A few more.
86. 24(5) in R1C7 needs one of {459} in R2C6: no {12678}
86a. 24(5): no 2
87. Combining 45-test N3, step 70 and cage combinations 24(5) in R1C7 and 26(4) in R2C8
87a. R2C6 = 4 --> R4C9 = 9: 8 locked in N1 in 26(4): so 24(5) = {13479} : R3C9: no 7.
87b. R2C6 = 9 -->> 24(5) = {13479}: R3C9: no 7
87c. R2C6 = 5 -->> R4C9 = 8 -->> R3C9 = 9(step 71) : R3C9: no 7.
87d. R3C9: no 7
87e. Clean up: R9C8: no 7(step 70)
Para
Assassin 42
Our day away from home has turned out to be longer than expected but I've managed to get access to the forum from one of our daughters' computer.
Good to see that Ed, Para and Richard are continuing to make progress. I hope there will be something for me to work on after I've caught up with your new steps.
Since Assassin 43 is now out, I've converted my steps to normal text and also my v1 walkthrough.
Good to see that Ed, Para and Richard are continuing to make progress. I hope there will be something for me to work on after I've caught up with your new steps.
Since Assassin 43 is now out, I've converted my steps to normal text and also my v1 walkthrough.
-
rcbroughton
- Expert
- Posts: 143
- Joined: Wed Nov 15, 2006 1:45 pm
- Location: London
Wow - Para's been busy!!
Let's notch up the 90 . . .
89. 45 on n6. innies total 30.
89a. can't use any combo with {67} or {26} because of the 9(2)
89b. only combo with a 5 is {15789} - musdt use the 1 at r4c8 - no 5 at r4c8
90. 45 on c8 r1234789c8 total 36 (I know it's a big number but don't panic)!!
90a. can't use 2&3 because of the 9(2)c8
90b. can't use 2&3, 2&5 or 5&6 in r123c8 because of the8(2)n3
90c. only 2 possibilities {1245789} and {1345689}
90d. {1345689} - r23c8 can only be {45} or{58} - so from 90b - r1c8 can't be 6
Richard
Let's notch up the 90 . . .
89. 45 on n6. innies total 30.
89a. can't use any combo with {67} or {26} because of the 9(2)
89b. only combo with a 5 is {15789} - musdt use the 1 at r4c8 - no 5 at r4c8
90. 45 on c8 r1234789c8 total 36 (I know it's a big number but don't panic)!!
90a. can't use 2&3 because of the 9(2)c8
90b. can't use 2&3, 2&5 or 5&6 in r123c8 because of the8(2)n3
90c. only 2 possibilities {1245789} and {1345689}
90d. {1345689} - r23c8 can only be {45} or{58} - so from 90b - r1c8 can't be 6
Richard
Ok some big eliminations and digit number 2.
92. R4C789 = {489/469/468}: can't be {159}
92a. R6C6 = 3 -->> R4C789 = [519] -->> R2C6 = 4 --> R34C6 = [29]: contradiction: 2 9's in R4.
92b. R4C789: no 1,5
92c. 4 locked in R4C789 for R4 and N6
92d. R56C9 = {15} locked for C9
92e. Clean up: R2C4: no 3; R6C4: no 4.
92f. 4 locked in N4 for C3
93. R12C9 = {26} locked for C9 and N3
93a. 22(4) in R7C9 = {3478}: locked for N9
93b. 26(4) in R2C8 = {4589}: 5 locked in R23C8 for C8 and N3
93d. 5 locked in R4 for N5
94. 22(4) in R5C4 = {3469/3478}: 3 (and 4) locked for N5
95. 10(3) in R7C6 needs 3 or 4. Only place id R7C6: R7C6 ={34}
95a. R9C6 = {34} (45 on N9)
95b. {34} locked for N8 and C6 in R79C6
95c. Clean up: R4C9: no 9.
95d. R3C9 = 9 (hidden single in C9)
95e. Naked Pair {34} in R7C69 locked for R7
Para
92. R4C789 = {489/469/468}: can't be {159}
92a. R6C6 = 3 -->> R4C789 = [519] -->> R2C6 = 4 --> R34C6 = [29]: contradiction: 2 9's in R4.
92b. R4C789: no 1,5
92c. 4 locked in R4C789 for R4 and N6
92d. R56C9 = {15} locked for C9
92e. Clean up: R2C4: no 3; R6C4: no 4.
92f. 4 locked in N4 for C3
93. R12C9 = {26} locked for C9 and N3
93a. 22(4) in R7C9 = {3478}: locked for N9
93b. 26(4) in R2C8 = {4589}: 5 locked in R23C8 for C8 and N3
93d. 5 locked in R4 for N5
94. 22(4) in R5C4 = {3469/3478}: 3 (and 4) locked for N5
95. 10(3) in R7C6 needs 3 or 4. Only place id R7C6: R7C6 ={34}
95a. R9C6 = {34} (45 on N9)
95b. {34} locked for N8 and C6 in R79C6
95c. Clean up: R4C9: no 9.
95d. R3C9 = 9 (hidden single in C9)
95e. Naked Pair {34} in R7C69 locked for R7
Para
Ok the puzzle broke open, and ran to the end. So here are the remaining 79 digits.
