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Assassin 71
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CathyW
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Joined: 31 Jan 2007
Posts: 161
Location: Hertfordshire, UK

PostPosted: Tue Oct 09, 2007 8:30 pm    Post subject: Reply with quote

Thanks for mentioning those other Assassins Andrew. I did some of the puzzles from the archive when I first signed up but, like you, will try and find time to go back to the ones you've mentioned.

Regarding the A71, I've not attempted either of the variants having taken so long on the original. Addict that I am, I had to persevere to the finish but for the first time it really felt like a slog rather than an enjoyable pastime. Sad

Still looking forward to the A72 on Friday though Smile
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Afmob
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PostPosted: Tue Oct 09, 2007 8:40 pm    Post subject: Reply with quote

Another difficult V2 though it was a bit easier than V1. There were quite some interesting moves you could apply.

Assassin 71 V2 Walkthrough:

1. R12
a) Innies R12 = 13(2) -> no 1,2,3

2. R6789
a) Innies R89 = 10(2) -> no 5
b) Innies R6789 = 8(2) -> no 4,8,9

3. C1234
a) Outies C12 = 6(2) = {15/24}
b) Outies C1234 = 16(2) = {79} locked for C5

4. C6789
a) Innies C789 = 8(3) = 1{25/34} -> 1 locked for C7
b) Outies C89 = 7(2) = {25/34}
c) Outies C6789 = 14(2) = {68} locked for C5
d) Killer pair (12) of 6(2) + R5C6 = (12) -> 1,2 locked for C6
e) 10(2) = {37/46}

5. R5
a) 3(2) = {12} locked

6. N5
a) Hidden Quad (6789) in R456C4 + R6C4 -> no other candidates
b) All 13(2): R37C4 <> 8,9; R5C3 <> 8,9
c) 10(2): R3C6 <> 6,7

7. C4
a) 8,9 locked in R456C4
b) 17(4) must have 7 xor 9 since R2C5 = (79) -> 7,9 not elsewhere
-> R1C3 <> 8 because R1C3 + R12C4 = 8/10

8. N1
a) Innies+Outies: 1 = R4C23 - R1C3; R1C3 = (123456)
-> R4C23 = 3/4/5/6/7
-> R423 <> 7,8,9 and R1C3 <> 1
b) 10(2): R3C3 <> 1,2,3

9. N3
a) 25(4) <> 1 because {1789} not possible since R2C5 = (79)

10. C3
a) Innies = 18(3): R8C3 <> 1,2,3,4 since R15C3 <= 13

11. N5+C5
a) 3 locked in R45C5 for C5
b) 8 locked in 25(4) = 8{269/359/467}
-> R12C6 <> 4 since R2C7 <> 6,7,8
c) 8 locked in 23(4) @ C6 = 8{159/249/267/357/456}

12. C567 !
a) ! 6(2) @ C6 = {15} locked because of following conflict:
If 6(2) = {24} -> 3(2) = [12], 10(2) = [37] -> R259 = [521]
-> 25(4) = {3589} -> 3 must be in R12C6 -> 2 3's in C6
b) R5C6 = 2, R5C7 = 1
c) 4 locked in R456C5 for C5
d) 23(4): R9C7 <> 3,4 since both combos with 3,4 need a 5 which is only
possible @ R9C7 and R89C6 has no 2
e) Innies C789 = {125}

14. N2
a) 25(4) = 9{268/358} -> no 7; 9 locked for C6+N2
b) R2C5 = 7, R9C5 = 9
c) 13(2): R4C4 <> 6

15. R12
a) Innies = 13(2) = {49/58}

16. C1234 !
a) ! Innies C4 = 19(4) = 123{49/58/67}: R1289C4 = 123{4/5/6/7} (8,9 only @ R5C4)
-> R12C4 <> 4,5,6 since R89C4 would be {12/13/23} -> no possible combination for 23(4)
-> R1C3 = (56) (only possible there in 17(4))

17. R3
a) 4,5 locked in R3C46
b) 10(2): R4C3 <> 6

18. C3
a) 11(2) <> 5,6 because {56} is blocked by R1C3 = (56)

19. N2+C4
a) 17(4) = 37{16/25} -> 3 locked for C4+N2
b) R3C6 = 4, R4C6 = 6
c) Naked triple (789) in R456C4 locked for C4
d) 13(2) @ N2 = [58/67]
e) 25(4) = {2689} -> R1C5 = 6, R2C7 = 2, R9C7 = 5
-> 8,9 locked for C6+N2
f) R8C5 = 8, R1C3 = 5, R3C4 = 5, R4C4 = 8
g) 17(4) = {2357} -> R2C4 = 3, R1C4 = 2, R3C5 = 1

20. C5
a) 6(2) = {42} -> R6C5 = 4, R7C5 = 2
b) 23(4) = {1679} -> R8C3 = 7
c) R8C6 = 3, R9C6 = 7, R8C7 = 4, R1C7 = 3
d) 9(3) = {135} -> 3,5 locked for N5
e) R6C6 = 1, R7C6 = 5

21. R8
a) Hidden Single: R8C1 = 5
b) 19(4) = {2458} -> 2,4,8 locked for R9+N7
c) 15(4) = {2346} -> R8C8 = 2; R9C89 = {36} locked for R9+N9
d) R9C4 = 1, R8C4 = 6, R7C4 = 4, R6C4 = 9, R5C4 = 7, R5C3 = 6

22. C3
a) 10(2) = [82/91]
b) Killer pair (29) of 10(2) blocks [29] of 11(2)
c) R7C3 = 3, R6C3 = 8, R3C3 = 9, R4C3 = 1, R2C3 = 4, R9C3 = 2
d) R2C1 = 8, R9C1 = 4, R9C2 = 8, R2C6 = 9, R1C6 = 8, R2C8 = 5
e) 18(4) = {1467} -> R2C2 = 6; 1,7 locked for R1+N1

23. Rest is clean-up and singles.


Last edited by Afmob on Sun Oct 14, 2007 10:02 am; edited 1 time in total
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Andrew
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PostPosted: Wed Oct 10, 2007 3:56 am    Post subject: Reply with quote

Ruud wrote:
The border came first. In my original design, the interior had bigger cages, but to make this Assassin solvable, I needed to compensate the border complexity.

Solvable. Yes! But only after a very, very long time!!

CathyW wrote:
Finally! Took about 4 hours in total.

gary w wrote:
Cathy said this was a tough one..sure was..took me 5 hrs plus Exclamation

Congratulations to both of you and to Afmob for solving it so quickly!

I don't know how long I took, over several days, but it must have been at least twice that long. I must have sat staring at the position after step 35 for several hours wondering if I was ever going to make any more progress. Brick wall Then I eventually found a contradiction move that provided the first breakthrough. Still a lot of hard work after that. I'll stick with my earlier rating of 1.75.

