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I had this Assassin ready after a couple of minutes but I decided to play around with the larger cages and I came up with those three U-cages and the middle unholy cross.
Don't let it disctract you from solving!

Assassin 109



3x3::k:3072:2305:2305:2305:3332:5637:5637:5637:3080:3072:5130:5131:5131:3332:2830:2830:2320:3080:5130:5130:2068:5131:3332:2830:3096:2320:2320:4379:6684:2068:6684:8991:5664:3096:5664:4387:4379:6684:6684:6684:8991:5664:5664:5664:4387:4379:3630:3630:8991:8991:8991:2099:2099:4387:3126:3126:3630:7481:8991:7481:2099:3389:3389:3126:4160:4160:7481:7481:7481:6213:6213:3389:4160:4160:6218:6218:6218:6218:6218:6213:6213:

Solution:

4 2 1 6 3 5 9 8 7
8 9 7 4 2 1 3 6 5
6 5 3 9 8 7 4 2 1
1 6 5 3 7 2 8 4 9
9 8 4 5 1 6 7 3 2
7 3 2 8 4 9 1 5 6
5 4 9 7 6 3 2 1 8
3 1 6 2 9 8 5 7 4
2 7 8 1 5 4 6 9 3

SS Score (v3.2): 1.17
Estimated rating: Easy 1.25.

Hi Afmob,

Thanks for an enjoyable little puzzle! Used a trick near the start (step 4a) that may not appeal to all (sorry, folks, just couldn't resist it... ).

Estimated rating: 1.0 (with trick)

Edit: Thanks to Andrew for a couple of corrections!

_________________
Cheers,
Mike

Thanks Afmob for letting me have the time to solve this puzzle and post my WT first. I hope that you will now post your WT since it's clearly different from mine.

Although I don't use URs, I've got no problem with other people using them except, possibly, in a "tag" solution where I'm also taking part. It was a very neat trick, probably not too hard to spot for those who use URs, because the R12C1 and R12C9 cages both have the same total, and made the solution a lot quicker. Mike's rating is clearly correct, assuming that the use of UR can be considered part of a 1.0 rating; I'm not sure about that.

This was my first Assassin since returning from our holiday. Maybe that's why I found it a bit harder than the estimated rating. I was stuck for a while after step 20 before spotting my breakthrough moves in steps 21 and 23. I'll rate it as Hard 1.25 the way I solved it. I'm not sure whether Ed will accept that rating since in previous off-forum discussions he's suggested my ratings when I've used combined cages were possibly a bit too low.

Here is my walkthrough. Afmob has commented that my steps 10b,c and 15a,b,c were complicated. Originally I just used steps 10 and 15 to reduce R2C3 to {47} and R2C7 to {37}, then while stuck at step 20 I noticed the clashes in C3 and C7 and felt that I ought to rework those steps. Steps 10b,c probably don't contribute anything to the solution but steps 15a,b,c make step 16 simpler. The clashes in steps 10 and 15 can be ignored if one replaces step 16 by innies-outies for N3 which also deletes 7,8 from R1C6; that was how I originally did that step. I would still rate A109 at Hard 1.25 on this alternative way.

Prelims

a) R12C1 = {39/48/57}, no 1,2,6
b) R12C9 = {39/48/57}, no 1,2,6
c) R34C3 = {17/26/35}, no 4,8,9
d) R34C7 = {39/48/57}, no 1,2,6
e) R1C234 = {126/135/234}, no 7,8,9
f) R1C678 = {589/679}, 9 locked for R1, clean-up: no 3 in R2C1, no 3 in R2C9
g) 20(3) cage at R2C2 = {389/479/569/578}, no 1,2
h) 20(3) cage at R2C3 = {389/479/569/578}, no 1,2
i) 11(3) cage at R2C6 = {128/137/146/236/245}, no 9
j) 9(3) cage in N3 = {126/135/234}, no 7,8,9
k) 8(3) cage at R6C7 = {125/134}, CPE no 1 in R5C7

1. 45 rule on R123 2 outies R4C37 = 13 = [58/67], clean-up: R3C3 = {23}, R3C7 = {45}
1a. 1 in N1 locked in R1C23, locked for R1
1b. R1C234 = {126/135}, no 4
1c. Killer pair 5,6 in R1C234 and R1C678, locked for R1, clean-up: no 7 in R2C1, no 7 in R2C9