96. Hidden Pair {12} in R34C6
96a. 17(4) = {1268}: R4C78 = [86]; R4C9 = 4
96b. R2C6 = 9; R7C9 = 3; R7C6 = 4; R9C6 = 3
96c. R9C8 = 4; R8C1 = 4 (both hidden)
96d. R12C1 = [96]; R2C4 = 4; R4C1 = 3(45 on N1)
96e. R12C9 = [62]
97. Naked Pair {27} in R4C23: locked for R4, N4 and 20(4) in R3C4
97a. R4C4 = 5; R4C6 = 1; R3C6 = 1; R6C4 = 2; R4C5 = 9
97b. R56C8 = [27](only possible combination)
97c. R6C6 = 6; R7C8 = 1; R8C8 = 9; R7C7 = 5; R1C8 = 3
97d. R56C2 = [69]; R56C7 = [93]
97e. R7C1 = 2; R7C5 = 6
98. 14(4) in R7C1 = 24{17}: {17} locked in R9C12 for N7 and R9
98a. R7C34 = [97]; R9C4 = 9; R89C9 = [78]
98b. Hidden singles: R8C2 = 3; R3C2 = 4; R1C7 = 4; R2C2 = 5
98c. R3C1 = 1; R9C12 = [71]; R23C7 = [17]; R23C8 = [85]
98d. R3C4 = 6(hidden)
99. 20(3) in R2C5 = [389](only possible combination)
99a. R23C3 = [73]; R1C23 = [28]; R4C23 =[71]
99b. R1C4 = 1; R6C5 = 4; R5C456 = [378]
99c. R56C1 = [58]; R56C3 = [41]; R56C9 = [15]
99d. R1C56 = [57]; R9C5 = 2; R8C456 = [815]; R89C2 = [65]; R89C7 = [26]
Those were the last digits.
Para
96. Hidden Pair {12} in R34C6
96a. 17(4) = {1268}: R4C78 = [86]; R4C9 = 4
96b. R2C6 = 9; R7C9 = 3; R7C6 = 4; R9C6 = 3
96c. R9C8 = 4; R8C1 = 4 (both hidden)
96d. R12C1 = [96]; R2C4 = 4; R4C1 = 3(45 on N1)
96e. R12C9 = [62]
97. Naked Pair {27} in R4C23: locked for R4, N4 and 20(4) in R3C4
97a. R4C4 = 5; R4C6 = 1; R3C6 = 1; R6C4 = 2; R4C5 = 9
97b. R56C8 = [27](only possible combination)
97c. R6C6 = 6; R7C8 = 1; R8C8 = 9; R7C7 = 5; R1C8 = 3
97d. R56C2 = [69]; R56C7 = [93]
97e. R7C1 = 2; R7C5 = 6
98. 14(4) in R7C1 = 24{17}: {17} locked in R9C12 for N7 and R9
98a. R7C34 = [97]; R9C4 = 9; R89C9 = [78]
98b. Hidden singles: R8C2 = 3; R3C2 = 4; R1C7 = 4; R2C2 = 5
98c. R3C1 = 1; R9C12 = [71]; R23C7 = [17]; R23C8 = [85]
98d. R3C4 = 6(hidden)
99. 20(3) in R2C5 = [389](only possible combination)
99a. R23C3 = [73]; R1C23 = [28]; R4C23 =[71]
99b. R1C4 = 1; R6C5 = 4; R5C456 = [378]
99c. R56C1 = [58]; R56C3 = [41]; R56C9 = [15]
99d. R1C56 = [57]; R9C5 = 2; R8C456 = [815]; R89C2 = [65]; R89C7 = [26]
Those were the last digits.
Para
Great finish Para and Richard. Wow - ended up a real tough challenge. Really enjoyed the team-work too. And of course, a very big thankyou Ruud!
Andrew found a mistake in step 61e which affected many steps. So, here is a condensed/simplified walk-through which gets around that bump. Tried to only include the essential steps. Many steps have been combined or re-ordered to keep things clear. Please let me know if this can be improved.
Condensed/simplified Walk-through for Assassin 42V2
1. R12C1 = {69/78}
2. R12C9 = {17/26/35}, no 4,8,9
3. R56C1 = {49/58} (cannot be {67} which would clash with R12C1)
3a. Killer pair 8/9 in R1256C1 for C1
4. R56C2 = {69/78}
4a. Killer pair 8/9 in R56C12 for N4
5. R56C8 = {18/27/36/45}, no 9
6. R56C9 = {15/24}
7. 20(3) cage in R234C5 = {389/479/569/578}, no 1,2
8. 7(3) cage in N45 = {124}
9. 24(3) cage in R7C234 = {789}, locked for R7
10. 13(4) cage in N14 = {1237/1246/1345}, no 8,9
11. 26(4) cage in N36, no 1
12. 14(4) cage in N7, no 9
13. 45 rule on N7 2 outies R79C4 = 16 = {79}, locked for C4 and N8
14. 8 in R7 locked in R7C23, locked for N7
15. 45 rule on N9 2 outies R79C6 = 7 = {16/25/34}
16. 3 in N4 locked in R4C123, locked for R4
17. 45 rule on N1 2 outies R2C4 + R4C1 = 7 = {16/25/34}
18. 45 rule on N3 2 outies R2C6 + R4C9 = 13 = {49/58/67}
19. 45 rule on C6789 3 innies R158C6 = 20, no 1,2
27. Now need some hypotheticals to make progress
27a. "45" n4 -> r6c4 + 10 = r4c123 = 11, 12 or 14 and must have 3
27b. r6c4 = 1 -> r4c123 = 11 = {137} ({236} blocked by 2 in r56c3)
27c. r6c4 = 2 -> r4c123 = 12 = {237} ({345} blocked by 4 in r56c3)
27d. r6c4 = 4 -> r4c123 = 14 = {347}
27e. r6c4 = 4 -> r4c123 = 14 = {356}
28. However, r4c123 = 14 = {356} is blocked. Here's how.
28a. 20(4)n2 now = {1478/1568/2378/2468/2567/3458/3467}
28b. "45" n1 -> 2 outies = 7.
