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Here is my 1st ASSASSIN, completely computer generated but verified also using independent software.


ASSASSIN 147

SSS=1.13

PS code: 3x3::k:4865:4865:2306:2306:6915:6915:6915:2308:2308:4865:5125:5125:5125:3334:6915:6151:6151:2308:1032:5125:3337:3337:3334:1802:6151:6151:6155:1032:5125:3337:8204:8204:1802:1802:6155:6155:5133:4366:4366:8204:8204:8204:2063:2063:6155:5133:5133:4624:4624:8204:8204:4881:7698:1555:5133:4372:4372:4624:1301:4881:4881:7698:1555:4374:4372:4372:5655:1301:7698:7698:7698:4120:4374:4374:5655:5655:5655:2329:2329:4120:4120:

Thanks for the new Assassin! The solving path was pretty straightforward, I think.

A147 Walkthrough:

1. R456
a) Innies N5 = 13(2) = [49] -> R4C6 = 4, R6C4 = 9
b) 17(2) = {89} locked for R5+N4
c) Innies+Outies R6789: -1 = R5C1 - R6C56 -> R5C1 <> 1 and R6C56 <> 8 since R5C1 <= 7
d) 8 locked in R4C45 @ N5 for R4
e) Innies+Outies R1234: -11 = R5C9 - R4C45 -> 12 <= R4C45 = 8{5/6/7} -> R5C9 = (234)
f) 9 locked in 24(4) @ R4 for 24(4) = 9{258/267/348/357/456} <> 1 because R5C9 = (234); R3C9+R4C89 <> 2,3,4

2. R123
a) Innies N3 = 12(2) = [48/57/75]
b) 27(4) = 9{378/468/567} -> 9 locked for N2
c) 13(2) <> 4
d) 27(4) = 79{38/56} because {4689} blocked by Killer pair (68) of 13(2); CPE: R1C4 <> 7
e) Killer pair (68) locked in 27(4) + 13(2) for N2
f) 4 locked in R123C4 @ N2 for C4
g) Innies N3 = 12(2) = {57} locked for N3

3. C789 !
a) Outies C9 = 10(3) <> 8,9; R19C8 <> 5,6,7 since R4C8 >= 5
b) Hidden Single: R4C9 = 9 @ N6
c) ! 24(4) <> 4 because [5694] blocked by Killer pair (45) of 6(2)
d) Hidden Single: R5C1 = 4 @ R5
e) 8 locked in 16(3) @ C9 for N9 -> 16(3) = 8{17/26/35} <> 4; R89C9 <> 1,2,3 since R9C8 = (123)

4. R456
a) Innies R6789 = 5(2) = {23} locked for R6+N5
b) 2 locked in R5C789 @ R5 for N6
c) R4C7 = 1, R3C6 = 2, R4C1 = 3, R3C1 = 1
d) 20(4) = 14{69/78} since (89) only possible @ R7C1 -> R6C2 = 1; R7C1 = (89)
e) 18(3) = 9{27/36} -> R7C3 = (23)
f) Naked pair (67) locked in R6C13 for R6+N4
g) 13(3) = 2{38/47/56} <> 9 because R4C3 = (25) -> R4C3 = 2

5. C123
a) Innies N7 = 11(2) = [83] -> R7C1 = 8, R9C3 = 3
b) Cage sum: R6C1 = 7
c) R6C3 = 6 -> R7C4 = 3
d) 17(3) = {269} locked for N7 since R89C1 = (2569)
e) 5 locked in 19(3) @ C1 = {568} for N1 -> R1C2 = 8; 6 locked for C1+N1
f) 9(2) = {45} -> R1C3 = 4, R1C4 = 5
g) R3C3 = 7, R3C9 = 5

6. N69
a) 24(4) = {3579} -> R4C8 = 7, R5C9 = 3
b) R6C9 = 4 -> R7C9 = 2
c) 9(2) = {45} -> R9C6 = 5, R9C7 = 4
d) 19(3) = {568} -> R7C6 = 6, R7C7 = 5, R6C7 = 8

7. Rest is singles.

Rating: Hard 1.0. I used Killer pairs.

