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Hi,

I had much hesitations about the choice of the puzzle between two of them (the other one will be sent as an extra killer for JFF4 EDIT : Have talked about this with Andrew and have finally
decided to post it for further Assassin).
SSolver rating is 3.50, but fall down to 1.19 after a single step not seen by the solver.
The solving path is narrow, but no doubt that you will be able to find the right way :
must not be added to Tarek unsolvables

ASSASSIN A146






SSscore : 3.50

PS code : 3x3:d:k:5120:5120:4866:4866:4866:4866:4870:4870:4870:5120:3338:3083:3083:3341:4622:4622:1296:4870:5120:2835:3338:3083:3341:4622:1296:4633:5402:4891:2835:2835:11550:11550:11550:4633:4633:5402:4891:6693:6693:11550:11550:11550:5930:5930:5402:4891:6693:6693:11550:11550:11550:5930:5930:6197:6454:6693:2360:4409:4409:4409:1596:5930:6197:6454:2360:5697:5697:5697:5697:5697:1596:6197:6454:6454:6454:5195:5195:5195:5195:6197:6197:

Solution :

A146 Walkthrough:

1. D\/
a) Overlap of R19+C19 = R19C19 = 13(4) = 1{237/246/345} <> 8,9; CPE: R5C5 <> 1
b) ! Using R19C19 = 13(4): Innies D\/ + Overlap D\/ = R46C46+R5C5 + R5C5 = 44
-> R46C46+R46C5 = 35(5) = {56789} locked for N5 and R5C5 = 9
c) 13(2) <> 4
d) Naked quad (5678) locked in R2C2+R3C3+R4C4+R6C6 for D\
e) 6(2) = {24} locked for N9+D\
f) R19C19 = 13(4) = 13{27/45} since R1C1+R9C9 = {13} -> R1C9+R9C1 = {27/45}
g) Killer pair (24) locked in R19C19 + 5(2) for D/
h) 9(2) <> 5,7

2. N1247
a) Outies N124 = 16(1+1) = {79/88}
b) Innies N7 = 11(2) = [74/92] since (38) is a Killer pair of 9(2)
c) Outies N4 = 11(2) = [29/47]
d) Outies N124 = 16(2) = {79}; CPE: R2C2 <> 7

3. C789 !
a) ! Innies C789 = 19(3) = {379} locked for C7 because R2C7 = (79); 3 also locked for N9
b) R9C9 = 1, R1C1 = 3
c) ! Outies C9 = 19(2+1) <> 1 because R1C7 <> 9
d) Innies N3 = 21(3) <> 1,2,3
e) 1 locked in 5(2) @ N3 = {14} locked for N3+D/
f) 19(4) = 23{59/68} -> R2C9 = 3; 2 locked for R1

4. D\/+N7
a) R19C19 = 13(4) = {1237} -> R1C9 = 2, R9C1 = 7
b) 24(5) = {14568} -> R6C9 = 4; {568} locked for N9
c) R7C2 = 9, R7C8 = 7
d) Innie N7 = R8C3 = 2
e) R8C8 = 4, R2C8 = 1, R3C7 = 4, R3C2 = 2
f) 9(2) = {36} locked for N7+D/
g) 25(5) = {14578} -> 1 locked for C1

5. R123
a) 18(3) @ R3C8 = 9{18/36} -> 9 locked for C8
b) 19(4) @ N3 = {2368} -> 6,8 locked for R1+N3
c) R3C8 = 9, R2C7 = 7, R3C9 = 5
d) 20(4) = 34{58/67} because (17) only possible @ R1C2; 4 locked for N1
e) Hidden Single: R1C3 = 1 @ N1, R2C3 = 9 @ N1
f) 19(4) @ N2 = {1459} -> 4,5,9 locked for R1+N2
g) 13(2) @ N2 = {67} -> R2C5 = 6, R3C5 = 7
h) 13(2) @ N1 = {58} -> R3C3 = 8, R2C2 = 5
i) 12(3) = {129} -> R2C4 = 2, R3C4 = 1
j) 11(3) = 2{18/36/45}

6. R7
a) 17(3) = 8{36/45} -> 8 locked for R7+N8

7. Rest is singles.

Rating: 1.25 - Hard 1.25 with hardest move being step 1b.