2. 45 rule on N7 2 innies R79C3 = 17 = {89}, locked for C3 and N7
2a. 14(3) cage at R6C2 = {149/158/239/248} (cannot be {167/257347/356} because R7C3 only contains 8,9), no 6,7
2b. R7C3 = {89} -> no 8,9 in R6C2

3. 45 rule on N9 2 innies R79C7 = 8 = [17/26/35/53]

4. 45 rule on N3 2 outies R1C6 + R4C7 = 1 innie R2C7 + 10
4a. Max R1C6 + R4C7 = 17 -> max R2C7 = 7
4b. Min R1C6 + R4C7 = 12 -> min R2C7 = 2

5. 1 in N3 locked in 9(3) cage = {126/135}, no 4

6. R9C34567 = {12579/12678/13479/13569/13578/14568/23469/23478/23568} (cannot be {12489} because R9C7 only contains 3,5,6,7, cannot be {24567} because R9C3 only contains 8,9)
6a. R9C3 = {89} -> no 8,9 in R9C456

7. 45 rule on R789 3 innies R7C357 = 17 = {179/269/278/359/368/458} (cannot be {467} because R7C3 only contains 8,9)
7a. R7C3 = {89} -> no 8,9 in R7C5
7b. 1,2 of {179/269/278} must be in R7C7 -> no 1,2 in R7C5

8. 35(6) cage at R4C5 = {146789/236789/245789/345689}, 8,9 locked for N5

9. 4 in R1 locked in R1C159
9a. 45 rule on R1 3 innies R1C159 = 14 = {248/347}
9b. 2 of {248} must be in R1C5 -> no 8 in R1C5

10. 45 rule on N1 4 innies R1C23 + R23C3 = 13 = {1237/1246/1345}
10a. 4,7 only in R2C3 -> R2C3 = {47}
10b. {1246} must be [6142] (cannot be [1642] because R1C3 = 6 clashes with R34C3 = [26]), no 6 in R1C3
10c. {1345} must be [5143] (cannot be [1543] because R1C3 = 5 clashes with R34C3 = [35]), no 5 in R1C3

11. 20(3) cage at R2C3 = {479/578} (cannot be {389/569} because R2C3 only contains 4,7), no 3,6, CPE no 7 in R2C56

12. 20(3) cage at R2C2 = {389/569/578}, cannot be {479} which clashes with R2C3), no 4
[I had missed that {479} clashes with R12C1 after the Prelims]

13. 14(3) cage at R6C2 = {149/158/239/238} (step 2a)
13a. 8(3) cage at R6C7 = {125/134}
13b. 5 of {125} must be in R6C78 (R6C78 cannot be {12} which clashes with R6C23), no 5 in R7C7, clean-up: no 3 in R9C7 (step 3)

14. 45 rule on R789 3 innies R7C357 (step 7) = {179/269/278/359/368} (cannot be {458} because R7C7 only contains 1,2,3), no 4
14a. 5,6,7 only in R7C5 -> R7C5 = {567}

15. 45 rule on N3 4 innies R1C78 + R23C7 = 24 = {3489/3579/4578} (cannot be {2589/4569} which clashes with R12C9, cannot be {2679/3678} because R3C7 only contains 4,5), no 2,6
15a. {3489} must be [9834] (cannot be [8934] because R1C7 = 8 clashes with R34C7 = [48])
15b. {3579} must be [9735] (cannot be [7935] because R1C7 = 7 clashes with R34C7 = [57])
15c. {4578} must be [5874] (cannot be {78}{45} because R1C78 cannot be {78} which clashes with the combinations for R1C678, cannot be [8574] because R1C7 = 8 clashes with R34C7 = [48])
15d. -> R1C7 = {59}, R1C8 = {78}, R2C7 = {37}

16. R1C678 = {589/679}
16a. R1C8 = {78} -> no 7,8 in R1C6

17. 9(3) cage in N3 = {126} (cannot be {135} which clashes with R1C78 + R23C7), no 3,5
[Alternatively 2,6 in N3 locked in 9(3) cage = {126}]

18. 11(3) cage at R2C6 = {137/236} (cannot be {128/146/245} because R2C7 only contains 3,7), no 4,5,8, CPE no 3 in R2C5