Thanks Tarek for your first Assassin.

I found this more challenging than I'd expected. I'll accept that it's straightforward if one finds both of Afmob's key steps easily but it took me a long time to find the second one, in fact I left this puzzle to try other ones and only came back to it this week.

I'll rate A147 the way I solved it at Easy 1.25 to 1.25 because of steps 10a, 14 and 20; I've included steps 10a and 20 at this level because they each extend into two nonets and into two rows or columns. Also it has a narrow solving path until one has found both key steps.

Here is my walkthough for A147.

Prelims

a) R1C34 = {18/27/36/45}, no 9
b) R23C5 = {49/58/67}, no 1,2,3
c) R34C1 = {13}, locked for C1
d) R5C23 = {89}, locked for R5 and N4
e) R5C78 = {17/26/35}, no 4
f) R67C9 = {15/24}
g) R78C5 = {14/23}
h) R9C67 = {18/27/36/45}, no 9
i) 19(3) cage in N1 = {289/379/469/478/568}, no 1
j) 9(3) cage in N3 = {126/135/234}, no 7,8,9
k) 7(3) cage at R3C6 = {124}
l) 19(3) cage at R6C7 = {289/379/469/478/568}, no 1
m) 27(4) cage at R1C5 = {3789/4689/5679}, no 1,2

1. 45 rule on N5 2 innies R4C6 + R6C4 = 13 -> R4C6 = 4, R6C4 = 9, clean-up: no 5 in R9C7
1a. R3C6 + R4C7 = {12}, CPE no 1,2 in R3C7
1b. X-Wing for 1 in R34C1 and R4C6 + R6C4, locked for R34
1c. R6C4 = 9 -> R6C3 + R7C4 = 9 = [18]/{27/36/45}, no 1 in R7C4

2. 45 rule on N3 2 innies R1C7 + R3C9 = 12 = {39/48/57}, no 2,6

3. 45 rule on N7 2 innies R7C1 + R9C3 = 11 = {29/47/56}/[83], no 1,8 in R9C3

4. 45 rule on R1 3 outies R2C169 = 19 = {289/379/469/478/568}, no 1
4a. 2,3 of {289/379} must be in R2C9, no 2 in R2C1, no 3 in R2C6

5. 45 rule on R9 3 outies R8C149 = 19 = {289/379/469/478/568}, no 1

6. 45 rule on C9 3 outies R149C8 = 10 = {127/136/145/235}, no 8,9

7. R4C9 = 9 (hidden single in R4), clean-up: no 3 in R1C7 (step 2)

8. 8 in R4 locked in R4C45, locked for N5
8a. 45 rule on R1234 2 innies R4C45 = 1 outie R5C9 + 11
8b. Max R4C45 = 15 -> max R5C9 = 4
8c. Min R5C9 = 1 -> min R4C45 = 12, no 2,3 in R4C45
8d. Min R4C45 = {58} = 13, min R5C9 = 2

9. 24(4) cage at R3C9 = {2589/2679/3489/3579/4569}
9a. Max R345C9 = 21 -> min R4C8 = 3
9b. Max R4C89 + R5C9 = 20 and contains 4 -> min R3C9 = 5, clean-up: no 8,9 in R1C7 (step 2)
9c. Min R14C8 = 4 -> max R9C8 = 6 (step 6)

10. 27(4) cage at R1C5 = {3789/4689/5679}, 9 locked for N2, clean-up: no 4 in R23C5
10a. 27(4) cage at R1C5 = {3789/5679} (cannot be {4689} which clashes with R23C5), no 4, CPE no 7 in R1C4, clean-up: no 2 in R1C3, no 8 in R3C9 (step 2)
10b. 5 of {5679} must be in R1C7 (R1C56 + R2C6) cannot be {569} which clashes with R23C5), no 5 in R1C56 + R2C6
10c. Killer pair 6,8 in R1C56 + R2C6 and R23C5, locked for N2, clean-up: no 1,3 in R1C3
10d. 4 in N2 locked in R123C4, locked for C4, clean-up: no 5 in R6C3 (step 1c)
[I could also lock 7 for N2 using interactions between the 13(2) and 27(4) cages but that’s a higher rated step so I won’t use it.]