I haven't yet gone through the posted walkthroughs, I need a break from this puzzle before I do that, but I'll assume that their solving paths will be different so here is my walkthrough

Walkthrough for A71

1. R34C3 = {39/48/57}, no 1,2,6

2. R34C4 = {19/28/37/46}, no 5

3. R34C6 = {19/28/37/46}, no 5

4. R34C7 = {49/58/67}, no 1,2,3

5. R5C34 = {17/26/35}, no 4,8,9

6. R5C67 = {17/26/35}, no 4,8,9

7. R67C3 = {18/27/36/45}, no 9

8. R67C4 = {29/38/47/56}, no 1

9. R67C5 = {29/38/47/56}, no 1

10. R67C6 = {49/58/67}, no 1,2,3

11. R67C7 = {14/23}

12. R345C5 = {289/379/469/478/568}, no 1

13. 14(4) cage in N3 = {1238/1247/1256/1346/2345}, no 9

14. 27(4) cage in N6 = {3789/4689/5679}, 9 locked for N6, clean-up: no 4 in R3C7

15. 14(4) cage at R8C3 = {1238/1247/1256/1346/2345}, no 9

16. 45 rule on R12 2 innies R2C18 = 12 = {39/48/57}, no 1,2,6

17. 45 rule on R6789 2 innies R6C29 = 15 = {69/78}

18. 45 rule on R89 2 innies R8C29 = 8 = {17/26/35}, no 4,8,9

19. 45 rule on C12 2 outies R29C3 = 10 = {19/28/37/46}, no 5

20. 45 rule on C1234 2 outies R29C5 = 7 = {16/25/34}, no 7,8,9

21. 45 rule on C89 2 outies R18C7 = 7 = {16/25} (cannot be {34} which clashes with R67C7)

22. Killer pair 1,2 in R18C7 and R67C7, locked for C7, clean-up: no 6,7 in R5C6

23. 45 rule on C789 3 innies R259C7 = 20 = {389/479/578} (cannot be {569} which clashes with R34C7), no 6, clean-up: no 2 in R5C6
23a. 3 of {389} must be in R5C7 -> no 3 in R29C7

24. 45 rule on C6789 2 outies R18C5 = 8 = {17/26/35}, no 4,8,9

25. 45 rule on N3 2 innies R23C7 – 14 = 1 outie R4C9 -> min R23C7 = 15, R23C7 = {6789}, max R23C7 = 17 -> max R4C9 = 3, clean-up: no 8 in R4C7

26. 45 rule on N9 2 innies R79C7 – 6 = 1 outie R6C8, max R79C7 = 13 -> max R6C8 = 7

27. 45 rule on N7 2 outies R6C13 – 5 = 1 innie R8C3
27a. IOU no 5 in R6C1

28. 8,9 in C5 locked in R34567C5 = 30 = 89{247/256/346}
28a. 3 of {34689} must be in R67C5 -> no 3 in R345C5
28b. R18C5 (step 24) = {17/35} (cannot be {26} which clashes with R34567C5), no 2,6

29. 45 rule on C123 3 innies R158C3 = 14 = {149/158/167/239/248/257/356} (cannot be {347} which clashes with R34C5)

30. 45 rule on C6 5 innies R12589C6 = 22 = {12379/12469/12568/13459/13567/23458/23467} (cannot be {12478/13468} which clash with R67C6)

31. 45 rule on C4 5 innies R12589C4 = 24 = {12489/12579/13479/13569/13578/14568/23478/23568/24567} (cannot be {12678/23469} which clash with R34C4)

32. 8,9 in N6 locked in 27(4) cage (step 14) = {3789/4689}, no 5

33. 45 rule on N1 2 outies R4C23 – 7 = 1 innie R1C3
33a. IOU no 7 in R4C2

34. 45 rule on R5 5 innies R5C12589 = 29 = {14789/24689/34589} [1/2/3, 5/6/7]

35. 45 rule on C3 5 innies R12589C3 = 24 = {12489/12579/12678/13569/14568/23469/24567} (cannot be {13479/13578/23478/23568} which clash with R34C4)

36. No 4 in R4C7, here’s how
36a. 27(4) cage in N6 (step 32) = {3789/4689}
36b. If 27(4) = {3789} and R4C9 = 1 => R23C7 = 15 (step 25) = {78}/[96] -> no 9 in R3C7 -> no 4 in R4C7
36c. If 27(4) = {3789} and R4C9 = 2 => R23C7 = {79} => R4C7 = {46}
36ca. Then if R4C7 = 4, R5C7 = 5, R6C8 = 6, R67C7 = [14] clashes with R4C7
36cb. Then if R4C7 = 6 -> no 4 in R4C7
36d. If 27(4) = {4689} -> no 4 in R4C7
36e. -> no 4 in R4C7, clean-up: no 9 in R3C7

37. 9 in C7 locked in R29C7
37a. R259C7 (step 23) = {389/479}, no 5, clean-up: no 3 in R6C5
37b. 7 of {479} must be in R5C7 -> no 7 in R29C7

38. 27(4) cage in N6 (step 32) = {4689} (only remaining combination, cannot be {3789} which clashes with R5C7), locked for N6, clean-up: no 7 in R3C7, no 8 in R6C2 (step 17), no 1 in R7C7
38a. 7 in C7 locked in R45C7, locked for N6
38b. R23C7 cannot total 16 -> no 2 in R4C9 (step 25)
38c. 2 in N6 locked in R6C78, locked for R6, clean-up: no 7 in R7C3, no 9 in R7C45
38d. 4 in C7 locked in R79C7, locked for N9

39. R23C7 – 14 = R4C9 (step 25)
39a. R4C9 = 1 => R23C7 = [96]
39b. R4C9 = 3 => R23C7 = [98]
39c. -> R2C7 = 9, clean-up: no 3 in R2C18 (step 16), no 1 in R9C3 (step 19)

40. 20(4) cage at R1C5 = {1289/1379/1469/2369/2459}
40a. 5 of {2459} must be in R1C5 -> no 5 in R12C6

41. 17(4) cage at R2C8 = {1358/1367/1457/2357} (cannot be {1268} which clashes with R3C7, cannot be {2348} which clashes with 14(4) cage, cannot be {2456} because R4C9 only contains 1,3)
41a. 14(4) cage in N3 (step 13) = {1238/1247/1346/2345} (cannot be {1256} which clashes with 17(4) cage)