28c. Since r6c4 = 4 (step 27e) in this hypothetical -> r4c1 != 3
28c. -> r4c23 = 3{5/6}
28d. the only combo's in 20(4) that allow 3{5/6} are {3458/3467} with {48/47} in r34c4
28e. but this means 2 4's in c4
28f. -> r4c123 cannot be {356}
29. r4c123 = {137/237/347} = 37{1/2/4}(no 5 or 6)
29a. no 12 r2c4
30. 7 Locked in r4c23 for n4, r4 and must be in 20(4)n2 = 7{148/238/256/346}
30a. no 6 r2c6 (step 18)
31. 13(2)n4 = {58}(hidden 5 n4): Locked n4, c1
32. 15(2)n1 and n4 = {69}:locked for c12, n14
33. 14(4)n7 = {1247/2345} = 24{17/35}: 2 and 4 locked n7
33a. 5 only in r9c2 -> no 3 r9c2
33b. 23(4)n7 = {1679/3569} = 69{17/35}
35. 13(4)n1 = {1237/1345} = 13{27/45}
36a. 13(4) must have both 1 and 3, only 1 of which can 'hide' in r4c1 -> {13578} blocked from 24(5) (note: 3 can't hide in r2c4 when 1 in r4c1 since 2 outies n1 = 7)
25b. 24(5)n1 must have 8 for n1 -> {24567} combo not possible
36aa. 24(5)n1 now = {12678/14568/23478/23568}
36b. 24(5), only combo's with 5 also have 6 {14568/23568} which is only in r2c4 -> no 5 r2c4
36c. no 2 r4c1
37. Any 6 in the 24(5) cage in N12 must be in R2C4. If R2C4 = 6, R4C1 = 1 (step 17) -> 1 in N1 must be in 24(5) cage
37a. No {23568} in 24(5) cage
38-39. [note: modified these steps for simplicity] Remembering 2 outies n1 = 7, r4c123 must have 3 and 7, r4c123 - 10 = r6c4
39a. R2C4 = 3 -> R4C1 = 4 -> R4C23 = {37} and r6c4 = 4
->20(4) = {2378} ({3467} clashes with R6C4)
39b. R2C4 = 4 -> R4C1 = 3, R4C23 = {17} Blocked:
since 20(4) = {1478} but this clashes with R2C4
39c. R2C4 = 4 -> R4C1 = 3, R4C23 = {27} and r6c4 = 2
-> 20(4) = 7{238/256}
39d. R2C4 = 4 -> R4C1 = 3 and R4C23 = {47} -> r6c4 = 4 Blocked: 2 4's c4
39e. R2C4 = 6 -> R4C1 = 1 -> R4C23 = {37} and r6c4 = 1
-> 20(4) = {2378} ({3467} clashes with R2C4)
40. To summarise
40b. 20(4) cage in N254 = 7{238/256} = 27{38/56}, no 1,4
41. To continue further and look at the effect of these hypotheticals on the 24(5) cage in N12
41a. R2C4 = 3, R6C4 = 4, R56C3 = {12}, 24(5) cage = {23478} -> R1C2 = 2, R123C3 = {478}
41b. R2C4 = 4, R6C4 = 2, R56C3 = {14}, 24(5) cage = {23478} -> R1C2 = {237}, R123C3 = 8{2/3/7} (because r4c3 = {237} -> 1 of 2,3 or 7 have to be in r1c2 and 8 in c3)
41c. R2C4 = 6, R6C4 = 1, R56C3 = {24}, 24(5) cage = {12678} -> R1C2 = 2, R123C3 = {178}
41d. R2C4 = 6, R6C4 = 1, R56C3 = {24}, 24(5) cage = {14568} -> R1C2 = 4, R123C3 = {158}
41e. In summary, combining all these hypotheticals, R1C2 = {2347}, no 1,5,8
42. r7c2 = 8 (hidden single c2)
Moving now to n56
44. 9(2) in R5C8 can't be {45} because of 6(2) in R5C9.
24. 1 locked for r6 in r6c349. Here's how.
