Assassin 41

[sudokuEd]

Finally managed to finish this thing. Had to redo Richard's step 73 - but ultimately that led to some momentum. So, thanks Richard for showing the door.

Worryingly, the first placement comes on step 87 - a bad luck number here . Hope there is no mess up this time.

Thanks to everyone for helping with this one Don't think there is any need for a condensed walk-through - pretty much every move was needed.

Think there is a mistake in Richards 73. This is the way the outies of n1 look to me.

75. from step 64, r12c4 = [17/29] -> r1234c4 = [1748/2957/2967]. Here's how.
75a.[17] -> r12c5 = [56] -> r3c4 = 4 (single n2) -> r1234c4 = [1748]
75b. [294]-> r12c5 = [56] -> r3c5 = 2: two 2's n2
75c. [2957] OK
75d. [2958] clashes with 11(2)r56c4
75e. [2967] OK
75f. [2968] clash with 11(2)r56c4

76. "45"n1 -> 8 outies = 46
76a. r1234c4 = [1748] = 20 -> r45c1 = [38] = 11 -> r4c23 = 15 = {69}
76b. r1234c4 = [2957] = 23 -> r45c1 = [81] = 9 ({38} = 11 blocked by r4c23 = 12 = {39}) -> r4c23 = 14 = {59} only. But this means [57] and {59} in the same 28(5) cage - two 5's.
76c. r1234c4 = [2967] = 24 -> r45c1 = {38} = 11 -> r4c23 = 11 = {29}
.....r1234c4 = [2967] = 24 -> r45c1 = [81] = 9 -> r4c23 = 13 = {49}

77. In summary
77a. r1234c4 = [1748/2967] (no 5 r3c4)
77b. 5 in n2 only in r1:Locked for r1
77c. no 6 r2c1
77d. {46} naked pair n2:Locked for n2
77e. no 8 r1c78
77f. r4c23 = {69/29/49}(no 3,5)
77g. 28(5) = {14689/24679}

78. no 5 r7c5 or r4c6 since no 5 r123c4 (same logic as step 34)

79. from 65c. r3c123 = {156/249} = [4/6]
79a. Killer pair {46} in r3c1234: locked for r3

80. 20(3)c6 the {569} combo, 6 only in r7c5 -> no 6 r56c5

81. 5 in r4 only in n6:Locked for n6

82. 19(4)n36: combinations with 5 are {1459/2359/3457}
82a. {1459/2359} 5 can only be in r3c89
82b. {3457} must have [47] in r45c9
82c. no 5 r4c9

83. 5 in r4 only in 22(5) at r3c6
83a. no 5 r3c7

84. 19(4) at r3c8 = {1279/1378/1459/2359/2368/3457} ({1468/2467} blocked by {46} only in r4c9)
cannot have {13/23} in r4c89 because of r2c78
84a.-> r45c9 = [29/37/49/29/62/47] (no 8 r4c9)
84b. -> min r45c9 = [62] = 8

85a. min r45c9 = 8, min r12c4 = [51] = 6 -> min 4 outies = 14
85b. min r3c7 = 3 (no 1)

86. 22(5) at r3c6 must have 5 = {12568/13459/13567} ({23458} blocked by r4c6)
86a. -> must have 1
86b. -> 1 locked for c6

87. YEAH! r2c6 = 3
87a. r2c78 = {12}:Locked for n3

88. 22(5) at r3c6 = {12568/13459/13567}
88a. -> r4c78 = {2/3/4[5}} (no 6,8)

89. 19(4) at r3c8 = {2359/2368/3457}
89a. "45" n3 -> r1c6 + 10 = r3c789 = 15/18
89b. addition combo's from {3578} -> r3c789 = {357/378}
89c.r3c89 must have two of from the combinations {357/378}
89d. -> r3c89 + r45c9 = {35}[29/47]/{38}[62]
89e. r3c89 = 3{5/8}(no 7)
89f. r3c7 = 7 (single n3)
89g. no 3 r4c9

