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The first version of the cage pattern came quite fast but the difficulty was too low (about 0.9), so I changed the cage pattern in the middle and a 2.5+ Killer was the result. After some fiddling with the cages in the first rows this one came out.

Despite the high SS Score this Assassin can be solved without using any chains, so I hope you like it!

Assassin 158



3x3::k:3862:5400:1562:7196:7196:7196:1819:2841:5655:2068:3862:5400:1562:7196:1819:2841:5655:2581:3332:2068:3862:5400:7196:2841:5655:2581:4355:3332:4359:4359:4359:3859:5384:5384:5384:4355:3332:3845:4359:3845:3859:3078:5384:3078:4355:2561:2561:3845:3345:3859:2834:3078:3586:3586:2561:2569:7179:3345:2832:2834:4110:5386:3586:2569:2569:7179:7179:2832:4110:4110:5386:5386:3340:3340:7179:3343:3343:3343:4110:1805:1805:


SS Score: 1.52
Estimated rating: 1.25 - Hard 1.25.

Not the most elegant solution - but here it is:

Thank you Afmob, and Well Done Frank!

My efforts were in the same direction as yours, but you beat me to it. I too had to do some rather inelegant things, like staring at the grid for several hours.

cheers

_________________
Joe

Thanks Afmob for this puzzle (and a big headache ! ) I had to work hard for avoiding contradiction steps...Above all, I wanted to use a particular aspect of this puzzle (see the WT intro below). Not really satisfied with my solution, since I could not avoid the chainy step 4)b)... I wait for the others wts.

This was really, really hard so I may have missed something. Wonderful punishment. Thanks very much Afmob! Very happy with this solution. It's cracked from step 14 but the key step is step 3. Please let me know of any corrections or clarifications.

Assassin 158

NOTE: this is an optimised solution so many obvious eliminations are not included since they are not needed for this solution.

Prelims
i. 21(3)n1: no 1,2,3
ii. 6(2)n1 = {15/24}
iii. 7(2)n3: no 7,8,9
iv. 11(3)n3: no 9
v. 22(3)n3: no 1,2,3,4
vi. 8(2)n1: no 4,8,9
vii. 10(2)n3: no 5
viii. 10(3)n4: no 8,9
ix. 13(2)n5: no 1,2,3
x. 11(2)n5: no 1
xi. 10(3)n7: no 8,9
xii. 28(4)n7: no 1,2,3
xiii. 11(2)n8: no 1
xiv. 21(3)n9: no 1,2,3
xv. 7(2)n9: no 7,8,9

1. "45" c12: 1 outie r3c3 + 21 = 3 innies r145c2
1a. max. 3 innies = 24 -> max. r3c3 = 3
1b. min. 3 innies = 22 = {589/679 etc}(no 1..4)
1c. 3 innies = 22/23/24 -> 9 locked for c2
1d. no 4 in r9c1

2. "45" c1234: 2 innies r19c4 = 11 (no 1)

3. hidden grouped killer triple {123} in c34. Like this.
3a. 6(2)n1 = {15/24}: has one of 1/2/3
3b. r3c3 = (123): has one of 1/2/3
3c. 17(4)n4 cannot have more than two of 1/2/3 since {123.} cannot reach the cage sum
3d. 15(3)n4 cannot have more than one of 1/2/3 since {23.} cannot reach the cage sum
3e. so at most five spots are taken for 1,2,3 in c34 but six are needed
3f. -> h11(2)r19c4 must have one of 1/2/3 = {29/38}

4. "45" n7: 1 outie r8c4 - 6 = 1 innie r7c1
4a. r8c4 = (789), r7c1 = (123)

5. 13(2)n5 = {49/58/67} -> Killer triple 7,8,9 in c4 with h11(2) (step 3f) & r8c4
5a. all locked for c4

6. 21(3)n1 = {489/579/678} -> (456) only in r3c4
6a. r1c2 + r2c3 have two of (789)

7. max. r3c3 = 3 -> min. r1c1 + r2c2 = 12 (no 1,2: no 3 since 3 already in r3c3) and must have one of 7/8/9 to reach 12
7a. Killer triple (789) with r1c2 + r2c3: all locked for n1
7b. no 1 in 8(2)n1