24a. r6c34 = {24} -> r6c9 = 1 ([15] in r56c9 blocked by 1 in r5c3)
24b. only other options for r6c34 = {12/14} include 1
24c. -> 1 locked for r6
24d. no 8 r5c8
23. 26(4) n3 = 9{278/368/458/467} ({5678} blocked by 8(2)n3)
49. 45 on n5 - 5 innies total 23. no placement with 4 or 8 at r6c6
49a. {12479} - 7 must be at r6c6
49b. {14567} - 7 must be at r6c6
49c. {23459} - 3 must be at r6c6
49d. {23468} - ditto
49e. {13469} - ditto
49f. {12569} - no 4 or 8
49g. {12578} - 7 must be at r6c6
49h. {13568} - 3 must be at r6c6
49i. {12389} - ditto
50-61! "45" on N6. R4C789 - R6C6 = 12
a. R6C6 = 9 -->> R4C789 = 21 = {489}
...................................-> r56c7 = {27/36} and 9(2)n6 cannot be [18]
b. R6C6 = 7 -->> R4C789 = 19 = {289} Blocked
................................... :R56C9 = {15}, R56C8 = {36}, R56C7 = {47} but 18(3) cage cannot be {477} -> R4C789 cannot be {289}
c. R6C6 = 7 -->> R4C789 = 19 = {469}
...................................-> r56c7 = {38} and 6(2) = {15}-> 9(2)n6 cannot be [18]
d. R6C6 = 7 -->> R4C789 = 19 = {568} Blocked
................................... 9(2) = {27} and 6(2) = {24} cage in N6: 2 2's n6: R4C789 cannot be {568}
e. R6C6 = 6 -->> R4C789 = 18 = {189/459}Blocked
....................................: since r6c6 = 6 -> r5c2 = 6 -> 6 for n6 must be in r4-> R4C789 cannot be {189/459}
f. R6C6 = 6 -->> R4C789 = 18 = {468}
...................................-> r56c7 = {39/57} and 9(2)n6 cannot be [18]
h. r6c6 = 5 -->> r4c789 = 17 = {269} Blocked
...................................: 9(2) = {18} and 6(2) = {15}: 2 1's n6: R4C789 cannot be {269}
i. r6c6 = 5 -->> r4c789 = 17 = {458}Blocked
...................................: 6(2) Blocked: R4C789 cannot be {458}
j. R6C6 = 3 -->> R4C789 = 15 = {159}
................................... -> r56c7 = {78} and 9(2)n6 cannot be [18]
k. R6C6 = 3 -->> R4C789 = 15 = {168} Blocked
...................................: clashes with 6(2) and 9(2) cage in N6: R4C789 cannot be {168}
l. R6C6 = 3 -->> R4C789 = 15 = {249}
...................................-> r56c7 = {78} and 9(2)n6 cannot be [18]
m. R6C6 = 3 -->> R4C789 = 15 = {258} Blocked
...................................: clash with 6(2)
n. R6C6 = 3 -->> R4C789 = 15 = {456} Blocked
...................................: clashes with 6(2) cage in N6 : R4C789 cannot be {456}
o. R6C6 = 2 -->> R4C789 = 14 = {149} Blocked
...................................: clashes with 6(2) cage in N6 : R4C789 cannot be {149}
p. R6C6 = 2 -->> R4C789 = 14 = {158} Blocked
...................................: 4 remaining innies n5 can only be {1569} (step 49f) -> 2 5's r4 : r4c789 cannot be {158}
q. R6C6 = 2 -->> R4C789 = 14 = {248} Blocked
...................................4 remaining innies n5 can only be {1569} (step 49f) but r4c23 = {37} requires [2/8] in r4c4:r4c789 cannot be {248}
In summary
r. 18(3) in R5C7 = {279/369/378/567}: no 1, 4
s. 9(2) in N6: no [18]
t. r4c789 = {489/469/468/159/249} = [4/5..]
u. no 2 r6c6
67. killer pair 4/5 in R4C789 and R56C9 for N6, no 5 in r56c7
Now moving to c9
22. 8(2)c9 = {17/26/35}
22a. 6(2)c9 = {15/24}
22b. -> 2 locked for c9 in these 2 cages
20. 45 rule on C9: 2 innies R34C9 – 9 = 1 outie R9C8, max R34C9 = 17 -> max R9C8 = 8
56a. R9C8 = 1 -->> R34C9 = 10 = {46} Blocked
....................................: -> R56C9 = {15}: {46/15}c9 Clash with 8(2)n3
65b. r9c8 = 2 -> r34c9 = 11 = {38} Blocked
....................................: r239c8 = {69}[2] -> 9(2)n6 Clash
65c. r9c8 = 2 -> r34c9 = 11 = {47} Blocked
....................................: r239c8 = {69}[2] -> 9(2)n6 Clash
69a. R9C8 = 3 -->> R34C9 = 12 = {39} Blocked
....................................: R23C8 = {68} -->> R56C8 = {27} -->> R56C9 = {15}: {68/15}No options left for 8(2) in N1
69b. R9C8 = 3 -->> R34C9 = 12 = {48} Blocked
....................................: clashes with 22(4) in N9 since all combo's with 3 in r9c8 have 4/8 also in c9. r789c9 = {469/478/568}
69c. R9C8 = 4 -->> R34C9 = 13 = {49}
69d. R9C8 = 4 -->> R34C9 = 13 = {58} Blocked
....................................: -> R23C8 must be {49} but 2 4's in C8
69e. R9C8 = 4 -->> R34C9 = 13 = {67} Blocked
....................................: -> R23C8 must be {49} but 2 4's in C8
69f. R9C8 = 5 -->> R34C9 = 14 = {59}
69g. R9C8 = 5 -->> R34C9 = 14 = {68} Blocked
....................................: -> R23C8 = {39} -->> R56C8 = {27} -->> R56C9 = {15} -->> {68/15} no options left for 8(2)N1.
69h. R9C8 = 6 -->> R34C9 = 15 = {69}
69i. R9C8 = 6 -->> R34C9 = 15 = [78] Blocked
....................................: -> R239C8 = {29}[6] -> clash with 9(2) N6
69j. R9C8 = 7 -->> R34C9 = 16 = {79}
69k. R9C8 = 8 -->> R34C9 = 17 = {89}
In summary
69l. 9 locked in r34C9 for C9 and 26(4)
69m. no 1,2,3 r9c8
69n. r34c9 = {49/59/69/79/89}
71a. no 3 in R3C9
71b. 22(4) in R7C9: no {4567}: Here's how.
71c. 8(2)n3 = [5/6/7] -> 22(4)n9 the {4567} combo must have 4 in r789c9
71d. -> 6(2)r6 = {15} -> r9c8 = 5 -> r34c9 = {59} (step 69f): contradiction 2 5's c9
71e. -> 22(4): no {4567}
71f. 22(4) = {1678/3478/3568} = 8{167/347/356}: 8 locked for N9
71g. "45" on c9: outies r239c8 = 17
71h. ={278}/{368}/{458} = 8{27/36/45} ({467} blocked by 9(2)n6)
71i. 8 locked for c8
71j {4679} blocked from from 26(4)n3: no 2 digits over-lap with c9 outies
73. "45" on n9: 5 innies = 23
73a. can only have {12569/23459} (no 7)
73b. {13469} - blocked by 22(4)n9
73c. {14567} - blocked by 22(4)n9
73d. {23567} - blocked by 22(4)n9
73e. {12479} - blocked because r7c78 can only be {14} -> rest of innies = {279} which must be in 20(3) but this means 2 2's in 20(3)
73f. 7 locked in 22(4) = 78{16/34} (no 5)
73g. no 5 r34c9 (step 69f)
78. (cleanup) "45" n3: outies = 13: no 8 in r2c6
80. 8(2) in R1C9: no {17}. Here's how:
80a. 2 and 5 locked in cages 8(2) + 6(2) in C9.