42. R79C7 – 6 = R6C8 (step 26)
42a. R79C7 cannot total 8 with 4 locked in R79C7 -> no 2 in R6C8

43. R6C7 = 2 (hidden single in R7), R7C7 = 3, R5C7 = 7, R4C7 = 5, R3C7 = 8, R9C7 = 4 (hidden single in C7), R6C8 = 1 (step 26), R4C9 = 3, R5C6 = 1, clean-up: no 4 in R2C1 (step 16), no 6 in R2C3 (step 19), no 3 in R2C5 (step 20), no 7,9 in R3C3, no 7,9 in R3C46, no 4 in R4C3, no 2 in R4C46, no 9 in R4C6, no 6 in R6C3, no 8 in R6C45, no 8 in R7C3, no 5,7 in R8C2 (step 18)
43a. 1 in N4 locked in R4C12
43b. CPE no 1 in R3C1

44. R1C8 = 3 (hidden single in N3), clean-up: no 5 in R8C5 (step 24)
44a. 14(4) cage in N3 (step 41a) = {1346} (only remaining combination, cannot be {2345} because R1C7 only contains 1,6), locked for N3, clean-up: no 8 in R2C1 (step 16)
44b. 4 in N3 locked in R12C9, locked for C9
44c. 2 in N3 locked in R3C89, locked for R3, clean-up: no 8 in R4C46

45. Naked pair {57} in R2C18, locked for R2, clean-up: no 3 in R9C3 (step 19), no 2 in R9C5 (step 20)

46. R67C6 (step 10) = {49/58} (cannot be {67} which clashes with R34C6)

47. 22(4) cage at R8C5 = {2479/3469/3478/4567} (cannot be {1489} which clashes with R67C6), no 1, clean-up: no 7 in R1C5 (step 24)

48. 22(4) cage at R8C5 cannot be {3478}, here’s how
48a. If R8C5 = 3 => R89C6 = {78} => R34C6 = {46} and R67C6 = {49} clash
48b. If R8C5 = 7 => R89C6 = {38} => R34C6 = {46} and R67C6 = {49} clash
48c. -> 22(4) cage at R8C5 = {2479/3469/4567}, no 8
48d. R89C6 = {29/69/56}, no 3,7

49. 1 in N8 locked in 14(4) cage at R8C3 within N8 -> no 1 in R8C3

50. 18(4) cage at R6C8 = {1269/1278}, no 5, 2 locked for N9, clean-up: no 3 in R8C2 (step 18)
50a. 21(4) cage in N9 = {1569/1578}

51. 1 in R7 locked in R7C123, locked for N7, clean-up: no 7 in R8C9 (step 18)

52. Naked pair {26} in R8C29, locked for R8 -> R8C7 = 1, R1C7 = 6, clean-up: no 5,9 in R9C6 (step 48d)

53. 25(4) cage in N7 = {3589/3679/4579/4678} (cannot be {2689} which clashes with R8C2), no 2

54. 2 in R9 locked in R9C46, locked for N8, clean-up: no 9 in R6C45

55. 9 in N8 locked in R78C6, locked for C6, clean-up: no 4 in R7C6

56. 9 in C5 locked in R345C5
56a. R345C5 (step 12) = {289/469}, no 5,7

57. 7 in N2 locked in R1C46, locked for R1

58. 7 in N1 locked in 19(4) cage at R2C1 = {1279/1378/1567/2467/3457}
58a. 2 of {1279} must be in R4C2 and the 1 must be in R3C2 -> no 9 in R34C2

59. R158C3 (step 29) = {158/167/239/248/257/356} (cannot be {149} because no 1,4,9 in R5C3
59a. 3 of {239} must be in R8C3 and 6 of {356} must be in R5C3 -> no 3 in R5C3, clean-up: no 5 in R5C4
59b. 8 of {158}, 7 of {257} and 3 of {356} must be in R8C3 -> no 5 in R8C3

60. 14(4) cage at R8C3 (step 15) = {1238/1247/1346} (cannot be {1256} because 1,2,6 only in R9C45), no 5, clean-up: no 2 in R2C5 (step 20)
60a. 2 of {1238/1247} must be in R9C4 -> no 7,8 in R9C4
60b. R8C34 = {34/38/47} -> no 3 in R9C45, clean-up: no 4 in R2C5 (step 20)

61. Killer pair 3,7 in R8C34 and R8C5, locked for R8

62. Naked triple {126} in R9C456, locked for R9 and N8, clean-up: no 5 in R6C45, no 9 in R8C8 + R9C89 (step 50a)

63. Naked triple {578} locked in R8C8 + R9C89, locked for N9
63a. 7 in N9 locked in R9C89, locked for R9, clean-up: no 4 in R8C1 (step 53)
63b. 9 in N9 locked in R7C89, locked for R7, clean-up: no 4 in R6C6
63c. 25(4) cage in N7 (step 53) = {3589}, locked for N7, clean-up: no 4 in R6C3

64. Naked pair {16} in R29C5, locked for C5 -> R1C5 = 5, clean-up: no 4 in R345C5 (step 56a)
64a. R3C5 = 9 (naked single)
64b. Naked pair {28} in R45C5, locked for C5 and N5 -> R67C6 = [58], clean-up: no 3 in R6C5, no 4 in R7C3
64c. R7C5 = 3 (hidden single in C5)

65. 20(4) cage at R1C5 (step 40) = {2459} (only remaining combination)
65a. Naked pair {24} in R12C6, locked for C6 and N2 -> R9C6 = 6, R8C6 = 9, R9C45 = [21], R2C5 = 6, clean-up: no 4,6 in R4C4, no 6 in R5C3
65b. R34C6 = [37] -> R34C4 = [19], R34C3 = [48], R45C5 = [28], R67C5 = [47], R12C4 = [78], R1C3 = 2, R12C6 = [42], R12C9 = [14], R8C34 = [74], R56C3 = [53], R2C23 = [31], R7C3 = 6, R567C4 = [365], R9C3 = 9, R8C2 = 2, R8C9 = 6, R56C9 = [98], R7C89 = [92]

66. R3C8 = 2 (hidden single in R3), R5C1 = 2 (hidden single in R5), R9C1 = 3 (hidden single in R9)

67. R2C1 + R3C12 = {567} -> R4C2 = 1 (cage sum), R7C12 = [14], R6C1 = 9 (cage sum)

and the rest is naked singles


Last edited by Andrew on Fri Oct 12, 2007 12:51 am; edited 2 times in total
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sudokuEd
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Joined: 19 Jun 2006
Posts: 257
Location: Sydney Australia

PostPosted: Wed Oct 10, 2007 11:45 am    Post subject: Reply with quote

About A71 Andrew wrote:
Whether it's actually the hardest ever I don't know. There were several very difficult ones about a year ago; A24, A26, A31, A33 and A34.
Here's a few very tentative scores comparing these puzzles and the hardest 4 v1s and a couple of others of interest. These are from yesterdays version of the ever evolving scoring method that Richard and me are developing using Sudoku Solver . I'm getting more confident - Richard is still ....not. Wink

If anyone tries these earlier ones, would love to hear how you rate these scores.