11. Naked pair {57} in R1C7 + R3C9, locked for N3
11a. 9(3) cage in N3 = {126/234}, 2 locked for N3
11b. 24(4) cage at R3C9 (step 9) = {2679/3579/4569}
11c. R5C9 = {234} -> no 3 in R4C8
11d. 3 in R4 locked in R4C123, locked for N4, clean-up: no 6 in R7C4 (step 1c)
11e. Min R14C8 = 6 -> max R9C8 = 4 (step 6)
11f. Min R49C8 = 6 -> max R1C8 = 4 (step 6)

12. 8 in C9 locked in R89C9, locked for N9, clean-up: no 1 in R9C6
12a. 16(3) cage in N9 = 8{17/26/35}, no 4
12b. R9C8 = {123} -> no 1,2,3 in R89C9

13. R8C149 (step 5) = {289/379/478/568} (cannot be {469} because 4,9 only in R8C1)
13a. 4,9 of {289/379/478} must be in R8C1 -> no 2,7 in R8C1

14. Hidden killer triple 1,2,3 in R4C1, R4C23 and R4C7 for R4 -> R4C23 must contain one of 2,3 -> R4C23 must contain one of 5,6,7
[The final part of this could also be obtained from hidden killer triple 5,6,7 in R4C23, R4C45 and R4C8 for R4]

15. 20(4) at R5C1 = {1469/1478/1568/2459/2468/2567} (cannot be {1289} because 8,9 only in R6C1)
15a. 8,9 of {1469/1478/2459/2468} must be in R7C1 -> no 4 in R7C1, clean-up: no 7 in R9C3 (step 3)
15b. 2 of {2567} must be in R5C1 + R6C12 (R5C1 + R6C12 cannot be {567} which clashes with R4C23), 8,9 of {2459/2468} must be in R7C1 -> no 2 in R7C1, clean-up: no 9 in R9C3 (step 3)
15c. Killer triple 1,2,3 in R4C1, R4C23 and R5C1 + R6C12, locked for N4, clean-up: no 7,8 in R7C4 (step 1c)

16. 13(3) cage at R3C3 = {238/247/256/346}, no 9

17. 45 rule on R123 4 remaining outies R4C1237 = 1 innie R3C9 + 6
17a. R3C9 = {57} -> R4C1237 = 11,13 = {1235/1237}, no 6

18. 20(4) at R5C1 (step 15) = {1469/1478/1568/2459/2468/2567}
18a. 6 of {2567} must be in R5C1 + R6C12 (R5C1 + R6C12 cannot be {257} which clashes with R4C23), 8,9 of {1469/1478/2459/2468} must be in R6C1 -> no 6 in R7C1, no 5 in R9C3 (step 3)

19. 13(3) cage at R3C3 (step 16) = {238/247/256/346}
19a. 6,8 of {238/256/346} must be in R3C3 -> no 3,5 in R3C3

20. 24(4) cage at R3C9 (step 11b) = {2679/3579} (cannot be {4569} which clashes with R67C9), no 4, clean-up: no 7 in R4C45 (steps 8 and 8a)
[I missed that clash earlier; {4569} could have been eliminated in step 9.]
20a. R5C1 = 4 (hidden single in R5), clean-up: no 5 in R7C3 (step 1c)
20b. 6 in N4 locked in R6C123, locked for R6
[After fixing R5C1, Afmob found 45 rule on R6789 2 innies R6C56 = 5 = {23}, locked for R6 and N5, which makes the later stages quicker.]