8. 1 in c2 only in r678c2 -> no 1 in r7c1 (CPE)
8a. no 7 in r8c4 (i/o n7 step 4)

9. 7 in c4 only in 13(2)n5 = {67}
9a. 6 locked for c4

10. 21(3)n1 = {489/579}
10a. 9 locked for n1

11. 10(3)n4 must have (23) in r7c1 = {127/136/235}(no 4)

12. 28(4)n7 = {4789/5689} = [4/5..] in n7
12a. -> {145} blocked from 10(3)n7
12b. 10(3)n7 must have 1 for n7 = 1{27/36}(no 45)

13. "45" c12: 5 innies r1c1 + r1245c2 = 36
13a. max. r1245c2 = 30 -> min. r1c1 = 6

14. 4 in c1 only in 13(3) = 4{18/27/36}(no 5,9)

Now it's cracked. Just getting it to singles so missing lots of clean-up.
15. r9c1 = 9 (hsingle c1)
15a. r9c2 = 4

16. 28(5)n7 = {5689} -> r8c4 = 9
16a. r789c3 = {568}: all locked for n7 & c3

17. "45" n7: last remaining innie r7c1 = 3
17a. r3c2 = 3 (hsingle c2)
17b. r2c1 = 5 (cage sum)

18. "45" n1: 2 outies r23c4 - 5 = 1 innie r3c1
18a. max. r23c4 = [45] = 9 -> max. r3c1 = 4
18b. no 1 in r1c3 or r2c4

18c. "45" r123: 2 innies r3c19 = 7 = [16/25]

19. r1c3 = 4 (hsingle n1)
19a. r2c4 = 2

20. "45" r9: 2 innies r9c37 = 12 = [57] (only permutation)

21. 7(2)n9 = {16}: both locked for r9 & n9

22. naked triple {238} in r9c456: all locked for n8

23. 21(3)n9 = [9]{48}: 4 & 8 locked for n9 & r8

24. "45" n9: 1 outie r8c6 + 1 = 1 innie r7c9
24a. -> r8c6 = 1, r7c9 = 2

25. r78c7 = [53]
25a. r8c5 = 5 (hsingle n8)
25b. r7c5 = 6

26. 7(2)n3 = [16] (last permutation)

27. r1c8 = 2(hsingle r1)
27a. r2c7 + r3c6 = 9 = [45] (last permutation)

28. r3c9 = 6
28a. -> r3c1 = 1 (last innie n123)
28b. r7c2 = 1 (hsingle n7)

29. r6c12 = 7 = [25]

30. r45c1 = 12 = {48}: 8 locked for c1 & n4

31. r3c3 = 2 -> r1c1 + r2c2 = 13 = [67]
31a. 10(2)n3 = [37] (last permutation)

32. r45c9 = 11 (cage sum) = {47}: both locked for c9 & n6
32a. r6c89 = 12 = [39]

33. 12(3)n5 = [318] (only permutation)

34. 15(3)n4 = [951] (only permutation)

rest is naked singles.
Cheers
Ed

Thanks Afmob for what I initially thought was a hard puzzle but with hindsight it wasn't.

When I first tried it I got stuck because after step 9 I moved on to other things rather than doing the obvious follow up in step 10. Maybe subconsciously I'd been avoiding listing those combinations.

When I came back to this puzzle I found step 10 easily enough and realised its importance in providing the key killer triples in steps 11 and 14. The only difficult remaining part was step 16 as you will see from the comments in my walkthrough.

I'll rate A158 at 1.25; maybe step 6 could be omitted and then I'd make it Easy 1.25.

