked in 15(3) @ R8 = 1{59/68} -> R9C3 = (89)
g) Innies N7 = 15(3) = 1{59/68} -> 1 locked for C3+N7
h) 5 locked in 16(3) @ R9 for N8 = 5{29/38}
i) Hidden Single: R9C9 = 6 @ R9, R8C9 = 4
j) Innies+Outies N7: R8C4 = R7C3 = 1
k) 20(5) = {12467} -> R6C4 = 4, R7C4 = 7

7. R9+R123
a) Hidden Single: R9C1 = 4 @ R9 -> R8C1+R9C2 = {27} locked for N7
b) Innies R12 = 9(3) = 1{26/35} -> 1 locked for R2
c) Hidden Single: R1C7 = 1 @ N3
d) 12(3) = {237} locked for N1
e) Innies+Outies N1: 1 = R2C4 - R3C3 -> R3C3 <> 6,9; R2C4 = (569)
f) Hidden Single: R7C5 = 4 @ N8, R6C5 = 3 -> R8C5 = 6
g) 10(3) = {127} locked for C5
h) 13(3) @ N1: R34C4 <> 8,9 because R3C3 >= 4
i) R8C3 = 5 -> R9C3 = 9

8. C456
a) Innies C1234 = 19(3) = 8{29/56}
b) Hidden Single: R3C4 = 3 @ C4
c) 13(3) = [436/832]
d) 5 locked in 18(3) @ R1 = 5{49/67} for N2
e) 19(3) = {469} -> R2C4 = 9, {46} locked for N1
f) 16(3) = {358} -> R9C6 = 3, {58} locked for N8

9. Rest is singles

Rating: Hard 1.25. I used combo analysis of Outies to crack it.
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