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I found this one easier than recent Assassins which have generally gone up a notch for me. It is still a really nice challenge. If anyone wants to make a harder version out of this interesting cage pattern, please go ahead. Of course, we need someone to claim A163 first.

Assassin 162


SSscore: 1.30

Cheers
Ed

Thanks for the new Assassin Ed! I took me a while to find the important moves but after that it was just a matter of finishing it fast.

A162 Walkthrough:

1. R789 !
a) Innies N7 = 8(2) <> 4,8,9; R7C3 <> 6
b) 4 locked in 14(3) @ N7 = 4{19/28/37} <> 5,6 -> 4 locked for R8
c) 5 locked in Innies N7 + 8(2) -> One of them must be {35} -> 3 locked
in 8(2) + Innies N7 for N7
d) 14(3) <> 7
e) ! Innies+Outies R8: -7 = R7C4 - R8C56 -> R8C56 <> 7 (IOU @ N8)
f) ! Innies+Outies R8: -8 = R7C6 - R8C45 -> R8C45 <> 8 (IOU @ N8)
g) Innies R8 = 16(3) = 6{19/37} since {259} blocked by Killer pair (29) of 14(3)
-> 6 locked for R8+N8
h) 15(3) = 5{19/28/37} -> 5 locked for N9
i) 9(2) = [27/36/81]
j) 8(2) @ N8: R7C6 <> 1,3

2. R789 !
a) 2 locken in R7C46 @ N8 for R7
b) 4,9 locked in 43(8) @ N8 for 43(8)
c) Innies N7 = 8(2) <> 6
d) Innies N9 = 9(2) = [18/36/63]
e) Outies N8 = 15(3): R6C5+R9C3 <> 3 since R9C7 <> 5,7
f) Innies N7 = 8(2): R7C3 <> 5
g) ! Outies R9 = 17(3): R7C5 <> 5 since R6C5 <> 3,9 and R8C5 <> 4,8
h) Hidden Single: R7C6 = 5 @ R7 -> R8C6 = 3, R7C4 = 2 @ R7 -> R8C4 = 7, R8C5 = 6 @ N8
i) Outies N8 = 15(3) = {357} -> R9C7 = 3; CPE: R6C3 <> 5,7

3. R789
a) Innie N9 = R7C7 = 6
b) 10(2) = {19} locked for R7+N9
c) Innies N7 = 8(2) = {35} -> R7C3 = 3, R9C3 = 5
d) 9(3) = {126} -> 1,2 locked for C7+N6
e) 12(3) = [18/72/81]3
f) R6C5 = 7

4. N5
a) 4 locked in 29(5) @ N5 = 489{26/35} -> 8,9 locked for N5
b) 1 locked in R4C456 @ N5 for R4+41(8)

5. N235 !
a) ! Innies+Outies N3: 2 = R3C6+R45C8 - R2C7: R3C6 = (12), R45C8 <> 8,9 and R2C7 <> 4,5 since R45C8 >= 3
b) 7 locked in 17(3) @ C6 for 17(3) -> 17(3) = 7{19/28} since R2C7 = (89)
c) 17(3): R12C6 <> 8,9 since R2C7 = (89)
d) Killer pair (12) locked in 17(3) + R3C6 for C6+N2
e) R4C6 = 6
f) 29(5) = {34589} locked N5
g) 41(8) must have 3,7 -> 3 locked for C5+N2; 7 locked for R4
h) 11(3) = 4{16/25} since R12C4 <> 1,2 -> R2C3 = (12); 4 locked for C4
i) ! Innies R1 = 18(3) = {567} since R1C6 = (127) and R1C4 = (456) -> R1C6 = 7, R1C5 = 5, R1C4 = 6
j) R2C4 = 4 -> R2C3 = 1, R2C6 = 2 -> R2C7 = 8

6. C123
a) 19(3) = {289} locked for R1+N1
b) 12(3) = {237} -> R5C3 = 7, R6C3 = 2
c) Hidden Single: R3C3 = 6 @ C3
d) Innie N1 = R3C2 = 4
e) 26(5) = {34568} -> R3C4 = 8; 3,5 locked for C2+N4
f) R6C7 = 1
g) 20(4) = {1469} -> R5C1 = 1; 6 locked for R6, 9 locked for N4
h) R4C3 = 8, R2C2 = 7