Yes it is. My key moves were the mostly the same as Afmob's but sometimes for different reasons, particularly for the 19(4) cage in N3.

I'll rate A146 at Hard 1.25 mainly for the first two moves but also because I still had to work fairly hard until I found steps 13 and 13b.

Here is my walkthrough

This is a Killer-X.

Prelims

a) 13(2) diagonal cage at R2C2 = {49/58/67}, no 1,2,3
b) R23C5 = {49/58/67}, no 1,2,3
c) 5(2) diagonal cage at R2C8 = {14/23}
d) 9(2) diagonal cage at R7C3 = {18/27/36/45}, no 9
e) 6(2) diagonal cage at R7C7 = {15/24}
f) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
g) R456C1 = {289/379/469/478/568}, no 1
h) R345C9 = {489/579/678}, no 1,2,3

I’d done three routine steps before I spotted step 1, which more inspirational solvers will have spotted immediately, so I had to start again. Using an Excel worksheet with coloured cages may have made it harder for me to see the outer ring.

1. 45 rule on outer ring 4 innies R19C19 = 13
[Note that R19C9 can ‘see’ each other because of the diagonals but no need to use this yet.]

2. 45 rule on both diagonals 3 remaining innies on each diagonal = 44. This is only possible when the crossover value is 9 -> R5C5 = 9, placed for both diagonals, clean-up: no 4 in R2C2 + R3C3 and R23C5
2a. R46C46 + R5C5 (twice) = 44 -> R46C46 = 26 = {5678}, locked for N5
2b. R4C4 + R6C6 = {58/67} (other combinations clash with R2C2 + R3C3 on D\), R4C6 + R6C4 = {58/67}
2c. Naked quad {5678} in R2C2 + R3C3 + R4C4+ R6C6, locked for D\, clean-up: no 1 in R7C7 + R8C8
2d. Naked pair {24} in R7C7 + R8C8, locked for D\ and N9
2e. Naked pair {13} in R1C1 + R9C9, CPE no 1,3 in R1C9 + R9C1
2f. R1C1 + R9C9 = {13} = 4 -> R1C9 + R9C1 = 9 (step 1) = {27/45}, no 6,8
2g. Killer pair 2,4 in R1C9 + R9C1 and R2C8 + R3C7, locked for D/, clean-up: no 5,7 in R7C3 + R8C2

3. 45 rule on N3 3 innies R2C7 + R3C89 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on N4 2 outies R37C2 = 11 = [29]/{38/47/56}, no 1, no 2 in R7C2

5. 45 rule on C789 3 innies R289C7 = 19 = {379/469/478/568}, no 1

6. 45 rule on R789 2 innies R7C28 = 1 outie R6C9 + 12
6a. Min R7C28 = 13, no 1,3, clean-up: no 8 in R3C2 (step 4)
6b. Max R7C28 = 17 -> max R6C9 = 5
6c. 1 in N9 locked in R78C9 + R9C89 for 24(5) cage, no 1 in R6C9
6d. Min R7C28 = 14, no 4, clean-up: no 7 in R3C2 (step 4)

7. 45 rule on N7 2 innies R7C2 + R8C3 = 11 = {56}/[74/92] (cannot be [83] which clashes with R7C3 + R8C2) -> R7C2 = {5679}, R8C3 = {2456}, clean-up: no 3 in R3C2
7a. 11(3) cage at R3C2 = {128/146/236/245} (cannot be {137} because no 1,3,7 in R3C2), no 7

8. 45 rule on N1 3 innies R12C3 + R3C2 = 12 = {129/147/237/246/345} (cannot be {138} which clashes with R1C1, cannot be {156} which clashes with R2C2 + R3C3), no 8