80b. 6(2) = {15} -->> 8(2) = {26} (needs to use 2)
80c. 6(2) = {24} -->> 8(2) = {35} (needs to use 5)
80d. -> 8(2)n3 no {17}
84. 26(4) in R2C8: no {3689}: clashes with 8(2) in R1C9.
84a. 26(4): no 3 or 6
84b. Clean up: R2C6: no 7
NOW, for the puzzle breaker moves
91. R3C6: no 9
91a. R3C6 = 9 -->> R4C678 = {125} -->> R4C23 = {37} -->> R4C4 = 8 -->> R4C5 = 6: -->> R23C5 = {59}: 2 9's in N2.
91b. -> no 9 r3c6
88. R4C7: no 1, because of 1's in N3.
88a. R123C7 = 1: R4C7: no 1
88b. R1C8 = 1 -->> R3C6 = 1: R4C7: no 1
92a. from step 50j. R6C6 = 3 -->> R4C789 = [519] -->> R2C6 = 4 (outies n3)
--> R34C6 = Blocked ([29] but 2 9's in R4:{38} but 2 3's c6:{47} but 2 4's c6)
92b. (step 50t) R4C789 = {489/469/468/249}(no 1,5)
92c. 4 locked in R4C789 for R4 and N6
92d. Clean up: R2C4: no 3;
92dd. R6C4: no 4 (step 27d)
92de. R56C9 = {15} locked for C9
92f. 4 locked in N4 for C3
93. R12C9 = {26} locked for C9 and N3
93a. 22(4) in R7C9 = {3478}: locked for N9
93b. 26(4) in R2C8 = {4589}: 5 locked in R23C8 for C8 and N3
93d. 5 locked in R4 for N5
95. 10(3) in R7C6 needs 3 or 4. Only place is R7C6: R7C6 ={34}
95a. R9C6 = {34} (45 on N9)
95b. {34} locked for N8 and C6 in R79C6
95c. Clean up: R4C9: no 9.
95d. R3C9 = 9 (hidden single in C9)
95e. Naked Pair {34} in R7C69 locked for R7
96. Hidden Pair c6 {12} in R34C6: Locked for 17(4) cage
96a. 17(4) = {1268}: R4C78 = [86]; R4C9 = 4
96b. R2C6 = 9; R7C9 = 3; R7C6 = 4; R9C6 = 3
96c. R9C8 = 4; R8C1 = 4 (both hidden)
96d. R12C1 = [96]; R2C4 = 4; R4C1 = 3(45 on N1)
96e. R12C9 = [62]
97. Naked Pair {27} in R4C23: locked for R4, N4 and 20(4) in R3C4
97a. R4C4 = 5; R4C6 = 1; R3C6 = 2; R6C4 = 2; R4C5 = 9
97b. R56C8 = [27] (only possible combination)
97c. R6C6 = 6; R7C8 = 1; R8C8 = 9; R7C7 = 5; R1C8 = 3
97d. R56C2 = [69]; R56C7 = [93]
97e. R7C1 = 2; R7C5 = 6
98. 14(4) in R7C1 = 24{17}: {17} locked in R9C12 for N7 and R9
98a. R7C34 = [97]; R9C4 = 9; R89C9 = [78]
98b. Hidden singles: R8C2 = 3; R3C2 = 4; R1C7 = 4; R2C2 = 5
98c. R3C1 = 1; R9C12 = [71]; R23C7 = [17]; R23C8 = [85]
98d. R3C4 = 6(hidden)
99. 20(3) in R2C5 = [389](only possible combination)
99a. R23C3 = [73]; R1C23 = [28]; R4C23 =[72]
99b. R1C4 = 1; R6C5 = 4; R5C456 = [378]
99c. R56C1 = [58]; R56C3 = [41]; R56C9 = [15]
99d. R1C56 = [57]; R9C5 = 2; R8C456 = [815]; R89C2 = [65]; R89C7 = [26]
Andrew found a mistake in step 61e which affected many steps. So, here is a condensed/simplified walk-through which gets around that bump. Tried to only include the essential steps. Many steps have been combined or re-ordered to keep things clear. Please let me know if this can be improved.