7. C789
a) Innies N3 = 11(2) = {29} -> R3C7 = 9, R3C8 = 2
b) R8C7 = 5, R8C8 = 8
c) Hidden Single: R3C9 = 7 @ N3
d) 11(2) = {47} -> R9C9 = 4, R9C8 = 7
e) R8C9 = 2, R1C3 = 9, R8C3 = 4, R8C1 = 9

8. R456
a) R4C1 = 4, R6C1 = 6, R6C2 = 9, R4C4 = 1, R9C4 = 9, R9C6 = 8, R6C6 = 4
b) 26(4) = {3689} -> R6C8 = 3, R4C9 = 9, R6C9 = 8, R5C9 = 6

9. Rest is singles.

Rating: (Hard?) 1.0. I used IOU.

Thanks Ed. As you said a bit easier than some recent Assassins but still a good challenge.

I used CCCs for the early breakthrough in step 6 having seen another CCC in step 5. If I hadn't seen that first CCC I might have seen those breakthroughs with IOUs as in Afmob's WT; both ways gave the same result. Then I had to work hard until I found steps 23 and 25, after which the puzzle was cracked.

I'm happy to do that until further notice Ed; we wouldn't want to lose you from the forum.


Here is my walkthrough. I think there are a few places where I've omitted clean-ups because they are done by a sub-step immediately after.

Prelims

a) R7C12 = {69/78}
b) R78C4 = {18/27/36/45}, no 9
c) R78C6 = {17/26/35}, no 4,8,9
d) R7C89 = {19/28/37/46}, no 5
e) R9C12 = {17/26/35}, no 4,8,9
f) R9C89 = {29/38/47/56}, no 1
g) R1C123 = {289/379/469/478/568}, no 1
h) 11(3) cage at R1C4 = {128/137/146/236/245}, no 9
i) R1C789 = {125/134}, 1 locked for R1 and N3
j) R567C7 = {126/135/234}, no 7,8,9
k) 26(4) cage in N6 = {2789/3689/4589/4679/5678}, no 1
l) 41(8) cage at R1C5 = {12356789}, no 4
m) 43(8) cage at R6C5 = {13456789}, no 2

[There are immediate “tricky” moves R78C4 cannot be {36} and R78C6 cannot be {17}, each of which blocks the placement of 2 in N8. I’ve managed to avoid using them.]

1. 9 in N8 locked in 43(8) cage at R6C5, no 9 in R6C5 + R9C37

2. 45 rule on N1 3 innies R2C3 + R3C23 = 11 = {128/137/146/236/245}, no 9

3. 45 rule on N7 2 innies R79C3 = 8 = {17/35}/[26], no 4,8, no 6,9 in R7C3
3a. Killer triple 5,6,7 in R7C12, R79C3 and R9C12, locked for N7
3b. 4 in N7 locked in R8C123, locked for R8, clean-up: no 5 in R7C4
3c. R8C123 = {149/248}, no 3

4. 45 rule on N9 2 innies R79C7 = 9 = [18/27]/{36/45}, no 1 in R9C7

5. R56C3 cannot contain 4 because the other two cells of R567C3 would total 8 and therefore give a CCC with R79C3
[Ed pointed out that this step might be easier as 45 rule on N7 2 outies R56C3 = 1 innie R9C3 + 4, IOU no 4 in R56C3 but commented that this was a hard IOU to spot. Note that the similar 45 rule on N9 gives IOU no 0 in R56C7! ]

6. 45 rule on R8 3 innies R8C456 = 16 = {169/367} (cannot be {178/259} which clash with R8C123, cannot be {268/358} because of CCC with R78C6), no 2,5,8, 6 locked for R8 and N8 clean-up: no 1,4,7 in R7C4, no 3 in R7C6, no 3 in R8C4
6a. 7 of {367} must be in R8C4 (6 of {367} cannot be in R8C4 because of CCC with R78C4), no 7 in R8C56, clean-up: no 1 in R7C6
6b. {169} can only be [196] (cannot be [691] because cannot place 2 in N8), no 6 in R8C4, no 1 in R8C56, clean-up: no 3 in R7C4, no 7 in R7C6
6c. 2 in N8 locked in R7C46, locked for R7, clean-up: no 8 in R7C89, no 6 in R9C3 (step 3), no 7 in R9C7 (step 4)