19. 45 rule on R789 4 outies R6C2378 = 1 innie R7C5 + 5
19a. R7C5 = {567} -> R6C2378 = 10,11,12 = {1234/1235/1245}, 1,2 locked for R7

20. Hidden killer pair 1,2 in R6C2378 for R6, R6C23 contains one of 1,2 (step 2a) -> R6C67 must contain one of 1,2
20a. R6C78 cannot be {13/23} because cannot form 8(3) cage (no 4 in R7C7) -> no 3 in R6C78

21. Combined cage R1C1 + R23C12 = 32(5) = {35789/45689}, 5 locked for N1

22. R1C234 = {126/135} (step 1b)
22a. 5 of {135} must be in R1C4 -> no 3 in R1C4

23. 45 rule on N2 2 innies R1C46 = 2 outies R2C37 + 1
23a. R1C46 cannot total 12 -> R2C37 cannot total 11 -> no 4 in R2C3
23b. R2C3 = 7, R2C7 = 3, clean-up: no 5 in R1C2, no 9 in R2C9, no 1 in R3C6 (step 18)
23c. R1C46 = 11 (step 23) = [29/56/65]
23d. 3 in N2 locked in R13C5, locked for C5
23e. R123C5 = 3{19/28/46}, no 5,7

24. R3C6 = 7 (hidden single in R3), R2C6 = 1 (step 18), clean-up: no 9 in R23C5 (step 23e)

25. R1C7 = 9 (hidden single in N3)

26. 9 in N2 locked in R23C4, locked for C4
26a. 20(3) cage at R2C3 (step 11) = {479} (only remaining combination), no 5,8, 4 locked for C4 and N2, clean-up: no 6 in R23C5 (step 23e)

27. Naked triple {238} in R123C5, locked for C5 and N2
27a. Naked pair {56} in R1C46, locked for R1
27b. Naked triple {123} in R1C23 + R3C3, locked for N1, clean-up: no 9 in R2C9
27c. Naked pair {48} in R12C1, locked for C1 and N1

28. R456C1 = {179/269/359}, 9 locked for C1 and N4

29. R3C5 = 8 (hidden single in R3), R12C5 = [32], R3C3 = 3 (hidden single in R3), R4C3 = 5, R4C7 = 8 (step 1), R3C7 = 4, R23C4 = [49], R2C1 = 8, R1C1 = 4, R2C89 = [65], R2C2 = 9, R1C9 = 7, R1C8 = 8, R1C6 = 5 (step 16), R1C4 = 6, clean-up: no 3 in R456C1 (step 28)

30. R5C2 = 8 (hidden single in C2)

31. R456C9 = {269} (only remaining combination), locked for C9 and N6 -> R3C89 = [21]
31a. Naked triple {348} in R789C9, locked for N9

32. 8(3) cage at R6C7 = {125} (only remaining combination), no 4
32a. R7C7 = 2, R9C7 = 6 (step 3)
32b. Naked pair {15} in R6C78, locked for R6 and N6 -> R5C7 = 7
32c. Naked pair {34} in R45C8, locked for 22(5) cage
32d. Naked pair {26} in R45C6, locked for C6 and N5

33. 14(3) cage at R6C2 (step 2a) = {239/248}, 2 locked for N4, clean-up: no 6 in R456C1 (step 28)
33a. Naked triple {179}in R456C1, locked for C1 and N4
33b. 2 in C1 locked in R89C1, locked for N7

34. 13(3) cage in N9 = {148} (only remaining combination, cannot be {139/157} because 1,7,9 only in R7C8) -> R7C8 = 1, R78C9 = {48}, locked for C9 -> R8C7 = 5, R9C9 = 3, R9C6 = 4, R6C78 = [15]

35. R9C3 = 8 (hidden single in R9), R9C45 = {15} (step 6), locked for R9 and N8 -> R9C12 = [27], R89C8 = [79], R7C3 = 9

36. 12(3) cage in N7 = {345} (only remaining combination) -> R8C1 = 3

and the rest is naked singles and a cage sum

Now to catch up on other puzzles that have been posted since we went on holiday. Fortunately they have all had lower ratings than this one except for Ed's recently posted A110X V2. I probably won't post any walkthroughs for those puzzles, unless I come up with anything significantly different, but I hope to solve them all.