Condensed/simplified Walk-through for Assassin 42V2
1. R12C1 = {69/78}
2. R12C9 = {17/26/35}, no 4,8,9
3. R56C1 = {49/58} (cannot be {67} which would clash with R12C1)
3a. Killer pair 8/9 in R1256C1 for C1
4. R56C2 = {69/78}
4a. Killer pair 8/9 in R56C12 for N4
5. R56C8 = {18/27/36/45}, no 9
6. R56C9 = {15/24}
7. 20(3) cage in R234C5 = {389/479/569/578}, no 1,2
8. 7(3) cage in N45 = {124}
9. 24(3) cage in R7C234 = {789}, locked for R7
10. 13(4) cage in N14 = {1237/1246/1345}, no 8,9
11. 26(4) cage in N36, no 1
12. 14(4) cage in N7, no 9
13. 45 rule on N7 2 outies R79C4 = 16 = {79}, locked for C4 and N8
14. 8 in R7 locked in R7C23, locked for N7
15. 45 rule on N9 2 outies R79C6 = 7 = {16/25/34}
16. 3 in N4 locked in R4C123, locked for R4
17. 45 rule on N1 2 outies R2C4 + R4C1 = 7 = {16/25/34}
18. 45 rule on N3 2 outies R2C6 + R4C9 = 13 = {49/58/67}
19. 45 rule on C6789 3 innies R158C6 = 20, no 1,2
27. Now need some hypotheticals to make progress
27a. "45" n4 -> r6c4 + 10 = r4c123 = 11, 12 or 14 and must have 3
27b. r6c4 = 1 -> r4c123 = 11 = {137} ({236} blocked by 2 in r56c3)
27c. r6c4 = 2 -> r4c123 = 12 = {237} ({345} blocked by 4 in r56c3)
27d. r6c4 = 4 -> r4c123 = 14 = {347}
27e. r6c4 = 4 -> r4c123 = 14 = {356}
28. However, r4c123 = 14 = {356} is blocked. Here's how.
28a. 20(4)n2 now = {1478/1568/2378/2468/2567/3458/3467}
28b. "45" n1 -> 2 outies = 7.
28c. Since r6c4 = 4 (step 27e) in this hypothetical -> r4c1 != 3
28c. -> r4c23 = 3{5/6}
28d. the only combo's in 20(4) that allow 3{5/6} are {3458/3467} with {48/47} in r34c4
28e. but this means 2 4's in c4
28f. -> r4c123 cannot be {356}
29. r4c123 = {137/237/347} = 37{1/2/4}(no 5 or 6)
29a. no 12 r2c4
30. 7 Locked in r4c23 for n4, r4 and must be in 20(4)n2 = 7{148/238/256/346}
30a. no 6 r2c6 (step 18)
31. 13(2)n4 = {58}(hidden 5 n4): Locked n4, c1
32. 15(2)n1 and n4 = {69}:locked for c12, n14
33. 14(4)n7 = {1247/2345} = 24{17/35}: 2 and 4 locked n7
33a. 5 only in r9c2 -> no 3 r9c2
33b. 23(4)n7 = {1679/3569} = 69{17/35}
35. 13(4)n1 = {1237/1345} = 13{27/45}
36a. 13(4) must have both 1 and 3, only 1 of which can 'hide' in r4c1 -> {13578} blocked from 24(5) (note: 3 can't hide in r2c4 when 1 in r4c1 since 2 outies n1 = 7)
25b. 24(5)n1 must have 8 for n1 -> {24567} combo not possible
36aa. 24(5)n1 now = {12678/14568/23478/23568}
36b. 24(5), only combo's with 5 also have 6 {14568/23568} which is only in r2c4 -> no 5 r2c4
36c. no 2 r4c1
37. Any 6 in the 24(5) cage in N12 must be in R2C4. If R2C4 = 6, R4C1 = 1 (step 17) -> 1 in N1 must be in 24(5) cage
37a. No {23568} in 24(5) cage
38-39. [note: modified these steps for simplicity] Remembering 2 outies n1 = 7, r4c123 must have 3 and 7, r4c123 - 10 = r6c4
39a. R2C4 = 3 -> R4C1 = 4 -> R4C23 = {37} and r6c4 = 4
->20(4) = {2378} ({3467} clashes with R6C4)
39b. R2C4 = 4 -> R4C1 = 3, R4C23 = {17} Blocked:
since 20(4) = {1478} but this clashes with R2C4
39c. R2C4 = 4 -> R4C1 = 3, R4C23 = {27} and r6c4 = 2
-> 20(4) = 7{238/256}
39d. R2C4 = 4 -> R4C1 = 3 and R4C23 = {47} -> r6c4 = 4 Blocked: 2 4's c4
39e. R2C4 = 6 -> R4C1 = 1 -> R4C23 = {37} and r6c4 = 1
-> 20(4) = {2378} ({3467} clashes with R2C4)
40. To summarise
40b. 20(4) cage in N254 = 7{238/256} = 27{38/56}, no 1,4
41. To continue further and look at the effect of these hypotheticals on the 24(5) cage in N12
41a. R2C4 = 3, R6C4 = 4, R56C3 = {12}, 24(5) cage = {23478} -> R1C2 = 2, R123C3 = {478}
41b. R2C4 = 4, R6C4 = 2, R56C3 = {14}, 24(5) cage = {23478} -> R1C2 = {237}, R123C3 = 8{2/3/7} (because r4c3 = {237} -> 1 of 2,3 or 7 have to be in r1c2 and 8 in c3)
41c. R2C4 = 6, R6C4 = 1, R56C3 = {24}, 24(5) cage = {12678} -> R1C2 = 2, R123C3 = {178}
41d. R2C4 = 6, R6C4 = 1, R56C3 = {24}, 24(5) cage = {14568} -> R1C2 = 4, R123C3 = {158}
41e. In summary, combining all these hypotheticals, R1C2 = {2347}, no 1,5,8
42. r7c2 = 8 (hidden single c2)
Moving now to n56
44. 9(2) in R5C8 can't be {45} because of 6(2) in R5C9.
24. 1 locked for r6 in r6c349. Here's how.