9. 45 rule on R1 2 innies R1C12 = 1 outie R2C9 + 7
9a. Max R1C12 = 12 -> max R2C9 = 5
9b. Min R1C12 = 8 -> min R1C2 = 5

10. 45 rule on C9 2 innies R12C9 = 1 outie R9C8
10a. Min R12C9 = 3 -> min R9C8 = 3
10b. 1 in N9 locked in R789C9, locked for C9
10c. Min R12C9 = 5 -> min R9C8 = 5

11. 45 rule on N124 2(1+1) outies R2C7 + R7C2 = 16 = {79} (only remaining combination because no 8 in R7C2), CPE no 7 in R2C2, clean-up: no 5,6 in R3C2 (step 4), no 6 in R3C3, no 5,6 in R8C3 (step 7)
11a. Naked pair {24} in R8C38, locked for R8

12. R289C7 (step 5) = {379} (only remaining combination, cannot be {568} because R2C7 only contains 7,9), locked for C7, 3 locked in R89C7, locked for N9 -> R9C9 = 1, R1C1 = 3, clean-up: no 2 in R2C8
12a. R12C3 + R3C2 (step 8) = {129/147/246}, no 5

13. Hidden killer pair 2,3 in R12C9 and R6C9 for C9 -> R12C9 must contain at least one of 2,3
13a. 19(4) cage in N3 = {2359/2368} (cannot be {1279/1369/1378/2458/2467/3457} which clash with R2C8 + R3C7, cannot be {1459/1468/1567} which don’t contain one of 2,3), no 1,4,7, clean-up: no 2,5 in R9C1 (step 2f)
13b. 2 on D/ locked in R1C9 + R3C7, locked for N3
13c. 19(4) cage = {2359/2368} -> R12C9 = [23], R1C78 = [59/68/86], no 5 in R1C8

14. Naked pair {14} in R2C8 + R3C7, locked for N3 and D/ -> R9C1 = 7, placed for D/, R7C2 = 9, R3C2 = 2 (step 4), R8C3 = 2 (step 7), R8C8 = 4, R7C7 = 2, R2C8 = 1, R3C7 = 4, R2C7 = 7 (step 11), clean-up: no 6 in R3C5, no 8 in R7C3 + R8C2
14a. Naked pair {39} in R89C7, locked for N9
14b. Naked pair {36} in R7C3 + R8C2, locked for N7 and D/
14c. Naked pair {58} in R4C6 + R6C4, locked for N5
14d. Naked pair {67} in R4C4 + R6C6, locked for D\
14e. Naked pair {58} in R2C2 + R3C3, locked for N1

15. 1 in N7 locked in R78C1, locked for C1
15a. R1C3 = 1 (hidden single in N1), R2C3 = 9 (step 12a), R23C1 = [46], R1C2 = 7, clean-up: no 8 in R3C89 (step 3)
15b. R2C3 = 9 -> R23C4 = 3 = [21]
15c. Naked pair {59} in R3C89, locked for R3 and N3 -> R3C3 = 8, R2C2 = 5, R3C5 = 7, R2C5 = 6, R23C6 = [83], R4C6 = 5, R6C4 = 8

16. R456C1 = {289} (only remaining combination), locked for C1 and N4
16a. Naked pair {15} in R78C1, locked for N7 -> R9C23 = [84]

17. 11(3) cage at R3C2 (step 7a) = {236} (only remaining combination), R4C23 = {36}, locked for R4 and N4 -> R4C4 = 7, R6C6 = 6

18. 45 rule on R8 3 remaining innies R8C129 = 19 = {568} (only remaining combination) -> R78C1 = [15], R8C29 = [68], R7C3 = 3, R4C23 = [36]
18a. Naked pair {39} in R8C47, locked for R8 -> R8C56 = [17], R7C6 = 4

19. R345C9 = {579} (only remaining combination) = [597], R3C8 = 9, R4C78 = 9 = [18]

and the rest is naked singles