7. 5 in R8 locked in R8C789, locked for N9, clean-up: no 4 in R79C7 (step 4), no 6 in R9C89

8. 45 rule on R9 3 outies R678C5 = 17 = {179/359/368/467} (cannot be {458} because R8C5 only contains 3,6,9)
8a. 8 of {368} must be in R7C5 (R78C5 cannot be {36} which clashes with R8C6), no 8 in R6C5

9. Hidden killer pair 5,6 in 43(8) cage at R6C5 and R78C6 for N8 -> 43(8) cage at R6C5 must contain one of 5,6 within N8 -> 43(8) cage at R6C5 must contain one of 5,6 in R6C5 + R9C37
9a. 45 rule on N8 3 outies R6C5 + R9C37 (which are common peers because they are part of the 43(8) cage at R6C5) = 15 = {168/357} (cannot be {348} which doesn’t contain one of 5,6, cannot be {456} which contains both of 5,6), no 4
9b. {168} can only be [618], no 1 in R6C5, no 6 in R9C7, clean-up: no 3 in R7C7 (step 4)
9c. 3 of {357} must be in R9C7 -> no 3 in R6C5 + R9C3, clean-up: no 5 in R7C3 (step 3)
9d. 5 in R7 locked in R7C56, locked for N8
9e. R9C89 = {29/47} (cannot be {38} which clashes with R9C7), no 3,8

10. 6 in R9 locked in R9C12 -> R9C12 = {26}, locked for R9 and N7, clean-up: no 9 in R7C12, no 9 in R9C89
10a. Naked pair {78} in R7C12, locked for R7 and N7 -> R7C46 = [25], R8C4 = 7, R8C6 = 3, clean-up: no 1 in R79C3 (step 3)
10b. R79C3 = [35]
10c. Naked pair {47} in R9C89, locked for R9 and N7, clean-up: no 6 in R7C89
10d. Naked triple {189} in R9C456, locked for 43(5) cage at R6C5 -> R78C5 = [46], R6C5 = 7, R9C7 = 3, R7C7 = 6 (step 4)
10e. Naked pair {19} in R7C89, locked for N9
10f. 5 in N2 locked in R123C45, CPE no 5 in R4C4
10g. 7 in 41(8) cage at R1C5 locked in R4C37, locked for R4
10h. 6 in 41(8) cage at R1C5 locked in R4C346, locked for R4

11. R7C7 = 6 -> R56C7 = 3 = {12}, locked for C7 and N6

12. R7C3 = 3 -> R56C3 = 9 = [18/72/81], no 6,9, no 2 in R5C3

13. 45 rule on N5 3 remaining innies R4C456 = 9 = {126/135}, no 8,9, 1 locked for R4, N5 and 41(8) cage at R1C5

14. 4 in C7 locked in R123C7, locked for N3
14a. R1C789 = {125/134}
14b. 5 of {125} must be in R1C7 -> no 5 in R1C89

15. 45 rule on R1 3 innies R1C456 = 18 = {369/378/468/567} (cannot be {279} because no 2,7,9 in R1C4, cannot be {459} which clashes with R1C7), no 2
15a. 7 of {378} must be in R1C6, 8 of {468} must be in R1C5 -> no 8 in R1C6
15b. 5 of {567} must be in R1C5 -> no 5 in R1C4

16. 11(3) cage at R1C4 = {128/137/146/236/245}
16a. 8 of {128} must be in R1C4 -> no 8 in R2C34

17. 17(3) cage at R1C6 = {179/269/278/467} (cannot be {458} which can only be [485] and clashes with R1C7), no 5
17a. 1,2 of {179/269/278} must be in R2C6 -> no 8,9 in R2C6