Code:
A18 1.59 (may be unreliable)

A24 1.32

A26 0.94

A31 1.00

A33 1.10

A34 0.96

A50 1.64

A60 1.65

A60 RP Lite 2.56

A71 1.90

A71 V2 1.61


Been through this walk-through 4 times to get it correct and simple enough Confused . Still found some little mistakes. This puzzle drove me nuts - hate all the clean-up and fiddly stuff required. Can't bear to look at any other WTs for now. I'd rate the puzzle a 1.5 since it took me less than 10 hours to get a nice solution.

Step 23 is a really great piece of light relief - thanks to Andrew for finding it for me.

Assassin 71
Prelims
i. 14(4)n3: no 9
ii. 12(2)n1: no 126
iii. 10(2)r3c4 & r3c6: no 5
iv. 19(3)n2: no 1
v. 13(2)n3 & n5: no 123
vi. 27(4)n6: no 12
vii. 8(2)r5c3 & r5c6: no 489
viii. 9(2)n4: no 9
ix. 11(2)r6c4 & r6c5: no 1
x. 5(2)n6 = {14/23}
xi. 14(4)n7: no 9

1. "45" r89: r8c29 = h8(2): no 489

2. "45" r12: r2c18 = h12(2): no 126

3. "45" c12: r29c3 = h10(2): no 5

4. "45" c89: r18c7 = h7(2): no 789
4a. = {16/25}: {34} clashes with [3/4] required in 5(2)n6
4b. Killer Pair [12] in h7(2) & 5(2): both locked for c7
4c. no 67 in r5c6

5. "45" c789: r259c7 = h20(3) = {389/479/569/578}
5a. 3 in {389} must be in r5c7 -> no 3 in r29c7
5b. {569} clashes with h7(2)r18c7
5c. = {389/479/578}(no 6)
5d. no 2 r5c6

6. "45" c1234: r29c5 = h7(2): no 789

7. "45" c5: r18c5 = h8(2): no 489
7a. {26} clashes with 19(3) + 11(2) in c5 (thanks to Sudoku Solver for combining cages for me)
7b. = {17/35} = [3/7..]

8. 19(3)n2 = {289/469/478/568}(no 3) ({379} clashes with h8(2)r18c5

9. "45" r6789: r6c29 = h15(2) = {69/78}

10. 9 must be in 27(4)n6: 9 locked for n6
10a. no 4 r3c7

11. "45"n7: r6c13 - r8c3 = 5
11a. Since 1 innie r8c3 is in the same c as 1 outie r6c3 -> the 2nd outie r6c1 must be unequal to the difference betweeen the innie and

outies (IOU) -> no 5 r6c1

12. "45" n1: 2 outies - r1c3 = 7
12a. IOU -> no 7 in r4c2

13. "45" n3: 2 outies + 1 = r2c7
13a. min r4c79 = [41] = 5 -> min r2c7 = 6
13b. r2c7 = {789}
13c. max. r2c7 = 9 -> max r4c79 = 8 -> max r4c9 = 3 (can't have {44} = 8)
13d. max r4c79 = 8 -> max r4c7 = 7 -> no 8 r4c7 -> no 5 r3c7

14. "45" n3: r4c9 + 14 = r23c7 = 15/16/17 = {78}/[96]/{79}/{89}

15. h20(3)r259c7 = {389/479/578} = [839/938/974/758/875/857]

16. "45" n9: r6c78 + 1 = r9c7
16a. max r9c7 = 9 -> max r6c78 = 8
16b. no 8 r6c8

17. 8 in n6 only in 27(4) = 89{37/46}(no 5)
17a. if = 89{37} -> r5c7 = 5 -> r5c6 = 3 -> 3 in 27(4) only in r4c8
17b. no 3 in r5c89
17c. no 7 in r4c8 (must be 3 in {37..})

18. "45" c123: r158c3 = h14(3)
18a. {347} clashes with 12(2) n1

19. h10(2)r29c3 = {19/28/46}(no 37) ({37} clashes with 12(2) + 9(2) in c3)

20. "45" n69: 4 innies = 19: r4c9 + r459c7 =
20a. [1][738/459/657] ([1][639/675] clash with 27(4) = [3/6;6/7..]
20b. [2][539/458] ([2][638/674] clash with 27(4))
20c. [3][574/754] ([457/475] clash with 27(4)
20d. r9c7: no 5

21. 2 of the cells from step 20, r59c7, must overlap with 2 of the cells from h20(3)r259c7
21a. h20(3)r259c7=[839/938/974/758/857] (step 15) ([875] blocked by no 5 in r9c7
21b. -> from step 20, r459c7: [459/754] do not have a double cell overlap
21c. -> r459c7 = [738/657/539/458/574]

22. because of 13(2)n3: combo's in r459c7 that have 6 in r4c7 cannot have 7 etc
22a. -> r459c7 [657] is blocked
22b. ->r3459c7 = [6738/8539/9458/8574] = 8{..}
22c. no 7 r39c7
22d. no 6 r4c7
22e. 8 locked in r39c7 for c7

23. OK. Here's a fun one from Andrew. No 9 in r9c7. Here's how.
23a R1C5 and R2C7 both odd so R12C6 even (cage sum is even)
23b. R34C6 even, R5C6 odd, R67C6 odd -> R89C6 odd (since "45" is odd)
23c. since R8C5 odd and r89c6 odd (and an even cage sum) -> R9C7 must be even
23d. -> no 9 r9c7
23e. of course, combo placing in h20(3)r259c7 would have done the same thing. But much more fun!

24. 9 in c7 only in n3: 9 locked for n3

25. h20(3)r259c7 = {389/479/578} = [938/974/758]
25a. from 20a. innies n69 =
25b. [1][738]
25c. [2][458]
25d. [3][574]

26. innies n6 = 18(5)
26a. (from step 25) r4c9 + r45c7 + r6c78 =
26b. [1][73] = 11 -> r6c78 = 7 = [25]
26c. [2][45]= 11 -> r6c78 = 7 = [16]
26d. [3][57]= 15 -> r6c78 = 3 = {12}
26e. r6c7 = {12} -> r7c7 = {34}
26f. r6c8 = {1256}

27. from step 26b,c,d: the 5(2) cage restricts r45c7 <>3 with 2 in r6c7; <> 4 with 1 in r6c7
27a. -> r456c7 = [732/451] blocked
27b. -> r456c7 = [57]{12} only
27c. no 1 r5c34
27d. no 8 r6c2 (h15(2)r6c29)