Here is my walkthrough

Prelims

a) R1C3 + R2C4 = {15/24}
b) R1C7 + R2C6 = {16/25/34}, no 7,8,9
c) R2C1 + R3C2 = {17/26/35}, no 4,8,9
d) R2C9 + R3C8 = {19/28/37/46}, no 5
e) R67C4 = {49/58/67}, no 1,2,3
f) R67C6 = {29/38/47/56}, no 1
g) R78C5 = {29/38/47/56}, no 1
h) R9C12 = {49/58/67}, no 1,2,3
i) R9C89 = {16/25/34}, no 7,8,9
j) 21(3) cage at R1C2 = {489/579/678}, no 1,2,3
k) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
l) 22(3) cage in N3 = {589/679}, 9 locked for N3, clean-up: no 1 in 10(2) cage
m) 10(3) cage at R6C1 = {127/136/145/235}, no 8,9
n) 10(3) cage in N7 = {127/136/145/235}, no 8,9
o) 21(3) cage in N9 = {489/579/678}, no 1,2,3
p) 28(4) cage at R7C3 = {4789/5689}, no 1,2,3

1. 45 rule on R123 2 innies R3C19 = 7 = {16/25/34}, no 7,8,9

2. 45 rule on R9 2 innies R9C37 = 12 = {48/57}/[93], no 1,2,6, no 9 in R9C7

3. 45 rule on C1234 2 innies R19C4 = 11 = {29/38/47/56}, no 1

4. 45 rule on C6789 2 innies R19C6 = 11 = {29/38/47/56}, no 1

5. 45 rule on N7 1 outie R8C4 = 1 innie R7C1 + 6, R7C1 = {123}, R8C4 = {789}

6. Hidden killer triple 1,2,3 in R7C1 and 10(3) cage for N7 -> 10(3) cage must contain two of 1,2,3 = {127/136/235} (cannot be {145} which only contains one of 1,2,3), no 4

7. 45 rule on C12 3 innie R145C2 = 1 outie R3C3 + 21
7a. Max R145C2 = 24 -> max R3C3 = 3
7b. Min R3C3 = 1 -> min R145C2 = 22, no 1,2,3,4, 9 locked for C2, clean-up: no 4 in R9C1
7c. 15(3) cage in N1 can only contain one of 1,2,3, R3C3 = {123} -> no 1,2,3 in R1C1 + R2C2

8. 45 rule on C89 1 outie R3C7 = 3 innies R145C8 + 1
8a. Min R145C8 = 6 -> min R3C7 = 7
8b. Max R145C8 = 8, no 6,7,8,9, 1 locked for C8, clean-up: no 6 in R9C9

9. Hidden killer pair 1,2 in R9C456 and R9C89 for R9, R9C456 cannot have both of 1,2 -> R9C89 must contain one of 1,2 -> R9C89 = [25/52/61], no 3,4

10. R9C456 = {139/148/238/247} (cannot be {157/256} which clash with R9C89, cannot be {346} which don’t contain 1 or 2), no 5,6, clean-up: no 5,6 in R1C4 (step 3), no 5,6 in R1C6 (step 4)
10a. 1 of {139} must be in R9C5 -> no 9 in R9C5

11. Killer triple 7,8,9 in R19C4, R67C4 and R8C4, locked for C4

12. 45 rule on N9 1 innie R7C9 = 1 outie R8C6 + 1, no 1 in R7C9, no 9 in R8C6

13. 21(3) cage at R1C2 = {489/579/678}
13a. R3C4 = {456} -> no 4,5,6 in R1C2 + R2C3

14. 15(3) cage in N1 must contain one of 7,8,9 because R3C3 = {123}
14a. Killer triple 7,8,9 in R1C2, R2C3 and 15(3) cage, locked for N1, clean-up: no 1 in 8(2) cage

15. 45 rule on N3 4 innies R1C78 + R2C7 + R3C9 = 13 = {1237/1246/1345}, no 8

[I first saw the next step as
10(3) cage in N7 cannot be {235} because R6C2 = 1 (hidden single in C2) clashes with R7C1 = 1 (hidden single in N7) -> 10(3) cage in N7 (step 6) = {127/136}, no 5, 1 locked for N7, clean-up: no 7 in R8C4 (step 5)

Then I improved it to
1 in C2 locked in R678C2
1 in R6C2 => R8C1 = 1 => 10(3) cage in N7 (step 6) = {127/136}
1 in R78C2 => 10(3) cage in N7 (step 6) = {127/136}
-> 10(3) cage in N7 (step 6) = {127/136}, no 5, 1 locked for N7, clean-up: no 7 in R8C4 (step 5)

The first way ought to have given me the necessary clue. However it was only after I mentioned these two somewhat “chainy” ways to Ed and got his reply “Get the shoe ready for a self-inflicted kick Andrew. CPE!” that I immediately spotted what I ought to have seen earlier.]