90. 22(5) now 15(4) = 13{29/56}(no 4)
90a. 3 locked for n6, r4

91. r4c1 = 8, r4c456 = [716] then 13 singles

92. r89c5 = {23} Locked for c5, n8

93. r4c78 = {35}pair for r4,n6

94. {35} pair in r34c8: Locked for c8

95. r5c9 = {79}

96. 26(5) at r5c2 must have {8/9}, -> r7c3 = {89}

97. 1 in r8 only in 16(3) = 1{69/78}
97a. -> r8c4 = 1
97b. r8c23 = {69/78} = [7/9]
97c. Killer pair {79} with r9c1: Locked for n7
97d. r7c3 = 8
97e. r8c23 = {69}:locked for n7, r8
97f. 20(3) r8 = {578}: r8c7 = 5

the rest is straightforward. Now to Para's Killer-X.

[Andrew]

Congratulations to PsyMar, Ed, Richard and Para on solving what was clearly an extremely difficult puzzle. Names have been listed in the order in which they first made contributions to the solution.

That must be the most subtle v2 that Ed has produced. Just transferring one cell to a different cage took out the hidden single in R9.

I haven't yet looked at the v2 solution thread. Can I ask all four of you to convert your contributions to normal text? I doubt there's anyone out there still trying to solve it by themselves so there's no need for it to still be in tiny text.

[Andrew]

I've been working on the original version of Assassin 41 while PsyMar, Ed, Richard and Para have been solving v2. I kept making silly mistakes, "seeing" hidden singles and locked numbers which weren't valid and having to start again.

Nice walkthroughs from PsyMar and Para! Here is my walkthrough which takes a solving route fairly similar to that used by PsyMar but I think is sufficiently different to be worth posting as well. I hope I've got rid of all my errors.

Clean-up is used in various steps, using the combinations in steps 1 and 5 for further eliminations from these two cell cages; it is also used for the two cell sub-cages that are produced by applying the 45 rule.

1. R12C1 = {29/38/47/56}, no 1

2. R12C9 = {59/68}

3. R89C1 = {29/38/47/56}, no 1

4. R89C5 = {14/23}

5. R89C9 = {16/25/34}, no 7,8,9

6. R1C234 = {123}, locked for R1, clean-up: no 8,9 in R2C1

7. R2C234 = {789}, locked for R2, clean-up: no 4 in R1C1, no 5,6 in R1C9

8. R2C678 = {123}, locked for R2, clean-up: no 8,9 in R1C1

9. R9C234 = 1{25/34}, 1 locked for R9, clean-up: no 4 in R8C5, no 6 in R8C9

10. R9C678 = {689}, locked for R9, clean-up: no 2,3,5 in R8C1, no 1 in R8C9

11. 20(3) cage in R8, no 1,2

12. R9C1 = 7 (hidden single in R9), R8C1 = 4, clean-up: no 3 in R9C1

13. R12C1 = {56}, locked for C1 and N1
[At this stage I should have seen the hidden single in R2C5 but I completely missed it and only knew about it when I worked through PsyMar’s and Para’s walkthroughs. In this case it didn’t make much difference, for example I still got R89C5 in the next step.]

13. 45 rule on R9 2 remaining innies R9C59 = 7 = [25/34], clean-up: no 1 in R8C5, no 5 in R8C9
13a. {23} locked in R8C59 for R8
13b. {23} locked in R89C5 for C5 and N8

14. 1 in R8 locked in 16(3) cage = 1{69/78}, no 5, no 8 in R8C4
14a. 20(3) cage in R8 = 5{69/78}

15. R1C234, R8C234 and R9C234 must all have 1, no other 1 in C234
[This is a Swordfish, which is a 3 row, 3 column X-Wing]

16. 45 rule on R1 3 innies R1C159 = 21 = {579/678} -> R1C5 = 7
16a. R1C678 = 4{59/68}