28. r4c9 = 3 (step 26d)
28a. no 7 r3c46
28b. no 7, 9 r3c3

29. r3c7 = 8
29a. no 2 r4c46
29b. no 4 r4c3
29c. no 49 r2c1 (h12(2)r2c18)

30. r5c6 = 1
30a. no 9 r34c6
30b. no 9 r3c4

31. r2c7 = 9
31a. no 3 r2c1 (h12(2)r2c18)
31b. no 1 r9c3 (h10(2)r29c3)

32. r9c7 = 4 (h20(3)r259c7)
32a. no 3 r2c5 (h7(2)r29c5)
32b. no 6 r2c3 (h10(2)r29c3)

33. r67c7 = [23]
33a. no 8 r6c45
33b. no 6 r6c3
33c. no 9 r7c45
33d. no 7 r7c3
33e. no 5 r8c2 (h8(2)r8c29)

34. r6c8 = 1 (hsingle n6)
34a. no 8 r7c3

35. r1c8 = 3 (Hsingle n3)
35a. no 5 r8c5 (h8(2)r18c5)

36. 1 in r7 only in n7: 1 locked for n7

37. 17(4)n3 = 3{257} (3{167} blocked by r1c7)
37a. 2,5,7 all locked for n3 and 2 locked for r3
37b. no 8 r4c46
37c. no 8 r2c1 (h12(2)r2c18)

38. 4 in n3 only in c9: 4 locked for c9

39. h12(2) r2c18 = {57}: both locked for r2
39a. no 2 r9c5 (h7(2)r29c5)

40.deleted

41. 10(2)r3c6 = [37]/{46}(no 2) = [6/7..]

42. 13(2)n5 = {49/58} ({67} blocked by 10(2) step 41)
42a. = [8/9..]

43. 22(4)n8 must have 4 = 4{279/369/378/567}(no 1) ([1]{89} blocked by 13(2) step 42a)
43a. no 7 r1c5 (h8(2)r18c5)
43b. {378} combo must have 7 in r8c5 since {78} in r89c6 would clash with 10(2) + 13(2)c6 (thanks SS)
43c. -> no 7 r89c6

44. 21(4)n9 must have 1 for n9
44a. = 1{569/578}(no 2)
44b. 5 locked for n9

45. h8(2) r8c29 = {26}: both locked for r8
45a. r18c7 = [61]

46. 25(4)n7 = {3589/3679/4579/4678}(no 2)({2689} blocked by r8c2

47. 2 in r9 only in n8: 2 locked for n8
47a. no 9 r6c45

48. h10(2) r29c3, r9c3 = {689}
48b. r2c3 = {124}

49. 20(4)n2 = 9{128/137/146/245}
49a. = 1/5, not both
49b. no 5 r1c6

50. h7(2)r29c5 = {16}/[25/43]

51. 9 in n8 only in c6: 9 locked for c6
51a. no 4 r7c6

52. 14(4)n7 must have 1 in r9c45
52a. = 1{238/247/346}(no 5) ({1256} blocked by r8c34)
52b. no 2 r2c5 (h7(2)r29c5)
52c. h7(2)r29c5 = {16}/[43] = [4/6..]

53. 19(3)n2 must have 9 for c5 = {289} ({469} blocked by h7(2)
53a. all locked for c5 & 8 locked for n5
53b. no 3 r6c5
53c. no 5 r7c6
53d. no 2 r3c4

54. 18(4)r6c8 must have 1 and 2 = 12{69/78}
54a. r7c89 = [8/9..] -> Killer pair [89] with r7c6: both locked for r7
54b. no 3 r6c4

55. r5c4 = 3 (hsingle n5)
55a. no 7 r4c4

56. r5c3 = 5
56a. no 4 r67c3
56b. no 7 r4c3

57. should have seen this before: 2 in n5 only in r45c5 -> no 2 in r3c5
57a. r3c5 = 9
57b. r4c4 = 9

rest is straightforward. Finally.


Last edited by sudokuEd on Fri Oct 12, 2007 5:08 am; edited 2 times in total
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mhparker
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PostPosted: Wed Oct 10, 2007 11:45 am    Post subject: Reply with quote

To all my fellow forum members,

Para wrote:
Gotta stick to your convictions, Ed Wink ... Oh, btw. Love your doing an "old school" V2 again.


Andrew wrote:
I mention those earlier Assassins because newer members of the forum may not have come across them. They can make a change from doing variants, particularly those variants which have the same cage pattern but different cage totals. Variants where subtle changes have been made to the cage pattern are a different matter; they are more like new puzzles.


CathyW wrote:
Regarding the A71, I've not attempted either of the variants having taken so long on the original. Addict that I am, I had to persevere to the finish but for the first time it really felt like a slog rather than an enjoyable pastime. Sad

Still looking forward to the A72 on Friday though Smile


Andrew wrote:
I haven't yet gone through the posted walkthroughs, I need a break from this puzzle before I do that


I'm not sure I agree with the "more like new puzzles" phrase of Andrew's, especially if the variants with the subtly modified cage pattern are still based on the same solution as the original. Just take a look at the A71 V1 compared to the A71 V2. Same cage pattern, but a totally different character.

Maybe I picked a bad week to post another variant, having possibly underestimated just how fed up you all are, having suffered the slog and frustration of battling through the V1.

The point I want to make here, however, is a different one. I can only speak for myself, but IMO doing these puzzles, and my variants in particular, should not be a painful, unenjoyable, tedious, or demotivating experience! When I choose to publish one, I do so in the hope and/or belief that it will be interesting from some point-of-view, whether it be for training new skills, or because of some move(s) it contains, or for other similar reasons. In doing so, I am not trying to catch anybody out, and am certainly not trying to show off or go "one up" on anyone else. However, if (despite the effort I put into them) the interest in doing them is simply not there (for whatever reason), then there is no point in having them! It is as simple as that!

For this reason, I will not be posting any further variants on this forum, although I may from time-to-time publish completely new puzzles, with a totally custom cage pattern and solution.

I hope that you can understand and respect this decision.

In the meantime, I wish you all a lot of fun solving! Keep up the good work! Smile
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CathyW
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PostPosted: Wed Oct 10, 2007 3:10 pm    Post subject: Reply with quote

Mike - I respect your decision but I hope it wasn't based on a misunderstanding. Anxious

Most weeks I am more than happy to tackle a V2, V1.5 whether it's from Ruud, yourself, Para or anyone else. It was just this particular week's puzzle where I couldn't face looking at one with the same cage pattern.