16. 1 in C2 locked in R678C2, CPE no 1 in R7C1, clean-up: no 7 in R8C4 (step 5)
16a. 1 in N7 locked in 10(3) cage (step 6) = {127/136}, no 5

17. 10(3) cage at R6C1 = {127/136/235} (cannot be {145} because R7C1 only contains 2,3), no 4

18. R9C12 = [58/85/94] (cannot be {67} which clashes with 10(3) cage), no 6,7

19. R9C8 = 6 (hidden single in R9), R9C9 = 1, clean-up: no 4 in R2C9, no 5 in R8C6 (step 12), no 9 in R9C46 (step 10), no 2 in R1C4 (step 3), no 2 in R1C6 (step 4), no 6 in R3C1 (step 1)
19a. 21(3) cage in N9 = {489/579}, 9 locked for N9, clean-up: no 8 in R8C6 (step 12)
19b. 2 in R9 locked in R9C456, locked for N8, clean-up: no 9 in R78C5, no 3 in R7C9 (step 12)

20. R8C6 = 1 (hidden single in N8), R7C9 = 2 (step 12), R7C1 = 3, R8C4 = 9 (step 5), clean-up: no 6 in R1C7, no 5 in R3C1 (step 1), no 5 in R3C2, no 8 in R3C8, no 4 in R3C9 (step 1), no 4 in R67C4, no 2,8,9 in R6C6, no 8 in R8C5, no 2 in R9C4 (step 3), no 3 in R9C7 (step 2)

21. R7C2 = 1 (hidden single in R7), R8C12 = 9 = {27}, locked for R8 and N7, clean-up: no 4 in R7C5, no 5 in R9C7 (step 2)
21a. R9C1 = 9 (hidden single in R9), R9C2 = 4, clean-up: no 7 in R1C4 (step 3), no 7 in R1C6 (step 4), no 8 in R9C37 (step 2)
21b. R9C37 = [57], clean-up: no 4 in R1C4 (step 3), no 4 in R1C6 (step 4), no 1 in R2C4
21c. Naked pair {38} in R19C4, locked for C4, clean-up: no 5 in R67C4
21d. Naked pair {67} in R67C4, locked for C4
21e. Naked triple {238} in R9C456, locked for N8, clean-up: no 3 in R6C6

22. R8C7 = 3 (hidden single in R8), R7C7 = 5 (cage sum), clean-up: no 2,4 in R2C6, no 6 in R8C5

23. Naked pair {48} in R8C89, locked for R8 and N9 -> R7C8 = 9, R78C3 = [86], R8C5 = 5, R7C5 = 6, R67C4 = [67], R7C6 = 4, R6C6 = 7

24. R7C1 = 3 -> R6C12 = 7 = {25}, locked for R6 and N4

25. R3C2 = 3 (hidden single in C2), R2C1 = 5, R6C12 = [25], R8C12 = [72], clean-up: no 1 in R1C3, no 2 in R1C7, no 7 in R2C9, no 4 in R3C1, no 5 in R3C9 (both step 1)
25a. R3C19 = [16], R3C3 = 2, R1C3 = 4, R2C4 = 2, R1C7 = 1, R2C6 = 6, R2C7 = 4, R23C8 = [87], R2C9 = 3, R3C7 = 9, R1C89 = [25], R3C6 = 5 (cage sum), R3C45 = [48], R2C23 = [79], R1C12 = [68], R1C456 = [379], R9C4 = 8, R9C6 = 2 (step 4), R9C5 = 3, R8C89 = [48]
25b. R6C8 = 3, R6C9 = 9 (cage sum), R6C3 = 1, R5C4 = 5, R5C2 = 9 (cage sum)

and the rest is naked singles