24a. r6c34 = {24} -> r6c9 = 1 ([15] in r56c9 blocked by 1 in r5c3)
24b. only other options for r6c34 = {12/14} include 1
24c. -> 1 locked for r6
24d. no 8 r5c8
23. 26(4) n3 = 9{278/368/458/467} ({5678} blocked by 8(2)n3)
49. 45 on n5 - 5 innies total 23. no placement with 4 or 8 at r6c6
49a. {12479} - 7 must be at r6c6
49b. {14567} - 7 must be at r6c6
49c. {23459} - 3 must be at r6c6
49d. {23468} - ditto
49e. {13469} - ditto
49f. {12569} - no 4 or 8
49g. {12578} - 7 must be at r6c6
49h. {13568} - 3 must be at r6c6
49i. {12389} - ditto
50-61! "45" on N6. R4C789 - R6C6 = 12
a. R6C6 = 9 -->> R4C789 = 21 = {489}
...................................-> r56c7 = {27/36} and 9(2)n6 cannot be [18]
b. R6C6 = 7 -->> R4C789 = 19 = {289} Blocked
................................... :R56C9 = {15}, R56C8 = {36}, R56C7 = {47} but 18(3) cage cannot be {477} -> R4C789 cannot be {289}
c. R6C6 = 7 -->> R4C789 = 19 = {469}
...................................-> r56c7 = {38} and 6(2) = {15}-> 9(2)n6 cannot be [18]
d. R6C6 = 7 -->> R4C789 = 19 = {568} Blocked
................................... 9(2) = {27} and 6(2) = {24} cage in N6: 2 2's n6: R4C789 cannot be {568}
e. R6C6 = 6 -->> R4C789 = 18 = {189/459}Blocked
....................................: since r6c6 = 6 -> r5c2 = 6 -> 6 for n6 must be in r4-> R4C789 cannot be {189/459}
f. R6C6 = 6 -->> R4C789 = 18 = {468}
...................................-> r56c7 = {39/57} and 9(2)n6 cannot be [18]
h. r6c6 = 5 -->> r4c789 = 17 = {269} Blocked
...................................: 9(2) = {18} and 6(2) = {15}: 2 1's n6: R4C789 cannot be {269}
i. r6c6 = 5 -->> r4c789 = 17 = {458}Blocked
...................................: 6(2) Blocked: R4C789 cannot be {458}
j. R6C6 = 3 -->> R4C789 = 15 = {159}
................................... -> r56c7 = {78} and 9(2)n6 cannot be [18]
k. R6C6 = 3 -->> R4C789 = 15 = {168} Blocked
...................................: clashes with 6(2) and 9(2) cage in N6: R4C789 cannot be {168}
l. R6C6 = 3 -->> R4C789 = 15 = {249}
...................................-> r56c7 = {78} and 9(2)n6 cannot be [18]
m. R6C6 = 3 -->> R4C789 = 15 = {258} Blocked
...................................: clash with 6(2)
n. R6C6 = 3 -->> R4C789 = 15 = {456} Blocked
...................................: clashes with 6(2) cage in N6 : R4C789 cannot be {456}
o. R6C6 = 2 -->> R4C789 = 14 = {149} Blocked
...................................: clashes with 6(2) cage in N6 : R4C789 cannot be {149}
p. R6C6 = 2 -->> R4C789 = 14 = {158} Blocked
...................................: 4 remaining innies n5 can only be {1569} (step 49f) -> 2 5's r4 : r4c789 cannot be {158}
q. R6C6 = 2 -->> R4C789 = 14 = {248} Blocked
...................................4 remaining innies n5 can only be {1569} (step 49f) but r4c23 = {37} requires [2/8] in r4c4:r4c789 cannot be {248}
In summary
r. 18(3) in R5C7 = {279/369/378/567}: no 1, 4
s. 9(2) in N6: no [18]
t. r4c789 = {489/469/468/159/249} = [4/5..]
u. no 2 r6c6
67. killer pair 4/5 in R4C789 and R56C9 for N6, no 5 in r56c7
Now moving to c9
22. 8(2)c9 = {17/26/35}
22a. 6(2)c9 = {15/24}
22b. -> 2 locked for c9 in these 2 cages
20. 45 rule on C9: 2 innies R34C9 – 9 = 1 outie R9C8, max R34C9 = 17 -> max R9C8 = 8
56a. R9C8 = 1 -->> R34C9 = 10 = {46} Blocked
....................................: -> R56C9 = {15}: {46/15}c9 Clash with 8(2)n3
65b. r9c8 = 2 -> r34c9 = 11 = {38} Blocked
....................................: r239c8 = {69}[2] -> 9(2)n6 Clash
65c. r9c8 = 2 -> r34c9 = 11 = {47} Blocked
....................................: r239c8 = {69}[2] -> 9(2)n6 Clash
69a. R9C8 = 3 -->> R34C9 = 12 = {39} Blocked
....................................: R23C8 = {68} -->> R56C8 = {27} -->> R56C9 = {15}: {68/15}No options left for 8(2) in N1
69b. R9C8 = 3 -->> R34C9 = 12 = {48} Blocked
....................................: clashes with 22(4) in N9 since all combo's with 3 in r9c8 have 4/8 also in c9. r789c9 = {469/478/568}
69c. R9C8 = 4 -->> R34C9 = 13 = {49}
69d. R9C8 = 4 -->> R34C9 = 13 = {58} Blocked
....................................: -> R23C8 must be {49} but 2 4's in C8
69e. R9C8 = 4 -->> R34C9 = 13 = {67} Blocked
....................................: -> R23C8 must be {49} but 2 4's in C8
69f. R9C8 = 5 -->> R34C9 = 14 = {59}
69g. R9C8 = 5 -->> R34C9 = 14 = {68} Blocked
....................................: -> R23C8 = {39} -->> R56C8 = {27} -->> R56C9 = {15} -->> {68/15} no options left for 8(2)N1.