With hindsight and comments from others, it looks as though the A71 V2 and your version may have been easier than the original so I may come back to them some time. Smile
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PostPosted: Wed Oct 10, 2007 6:57 pm    Post subject: Reply with quote

Mike

Sorry to read that you won't be posting any more variants; of course I respect your decision on that. I look forward to your completely new puzzles when they appear.

mhparker wrote:
I'm not sure I agree with the "more like new puzzles" phrase of Andrew's, especially if the variants with the subtly modified cage pattern are still based on the same solution as the original. Just take a look at the A71 V1 compared to the A71 V2. Same cage pattern, but a totally different character.

Maybe I was wrong on that. Subtly modified cage patterns take away some previous steps. Different cage totals do the same. I suppose I was thinking that in most cases where the cage patterns have been modified that has been done to take away an easier start to a puzzle.

I started your A71V1.5 last night and will post a walkthrough if/when I finish it unless someone else has already posted one that is very similar to mine.

sudokuEd wrote:
Step 23 is a really great piece of light relief - thanks to Andrew for finding it for me.

Just to put this in context. I commented to Ed off-forum that I'd been looking at that idea but it didn't actually work in my solving path. It's good to see that Ed managed to use it and found it helpful.

sudokuEd wrote:
A18 1.59 (may be unreliable)
A24 1.32
A26 0.94
A31 1.00
A33 1.10
A34 0.96

I suppose I ought to have also added A18 to my list. That was the first one that I needed a hint from Ed to finish it although, in typical fashion, I interpreted the hint in a slightly different way from what had been intended and applied it to another part of the grid. I remember that Ed had a nice breakthrough based on hidden/split cages.

I must admit I'm surprised that the SS scores for A26, A31, A33 and A34 are that low. I'll look at them when I can find time but, since they are old puzzles, I won't then post any walkthroughs.

For A71 sudokuEd wrote:
I'd rate the puzzle a 1.5 since it took me less than 10 hours to get a nice solution.

IMHO something of the order of 10 hours is more than a 1.5. Ed has quoted the SS score as 1.90. I'll settle for 1.75.
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PostPosted: Wed Oct 10, 2007 11:12 pm    Post subject: assassin 71 v1.5 Reply with quote

Hi all,

I for one thoroughly enjoyed renewing my acquaintance with this cage..and many thanks to Mike for posting it.Slightly easier than v1 but I,m sure this is because I'ld slogged so hard through v1.Coming upon v1.5 in isolation I'm certain it would have taken me much longer to solve than it did...about 3 hours,in fact.My solution

depended on an early examination of the 9s in r4 and c5 eventually leading to placing a 9 at r3c5.Then,using r259c7=10 I was able to place a 4 at r5c7 and a 1 at r4c9 and the puzzle - slowly- yielded.I liked the symmetry of this puzzle..at one stage I had a number of {15} and {45} pairs dotted around all just waiting for a little bit of lateral thinking which was eventually provided by the two 7/2 cages in c6.


Regards

Gary
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PostPosted: Thu Oct 11, 2007 6:28 am    Post subject: Reply with quote

Thanks for the V1.5 Mike. Nice puzzle!

A lot easier than V1 but don't know how it compares with V2 because I didn't try to solve that one myself and I haven't yet looked at the later moves for that one or at Afmob's walkthrough.

I'll rate it at least a 1.25. Maybe it should be rated higher because it was a fairly narrow solving path and a lot of work after the breakthrough.

I had to use one hypothetical (step 37) and have commented on another one that I saw but didn't need to use. I'll be interested to see if anyone else posts a walkthrough without hypotheticals or "advanced" moves.

Here is my walkthrough for A71V1.5

1. R34C3 = {29/38/47/56}, no 1

2. R45C4 = {29/38/47/56}, no 1

3. R45C6 = {16/25/34}, no 7,8,9

4. R45C7 = {18/27/36/45}, no 9

5. R5C34 = {59/68}

6. R5C67 = {49/67} (cannot be {58} which clashes with R5C34)

7. R67C3 = {19/28/37/46}, no 5

8. R67C4 = {17/26/35}, no 4,8,9

9. R67C5 = {17/26/35}, no 4,8,9

10. R67C6 = {16/25/34}, no 7,8,9

11. R67C7 = {29/38/47/56}, no 1

12. R345C5 = {289/379/469/478/568}, no 1

13. 14(4) cage at R1C3 = {1238/1247/1256/1346/2345}, no 9

14. 13(4) cage at R2C8 = {1237/1246/1345}, no 8,9
14a. CPE no 1 in R12C9

15. Killer pair 6,9 in R5C34 and R5C67, locked for R5

16. 45 rule on R12 2 innies R2C18 = 10 = {37/46}/[81/92], no 5

17. 45 rule on R1234 2 innies R4C18 – 14 = 1 outie R5C5, max R4C18 = 17 -> max R5C5 = 3, min R5C5 = 2 -> min R4C18 = 16 -> R4C18 = {79/89}, 9 locked for R4, clean-up: no 2 in R3C34

18. R345C5 (step 12) with R5C5 = {23} = {289/379} -> R3C5 = 9, R4C5 = {78}, clean-up: no 2 in R4C34

19. Naked triple {789} in R4C158, locked for R4, clean-up: no 3,4 in R3C34, no 1,2 in R3C7

20. 45 rule on R6789 2 innies R6C29 = 10 = {19/28/37/46}, no 5

21. 45 rule on R89 2 innies R8C29 = 8 = {17/26/35}, no 4,8,9

22. 45 rule on C12 2 outies R29C3 = 9 = {18/27/36/45}, no 9

23. 45 rule on C1234 2 outies R29C5 = 9 = {18/27/36/45}

24. 45 rule on C6789 2 outies R18C5 = 9 = {18/27/36/45}

25. 45 rule on C89 2 outies R18C7 = 15 = {69/78}

26. 45 rule on C789 3 innies R259C7 = 10 = {127/136/145} (cannot be {235} because no 2,3,5 in R5C7) = 1{27/36/45}, no 8,9, 1 locked for C7, clean-up: no 8 in R3C7, no 4 in R5C6
26a. R5C7 = {467} -> no 4,6,7 in R29C7

27. Hidden killer pair 8,9 in R18C7 and R67C7 -> R67C7 = {29/38}, no 4,5,6,7

28. 45 rule on N1 2 outies R4C23 – 3 = 1 innie R1C3
28a. IOU no 3 in R4C2

29. 45 rule on N1 2 innies R13C3 – 8 = 1 outie R4C2

30. 45 rule on N3 2 outies R4C79 – 2 = 1 innie R2C7
30a. IOU no 2 in R4C9
30b. R2C7 = {1235} -> R4C79 = 3,4,5,7 = [21/31/23/41/25/34/43/61], no 5 in R4C7, no 6 in R4C9, clean-up: no 4 in R3C7
30c. 4 in C7 locked in R45C7, locked for N6, clean-up: no 6 in R6C2 (step 20)