17. 45 rule on R1234 2 outies R5C19 = 10, R5C1 = {12389} -> R5C9 = {12789}

18. 45 rule on C1234 2 innies R56C4 = 11 = {29/38/47/56}

19. 45 rule on C6789 2 innies R56C6 = 6 = {15/24}

20. 45 rule on C5 3 innies R567C5 = 20 = {569} (only valid combination), locked for C5 and 37(7) cage -> R2C5 = 4, clean-up: no 2 in R56C4, no 1 in R56C6
20a. R56C6 = {24}, locked for C6 and N5, clean-up: no 7 in R56C4
20b. R56C4 = {38}, locked for C4 and N5 -> R4C5 = 1, R3C5 = 8, R2C4 = 9
20c. R2C23 = {78}, locked for N1

21. 3 in R1 locked in R1C23, locked for N1

22. 4 in R1 locked in R1C78, locked for N3

23. 7 in N5 locked in R4C46, locked for R4

24. 45 rule on C9 3 outies R367C8 = 11 = {128/137/146/236/245}, no 9

25. 2 in R2 locked in R2C78, locked for N3

26. 9 in N1 locked in R3C123, locked for R3

27. 1 in N9 locked in R7C789, locked for R7

28. 1 in N8 locked in R89C4, locked for C4 -> R1C4 = 2, R1C23 = {13}, locked for N1

29. R1C16 = {56}, locked for R1

30. R1C6 + R3C4 = {56}, locked for N2

Deceiving Killer. Just when it seems to flow smoothly, it comes to a grinding halt. That's where you need to shift gears and open another bag of tricks.

True. It does flow smoothly up until now. Then I had to start working on some of the combinations.

31. 22(4) cage in N14 = {1489/2389} = 89{14/23}, 8 locked in R45C1 for C1 and N4, no 2,9 in R45C1, 9 locked in R3C12 for N1, clean-up: no 1,8 in R5C9

32. 28(5) cage in N1245 = {24679/34579} = 479{26/35} -> R4C4 = 7, 9 locked in R4C23 for R4 and N4, no 5,6 in R4C23
[At this stage PsyMar and Para both had nice eliminations from R56C3 which I missed]

33. 9 in N5 locked in R56C5, locked for C5

34. R14C6 = {56}, locked for C6

35. 5 in R8 locked in R8C78, locked for N9 -> R9C9 = 4 (naked single), R8C9 = 3, R89C5 = [23]

36. 6 in R9 locked in R9C78, locked for N9

37. 20(3) cage in R8 = {578}, locked for R8 -> 16(3) cage in R8 = {169}
37a. 9 in R8 locked in R8C23, locked for N7

38. 26(5) cage in N478 = {23678/24578/34568} = 8{2367/2457/3456} -> R7C3 = 8 -> R2C23 = [87]
38a. From combinations for 26(5) cage, no 2 in R5C2

39. 22(5) cage in N2356 must have {13} in R3C6 and {56} in R4C6, valid combinations are {12568/13468/13567/23467} (cannot be {23458} because 2,4,8 only in two cells)

40. 17(4) cage in N47 = {1367/2357} (cannot be {1259/1349} because 1,9 only in one cell, cannot be {1457} which doesn’t have 2/3, cannot be {2456} because no 4,5,6 in R67C1) = 37{16/25}, no 9, R6C2 = 7, no 2,3 in R7C2

41. R3C1 = 9 (hidden single in C1)

42. R7C25 = {56}, locked for R7 -> R7C4 = 4

43. R7C1 = 3 (hidden single in N7), R4C1 = 8, R5C1 = 1, R3C2 = 4, R3C3 = 2, R6C1 = 2, R7C2 = 5, R7C5 = 6, R56C6 = [24] (naked singles), R4C6 = 6 (hidden single in N5), R1C6 = 5, R1C1 = 6, R2C1 = 5, R2C9 = 6, R1C9 = 8, R9C2 = 2 (hidden single in C2), R4C3 = 4 (hidden single in C3), R4C2 = 9 (hidden single in R4) -> R3C4 = 6, R8C4 = 1, R8C2 = 6, R8C3 = 9, R5C2 = 3, R1C23 = [13], R56C4 = [83], R9C34 = [15]

44. R5C9 = 9 (step 17) -> R56C5 = [59], R56C3 = [65]

45. R6C9 = 1 (naked single), R7C89 = {27}, locked for R7 and N9 -> R7C67 = [91]

and the rest is naked and hidden singles, simple elimination and cage sums