18. 45 rule on N3 3 innies R2C7 + R3C78 = 19 = {289/379/469/478/568}
18a. 2,3,6 of {289/379/469/568} must be in R3C8 -> no 5,9 in R3C8

19. 45 rule on N4 3 remaining innies R4C23 + R5C2 = 16 = {169/259/349/358/367/457} (cannot be {178/268} which clash with R56C3)
19a. 8 of {358} must be in R4C3 -> no 8 in R45C2

20. 45 rule on N6 3 remaining innies R4C78 + R5C8 = 16 = {349/358/367/457}
20a. 9 of {349} must be in R4C7 -> no 9 in R45C8
20b. 7 of {367/457} must be in R4C7 (R45C8 cannot be {47} which clashes with R9C8), no 7 in R5C8

21. R2C3 + R3C23 (step 2) = {128/146/236/245} (cannot be {137} because R23C3 = {17} clashes with R56C7), no 7
21a. 8 of {128} must be in R3C3 (R3C12 cannot be {12} which clashes with R56C3), no 8 in R3C2

22. R1C123 = {289/379/469/478} (cannot be {568} which clashes with R1C456), no 5

23. All combinations for 21(5) cage at R3C6 contain 1 except for {23457}
23a. 1 only in R3C6, 2 of {23457} must be in R3C6 (R3C8 cannot be 2 because max R2C7 + R3C78 = [972] would be less than 19) -> R3C6 = {12}

24. 7 in C6 locked in R12C6, locked for 17(3) cage at R1C6, no 7 in R2C7
24a. 17(3) cage (step 17) = {179/278/467}
24b. 4,9 of {179/467} must be in R2C7 -> no 4,9 in R12C6
24c. 4 in C6 locked in R56C6, locked for N5

25. 45 rule on N3 3 outies R3C6 + R45C8 (which are common peers because they are part of the 21(5) cage at R3C6) = 1 innie R2C7 + 2
25a. Min R3C6 + R45C8 = 8 -> no 4 in R2C7
25b. Max R2C7 = 9 -> max R3C6 + R45C8 = 11 -> max R45C8 = 10, no 8

26. R4C78 + R5C8 (step 20) = {349/358/367/457}
26a. 7,8,9 only in R4C7 -> R4C7 = {789}

27. 17(3) cage at R1C6 (step 24a) = {179/278}, no 6 -> R1C6 = 7
27a. Naked pair {12} in R23C6, locked for C6 and N2 -> R4C6 = 6
27b. R4C456 (step 13) = {126} -> R4C45 = [12]
27c. 3,5 in 41(8) cage at R1C5 locked in R123C5, locked for C5 and N2
27d. R9C5 = 1 (hidden single in C5)

28. 11(3) cage at R1C4 = {146} (only remaining combination, cannot be {128} because 1,2 only in R2C3) -> R2C3 = 1, R12C4 = {46}, locked for C4, R23C6 = [21], R2C7 = 8 (step 27), R8C7 = 5, R1C7 = 4, R12C4 = [64], clean-up: no 2 in R1C89 (prelim i), no 8 in R56C3 (step 12)
28a. R56C3 = [72], R56C7 = [21]
29. R4C7 = 7 (hidden single in R4), R3C7 = 9, R3C8 = 2 (step 18), R3C4 = 8, R9C46 = [98], R8C89 = [82]
29a. R5C5 = 8 (hidden single in C5)

30. Naked pair {13} in R1C89, locked for R1 and N3
30a. Naked triple {289} in R1C123, locked for R1 and N1 -> R1C5 = 5, R23C5 = [93], R4C3 = 8, R1C3 = 9, R8C3 = 4, R3C3 = 6, R3C2 = 4 (step 21)

31. 45 rule on N1 2 remaining outies R45C2 = 8 = {35} (only remaining combination), locked for C2 and N4 -> R2C2 = 7, R7C12 = [78], R1C12 = [82], R9C12 = [26], R6C2 = 9, R456C1 = [416], R23C1 = [35], R3C9 = 7, R9C89 = [74], R56C6 = [94]

32. R5C8 = 4 (hidden single in R5), R4C8 = 5 (cage sum)

and the rest is naked singles.