21. R78C5 = {14} (cannot be {23} which clashes with R7C4), locked for C5 and N8

22. 20(4) at R5C1 (step 15) = {1469/1478/2459/2468}
22a. 8,9 only in R7C1 -> R7C1 = {89}, clean-up: no 4,6 in R9C3 (step 3)
22b. 1 of {1478} must be in R6C2 -> no 7 in R6C2

23. 22(4) cage at R8C4 = {2389/2569/2578/3568}
23a. 9 of {2389} must be in R9C5, 2,3 of other combinations must be in R9C3 -> no 2,3 in R9C5

24. 9 in C5 locked in R19C5
24a. 45 rule on C5 5 innies R14569C5 = 27 = {23589/23679}
24b. 2 locked in R56C5, locked for N5
24c. 6 of {23679} must be in R4C5 -> no 6 in R159C5

25. Killer triple 1,2,3 in R4C7, R5C78 and R5C9, locked for N6, clean-up: no 4,5 in R7C9

26. 3 in R6 locked in R6C56, locked for N5
26a. Hidden killer pair 1,2 in R6C12 and R6C56 for R6, R6C12 contains one of 1,2 -> R6C56 must contain one of 1,2 and also 3 (step 26) -> R6C5 = {23}, R6C6 = {13}
26b. 7 in N5 locked in R5C456, locked for R5, clean-up: no 1 in R5C78

27. R4C7 = 1 (hidden single in N6), R3C6 = 2, R4C1 = 3, R3C1 = 1, clean-up: no 7 in R1C3, no 8 in R9C6, no 7 in R9C7
27a. 2 in N6 locked in R5C789, locked for R5
27b. R6C5 = 2 (hidden single in C5), R6C6 = 3 (hidden single in R6), R6C2 = 1 (hidden single in R6), clean-up: no 6 in R9C7
27c. R1C5 = 3 (hidden single in C5), R9C5 = 9 (hidden single in C5), clean-up: no 6 in R1C3
27d. Killer pair 5,7 in R23C5 and R5C5, locked for C5

28. R1C5 = 3 -> 27(4) cage at R1C5 (step 10a) = {3789}, no 5,6 -> R1C7 = 7, R3C9 = 5, R6C9 = 4, R7C9 = 2, R5C9 = 3, R12C9 = [16], R1C8 = 2 (step 11a), R7C4 = 3, R6C3 = 6 (step 1c), clean-up: no 8 in R1C3, no 8 in R2C5, no 7 in R3C5, no 5,6 in R5C7, no 5 in R5C8
28a. R5C78 = [26], R4C8 = 7, clean-up: no 7 in R9C6

29. Naked pair {89} in R12C6, locked for C6 and N2, clean-up: no 5 in R2C5
29a. R23C5 = [76], R45C5 = [85], R4C4 = 6, R3C4 = 4, R1C34 = [45], R2C4 = 1, R5C46 = [71]
29b. Naked pair {28} in R89C4, locked for 22(4) cage at R8C4 -> R9C3 = 3, R9C7 = 4, R9C6 = 5, R9C8 = 1, R7C1 = 8 (step 3), R6C1 = 7 (step 22)

30. R3C4 = 4 -> R34C3 = 9 = [72], R4C2 = 5, R2C1 = 5, R2C8 = 4 (hidden singles in R2)
30a. R2C1 = 5 -> R1C12 = 14 = [68], R12C6 = [98], R89C1 = [92], R89C4 = [28], R89C9 = [87], R9C2 = 6, R5C23 = [98], R23C2 = [23], R2C3 = 9, R2C7 = 3

31. 5 in R6 locked in R6C78, CPE no 5 in R8C7
31a. R8C67 = [76], R7C6 = 6, R67C7 = 13 = [85]

and the rest is naked singles