31. 45 rule on N3 2 innies R23C7 – 7 = 1 outie R4C9

32. 45 rule on N7 2 outies R6C13 – 9 = 1 innie R8C3
32a. IOU no 9 in R6C1

33. 45 rule on N7 2 innies R78C3 – 1 = 1 outie R6C1, min R78C3 = 3 -> min R6C1 = 2

34. 45 rule on N9 2 outies R6C78 – 9 = 1 innie R9C7
34a. IOU no 9 in R6C8

35. 45 rule on N9 2 innies R79C7 – 2 = 1 outie R6C8

36. 18(4) cage at R4C1, min R4C1 = 7 -> max R5C12 + R6C2 = 11, no 9 in R6C2, clean-up: no 1 in R6C9 (step 20)

[There’s an interesting hypothetical here but it isn’t needed.
1 in C5 must be in R67C6 or in one of the 9(2) split-cages
If one of the 9(2) split-cages = {18} => R45C5 = [73] => R67C6 = {26}
-> R67C6 = {17/26}, no 3,5]

37. No 4 in R6C2, here’s how
37a. 18(4) cage in N4 = {1278/1359/1458/2349/2358/2457}
37b. If {1458} with R6C2 = 4 => R5C12 = {58} clashes with R34C5
37c. If {2349} with R6C2 = 4 => R5C12 = {23} clashes with R5C5
37d. If {2457} with R6C2 = 4 => R4C1 = 7, R5C12 = {25} => R5C5 = 3, R4C5 = 7 clashes with R4C1
37e. -> no 4 in R6C2, no 6 in R6C9 (step 20)

38. 24(4) cage in N6 = {2589/3579} = 59{28/37}, no 1, 5,9 locked for N6, clean-up: no 2 in R7C7

39. 5 in N6 locked in R5C89, locked for R5, clean-up: no 9 in R5C34
39a. Naked pair {68} in R5C34, locked for R5, clean-up: no 7 in R5C67 -> R5C67 = [94], clean-up: no 5 in R3C7
39b. 9 in N8 locked in R89C4, locked for 22(4) cage -> no 9 in R8C3

40. R259C7 (step 26) = {145} (only remaining combination) -> R29C7 = {15}
[Alternatively R29C7 = {15} (hidden pair in C7).]

41. 1 in R5 locked in R5C12, locked for N4, clean-up: no 9 in R6C9 (step 20), no 9 in R7C3

42. R4C8 = 9 (hidden single in N6), R6C3 = 9 (hidden single in R6), R7C3 = 1, clean-up: no 8 in R29C3 (step 22), no 7 in R6C45, no 6 in R6C6, no 7 in R8C9 (step 21)

43. 18(4) cage in N4 (step 38a) = {1278} (only remaining combination), locked for N4 -> R5C34 = [68], R45C5 = [73], R4C1 = 8, clean-up: no 3 in R29C3 (step 22), no 5 in R34C3, no 4 in R3C6, no 1 in R6C5, no 5 in R67C5, no 2,7 in R6C9 (step 20), no 5 in R7C4, no 4 in R7C6

44. Naked pair {26} in R67C5, locked for C5

45. R6C13 – 9 = R8C3 (step 32), R6C3 = 9 -> R6C1 = R8C3 -> R8C3 = {345}

46. 45 rule on C123 2 remaining innies R18C3 = 9 = {45} (only remaining combination), clean-up: no 3 in R6C1 (step 45)
46a. Naked pair {45} in R18C3, locked for C3
46b. R3C3 = 8 (hidden single in C3), R4C3 = 3, R4C9 = 1, clean-up: no 6 in R3C67

47. R6C78 – 9 (step 34) = R9C7, R9C7 = {15} -> R6C78 = 10,14 = [28/37/82/86], no 3 in R6C8

48. 45 rule on N6 3 remaining innies R4C7 + R6C78 = 16 = {268/367}
48a. R46C7 cannot be [68] which would make R3C7 and R7C7 clash -> no 2 in R6C8

49. 13(4) cage at R2C8 (step 14) = {1246/1345} (cannot be {1237} which clashes with R3C7), no 7

50. 14(4) cage at R1C3, min R1C3 = 4 -> max R1C4 + R2C45 = 10, no 8, clean-up: no 1 in R9C5 (step 23)

51. 8 in N2 locked in 20(4) cage at R1C5 = {1478/1568/3458} (cannot be {2378/2468} because R2C7 only contains 1,5), no 2

52. 22(4) cage at R8C3 must contain 9 and at least two of 4,5,8 = {1489} (only remaining combination) -> R8C3 = 4, R9C5 = 8, R2C5 = 1 (step 23), R29C7 = [51], R18C5 = [45], R89C4 = [19], R1C3 = 5, clean-up: no 6 in R4C6, no 2 in R6C6, no 7 in R7C4

53. Naked triple {236} in R7C456, locked for R7 and N8 -> R89C6 = [74], clean-up: no 8 in R1C7 (step 25), no 3 in R37C6, no 8 in R6C7

54. R6C6 = 1 (hidden single in R6), R7C6 = 6, R67C5 = [62], R67C4 = [53], clean-up: no 6 in R34C4

55. R34C4 = [74], R34C7 = [36], R6C1 = 4, R4C2 = 5, R34C6 = [52]

56. R6C9 = 3 (hidden single in R6), R6C2 = 7 (step 20), R6C8 = 8, R67C7 = [29], R18C7 = [78], R7C2 = 8

57. Naked triple {246} in R2C89 + R3C9, locked for N3 -> R1C8 = 1

58. 23(4) cage at R6C1, R6C1 = 4, R7C2 = 8 -> R7C1 + R8C2 = 11 = [56], R8C89 = [32], R8C1 = 9
58a. Naked triple {237} in R9C123, locked for R9

59. 16(4) cage at R2C1 = {1456/2356} (cannot be {1357} because 3,7 only in R2C1), no 7
59a. 4 of {1456} must be in R3C2 -> no 1 in R3C2
59b. 2 of {2356} must be in R3C2 -> no 2 in R3C1

60. R9C1 = 7 (hidden single in C1), R9C23 = [32], R2C3 = 7

61. R5C2 = 1 (hidden single in C2), R5C1 = 2

62. R3C1 = 1 (hidden single in C1)
62a. 16(4) cage at R2C1, R3C1 = 1, R4C2 = 5 -> R2C1 + R3C2 = 10 = [64]

and the rest is naked singles

3 2 5 6 4 8 7 1 9
6 9 7 2 1 3 5 4 8
1 4 8 7 9 5 3 2 6
8 5 3 4 7 2 6 9 1
2 1 6 8 3 9 4 5 7
4 7 9 5 6 1 2 8 3
5 8 1 3 2 6 9 7 4
9 6 4 1 5 7 8 3 2
7 3 2 9 8 4 1 6 5


Last edited by Andrew on Mon Oct 15, 2007 9:42 pm; edited 1 time in total
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Afmob
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PostPosted: Thu Oct 11, 2007 9:42 am    Post subject: Reply with quote

A71 V1.5 was the easiest of the bunch. It didn't need any complicate or long contradiction moves so given rating of 1.25 should be right.