Even though I'm not a fan of uniqueness moves, I have to admit that Mike's step 4a was quite neat. As you can see in my walkthrough, you only need to focus on one area to crack this killer and Andrew and Mike also had their main steps in R123.

A109 Walkthrough:

1. R123
a) Innies = 7(2) = [25/34]
b) 1 locked in 9(3) @ N1 = 1{26/35}; R1C4 <> 1 and 1 locked for R1
c) 4 locked in Innies R1 = 4{28/37};
d) Both 12(2) @ R1: R2C19 <> 3,7
e) 2 locked in Innies N1 = 13(4) = 12{37/46} must have one of (47) and it's only possible @ R2C3
-> R2C3 = (47)
f) 20(3) @ N2 = 7{49/58} because R2C3 = (47);
g) 8(2) = [26/35]
h) 12(2) @ R3 = [48/57]
i) 9(3): R1C4 <> 3 because R1C23 <> 5

2. R123 !
a) ! 9(3) can only have one (345) because two of (345) @ N3 must be @ R3C7 and 12(2) @ C9
-> 9(3) = {126} locked for N3
b) 22(3): R1C6 <> 7 because 6 only possible there
c) ! Innies+Outies N2: -1 = R2C37 - R1C46; R2C3 = (47):
- R2C7 <> 4,7 because R1C46 cannot be 12(2)
d) 7 locked in R1C789 @ N3 for R1
e) 12(2) @ N1 <> 5
f) 5 locked in 20(3) @ R2C2 @ N1 = 5{69/78}
g) Innies R1 = 14(3): R1C9 <> 3 because 7 only possible there
h) 12(2) @ C9 <> 9
i) Hidden Single: R2C7 = 3 @ N3
j) Killer pair (45) locked in 12(2) @ C9 + R3C7 for N3

3. R123
a) 5 locked in R1C46 @ R1 for N2
b) 20(3) @ N2 = {479} -> 9 locked for C4+N2
c) 22(3) must have one of (56) and it's only possible @ R1C6 -> R1C6 <> 8
d) 11(3) = 3{17/26}
e) 8 locked in 13(3) @ N2 = 8{14/23} -> 8 locked for C5
f) Killer pair (12) locked in 13(3) @ 11(3) for N2
g) 9(3): R1C23 <> 6 because R1C4 >= 5
h) Innies N1 = 13(4) = {1237} -> R2C3 = 7; 3 locked for N1
i) Hidden Single: R3C6 = 7 @ N2 -> R2C6 = 1
j) 13(3) = {238} locked for C5

4. R123
a) 12(2) @ R1C1 = {48} locked for C1+N1
b) Hidden Single: R3C5 = 8 @ R3, R3C3 = 3 @ R3 -> R4C3 = 5
c) 9(3) @ N1 = {126} -> R1C4 = 6
d) 22(3) = {589} -> R1C6 = 5; 8 locked for R1+N3
e) 12(2) @ C9 = {57} -> R1C9 = 7, R2C9 = 5
f) R3C7 = 4 -> R4C7 = 8

5. C789
a) 17(3) = {269} locked for C9+N6
b) 8(3) = {125} because R67C7 <> 3,4 -> R7C7 = 2, {15} locked for R6+N6
c) Innies N9 = R9C7 = 6
d) R3C9 = 1
e) 13(3) = {148} because R78C9 = (348) -> R7C8 = 1, {48} locked for N9
f) 22(5) = {23467} -> R5C7 = 7, 3 locked for C8, R45C6 = {26} locked for C6+N5

6. N47
a) Innies N7 = 17(2) = {89} locked for C3+N7
b) 14(3) = 2{39/48} because R7C3 = (89) -> 2 locked for R6+N4; R6C2 <> 8,9
c) 17(3) = {179} locked for C1+N4

7. N579
a) 35(6) = 4689{17/35} -> R7C5 = 6; {48} locked for N5
b) 26(5) = 468{17/35} -> R5C2 = 8; 4 locked for N4
c) R6C3 = 2, R6C2 = 3 -> R7C3 = 9
d) R9C3 = 8, R9C9 = 3
e) 24(5) = 168{27/45} -> 1 locked for R9+N8
f) 35(6) = {146789} -> 1,7 locked for N5 and 1 also locked for C5

8. Rest is singles.

Rating: 1.25. I used a Killer triple which can also be seen as a cage blocker.