69h. R9C8 = 6 -->> R34C9 = 15 = {69}
69i. R9C8 = 6 -->> R34C9 = 15 = [78] Blocked
....................................: -> R239C8 = {29}[6] -> clash with 9(2) N6
69j. R9C8 = 7 -->> R34C9 = 16 = {79}
69k. R9C8 = 8 -->> R34C9 = 17 = {89}
In summary
69l. 9 locked in r34C9 for C9 and 26(4)
69m. no 1,2,3 r9c8
69n. r34c9 = {49/59/69/79/89}
71a. no 3 in R3C9
71b. 22(4) in R7C9: no {4567}: Here's how.
71c. 8(2)n3 = [5/6/7] -> 22(4)n9 the {4567} combo must have 4 in r789c9
71d. -> 6(2)r6 = {15} -> r9c8 = 5 -> r34c9 = {59} (step 69f): contradiction 2 5's c9
71e. -> 22(4): no {4567}
71f. 22(4) = {1678/3478/3568} = 8{167/347/356}: 8 locked for N9
71g. "45" on c9: outies r239c8 = 17
71h. ={278}/{368}/{458} = 8{27/36/45} ({467} blocked by 9(2)n6)
71i. 8 locked for c8
71j {4679} blocked from from 26(4)n3: no 2 digits over-lap with c9 outies
73. "45" on n9: 5 innies = 23
73a. can only have {12569/23459} (no 7)
73b. {13469} - blocked by 22(4)n9
73c. {14567} - blocked by 22(4)n9
73d. {23567} - blocked by 22(4)n9
73e. {12479} - blocked because r7c78 can only be {14} -> rest of innies = {279} which must be in 20(3) but this means 2 2's in 20(3)
73f. 7 locked in 22(4) = 78{16/34} (no 5)
73g. no 5 r34c9 (step 69f)
78. (cleanup) "45" n3: outies = 13: no 8 in r2c6
80. 8(2) in R1C9: no {17}. Here's how:
80a. 2 and 5 locked in cages 8(2) + 6(2) in C9.
80b. 6(2) = {15} -->> 8(2) = {26} (needs to use 2)
80c. 6(2) = {24} -->> 8(2) = {35} (needs to use 5)
80d. -> 8(2)n3 no {17}
84. 26(4) in R2C8: no {3689}: clashes with 8(2) in R1C9.
84a. 26(4): no 3 or 6
84b. Clean up: R2C6: no 7
NOW, for the puzzle breaker moves
91. R3C6: no 9
91a. R3C6 = 9 -->> R4C678 = {125} -->> R4C23 = {37} -->> R4C4 = 8 -->> R4C5 = 6: -->> R23C5 = {59}: 2 9's in N2.
91b. -> no 9 r3c6
88. R4C7: no 1, because of 1's in N3.
88a. R123C7 = 1: R4C7: no 1
88b. R1C8 = 1 -->> R3C6 = 1: R4C7: no 1
92a. from step 50j. R6C6 = 3 -->> R4C789 = [519] -->> R2C6 = 4 (outies n3)
--> R34C6 = Blocked ([29] but 2 9's in R4:{38} but 2 3's c6:{47} but 2 4's c6)
92b. (step 50t) R4C789 = {489/469/468/249}(no 1,5)
92c. 4 locked in R4C789 for R4 and N6
92d. Clean up: R2C4: no 3;
92dd. R6C4: no 4 (step 27d)
92de. R56C9 = {15} locked for C9
92f. 4 locked in N4 for C3
93. R12C9 = {26} locked for C9 and N3
93a. 22(4) in R7C9 = {3478}: locked for N9
93b. 26(4) in R2C8 = {4589}: 5 locked in R23C8 for C8 and N3
93d. 5 locked in R4 for N5
95. 10(3) in R7C6 needs 3 or 4. Only place is R7C6: R7C6 ={34}
95a. R9C6 = {34} (45 on N9)
95b. {34} locked for N8 and C6 in R79C6
95c. Clean up: R4C9: no 9.
95d. R3C9 = 9 (hidden single in C9)
95e. Naked Pair {34} in R7C69 locked for R7
96. Hidden Pair c6 {12} in R34C6: Locked for 17(4) cage
96a. 17(4) = {1268}: R4C78 = [86]; R4C9 = 4
96b. R2C6 = 9; R7C9 = 3; R7C6 = 4; R9C6 = 3
96c. R9C8 = 4; R8C1 = 4 (both hidden)
96d. R12C1 = [96]; R2C4 = 4; R4C1 = 3(45 on N1)
96e. R12C9 = [62]
97. Naked Pair {27} in R4C23: locked for R4, N4 and 20(4) in R3C4
97a. R4C4 = 5; R4C6 = 1; R3C6 = 2; R6C4 = 2; R4C5 = 9
97b. R56C8 = [27] (only possible combination)
97c. R6C6 = 6; R7C8 = 1; R8C8 = 9; R7C7 = 5; R1C8 = 3
97d. R56C2 = [69]; R56C7 = [93]
97e. R7C1 = 2; R7C5 = 6
98. 14(4) in R7C1 = 24{17}: {17} locked in R9C12 for N7 and R9
98a. R7C34 = [97]; R9C4 = 9; R89C9 = [78]
98b. Hidden singles: R8C2 = 3; R3C2 = 4; R1C7 = 4; R2C2 = 5
98c. R3C1 = 1; R9C12 = [71]; R23C7 = [17]; R23C8 = [85]
98d. R3C4 = 6(hidden)
99. 20(3) in R2C5 = [389](only possible combination)
99a. R23C3 = [73]; R1C23 = [28]; R4C23 =[72]
99b. R1C4 = 1; R6C5 = 4; R5C456 = [378]
99c. R56C1 = [58]; R56C3 = [41]; R56C9 = [15]
99d. R1C56 = [57]; R9C5 = 2; R8C456 = [815]; R89C2 = [65]; R89C7 = [26]