By the way, it was the most fun to solve, since the other versions had a point after there was no going further and you could see the next step only after long thinking Confused .

Assassin 71 V1.5 Walkthrough

1. R1234
a) Innies R12 = 10(2) = [37/46/64/73/82/91]
b) Innies+Outies: -14 = R5C5 - R4C18 -> R5C5 = (23), R4C18 = 16/17 = {79/89}
-> 9 locked for R4
c) 19(3) = 9{28/37} since R5C5 = (23) -> R3C5 = 9, R4C5 = (78)
d) Naked triple (789) in R4C158 locked for R4
e) Both 11(2) = [56/65/74/83]
f) 9(2): R3C7 <> 1,2

2. R6789
a) Innies R89 = 8(2) -> no 4,8,9
b) Innies R6789 = 10(2) -> no 5

3. R5
a) Killer pair (58) of 14(2) blocks {58} of 13(2)
b) 9 locked in R5C46
c) 14(2): R5C4 <> 5
d) 13(2): R5C6 <> 4
e) Killer pair (69) in 14(2) + 13(2) locked

4. C1234
a) Outies C12 = 9(2) -> no 9
b) Outies C1234 = 9(2)

5. C6789
a) Outies C89 = 15(2) = {69/78}
b) Innies C789 = 10(3) = 1{27/36/45}; {235} impossible because R5C7 = (467)
c) Innies C789 = 10(3): R29C7 <> 4,6,7 since R5C7 is at least 4 and R5C7 <> 5
d) 1 locked in Innies C789 for C7
e) 9(2): R3C7 <> 8
f) Outies C6789 = 9(2)

6. C5
a) Innies = 18(4) = 9(2) + 9(2) (step 4b, 5f); 4 locked in 18(4)
-> since 4 is locked, one of the 9(2) must be {45} -> 5 locked
-> 18(4) = 45{18/27/36}
b) 8(2) = {17/26}
c) Killer pair (27) in 19(3) + 8(2) locked -> 18(4) = 45{18/36}

7. N7
a) Innies+Outies: 9 = R6C13 - R8C3; R6C13 <= 17 -> R8C3 <> 9
b) 9 locked in 10(2) for C3 -> 10(2) = {19} locked for C3
c) Innies+Outies: 9 = R6C13 - R8C3; R8C3 >= 2 -> R6C13 >= 11
-> R6C13 <> 1
d) R6C3 = 9, R7C3 = 1
e) Hidden Single: R4C8 = 9 @ R4
f) Outies C12 <> 8

8. R6789
a) Innies R6789 = 10(2): R6C29 = {28/37/46} -> no 1
b) 8(2) @ C4: R6C4 <> 7
c) 8(2) @ C5: R6C5 <> 7
d) 7(2): R6C6 <> 6
e) 11(2): R7C7 <> 2

9. N5
a) Hidden triple (789) in R4C5+R5C4+R5C6 -> no other candidates
b) 14(2) = [59/68]
c) 13(2) = [76/94]

10. C123
a) 11(2) <> {56} because R5C3 = (56)
b) Innies = 15(3) <> 3 because:
- <> {348} since R5C3 = (56)
- <> {357} is blocked by Killer pair (37) of 11(2)

11. C789
a) Innies = 10(3) = 1{36/45} -> no 2 since R5C7 = (46)
b) 2 locked in R46C7 for N6
c) Consider positions of 2 in N6:
- Either 9(2) = [72] -> 11(2) <> {47}
- Or 11(2) = [29] -> 11(2) <> {47}
-> 11(2) <> {47}

12. N1
a) Innies+Outies: 3 = R4C23 - R1C3; R4C23 = 4/5/6/7/8/9/10; R1C3 = (245678)
-> R4C23 = 5/6/7/8/9/10
-> R1C3 <> 8

13. N69 !
a) ! Innies = 12(1+3) = R9C7 + R45C7+R4C9
= 1+{146/236/245} 3+{126/234} 5+{124} -> other combos impossible since R5C7 = (46)
-> R4C9 <> 4,6 since R4C79+R5C7 would be at least 12
-> R4C7 <> 5 since Innies would be 1+{245} and R4C9 <> 2,4
-> R4C7 <> 3 since Innies would be 1+{236} and R4C9 <> 2,6
b) 9(2) = [36/54/72]
c) 4 locked in R45C7 for N6
d) 24(4) = 9{168/357}: R6C9 <> 8 because R5C89 <> 6
e) Innies R6789 = 10(2) = [37/46/73]

14. R456
a) Killer pair (58) of 14(2) + 24(4) in R5C89 locked
b) 18(4) = {1278} locked for N4 -> R4C1 = 8, R6C2 = 7
c) R4C5 = 7, R5C5 = 3, R5C6 = 9, R5C7 = 4, R5C4 = 8, R5C3 = 6
d) 24(4) = {3579} locked for N6 -> R6C9 = 3
e) R4C9 = 1

15. C789
a) 9(2) = [36/72]
b) Innies 10(3) = {145} locked
c) 11(2) = [29/83]

16. R67
a) 8(2) @ C4: R7C4 <> 5
b) 8(2) @ C5 = {26} locked for C5
c) 7(2): R7C6 <> 4

17. C1234
a) Innies C123 = 15(3) = 6{27/45} -> R8C3 <> 8
b) Hidden Single: R3C3 = 8 @ C3
c) R4C3 = 3

18. R6
a) Naked triple (268) in R6C278 locked
b) 8(2) @ C4 = [17/53]

19. N8
a) 17(4) = 15{38/47} -> other combos blocked by R7C4 = (37) and R7C5 = (26)
and it must have 1 or 5 since R9C7 = (15)
-> 1,5 locked -> R9C45 <> 1,5
b) 9 locked in 22(4) = 9{148/238/247/346} -> it must have 4 or 8 since R9C5 = (48)
-> no 5

20. N7
a) Innies+Outies: R6C1 = R8C3 = 4

21. After clean-up and singles:
-> 16(4) @ N1 <> {1357} since R3C12 <> 3,7
-> R2C1 <> 7
-> Hidden Single: R2C3 = 7 @ N1
-> 21(4) @ N7 = {2379} -> R9C3 = 2, R9C1 = 7, R9C2 = 3
-> 21(4) @ N1 = {2379}

22. Rest is singles.

I got a bit lazy in the end because there were lots of singles but it still wasn't finished after that.
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