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3x3::k:8449:1538:1538:4355:4355:4355:2308:2308:6661:8449:8449:5894:5894:4355:6663:6663:6661:6661:3592:8449:5894:5894:1289:6663:6663:6661:4362:3592:8449:8449:4107:1289:6668:6661:6661:4362:3592:3853:4107:4107:5134:6668:6668:5391:4362:3853:3853:2832:4107:5134:6668:3345:5391:5391:3853:3346:2832:4883:5134:4372:3345:3093:5391:4630:3346:4883:4883:5143:4372:4372:3093:2072:4630:4630:4883:5143:5143:5143:4372:2072:2072:

I didn't think that I was the first to post a walkthrough for this assassin since it's quite late .
This killer was strange since it took me a long time to find the key moves although they were quite easy to see (step 5a, 8a).

Note that step 5a could be applied right after step 1a though in a different form and probably more easier way:

(Triple click to see)


A86 Walkthrough:

1. C6789
a) Outies C89 = 3(2) = {12} locked for C7
b) 9(2) = [18/27]
c) Innies = 5(2) = {14/23}
d) 8(3) = 1{25/34} -> 1 locked for N9

2. R1+C56
a) Killer pair (12) locked in 6(2) + 9(2) for R1
b) 17(4) must have 1 or 2 and it's only possible @ R2C5 -> R2C5 = (12)
c) Innies+Outies R1: -13 = R2C5 - R1C19 -> R1C19 <> 3,4
d) 3 locked in R1C456 @ 17(4) for N2
e) 5(2): R4C5 <> 2
f) Killer pair (12) locked in R2C5 + 5(2) for C5
g) 2 locked in R23C5 for N2
h) Innies C6789 = 5(2): R9C6 = (12)
i) Killer pair (12) locked in 17(4) @ N8 + R9C6 for C6+N8
j) 2 locked in 16(4) @ C4 -> R5C3 <> 2

3. C1234
a) Outies C12 = 9(2) -> R4C3 = (4578)
b) Innies C1234 = 12(2) <> 6
c) Innies N7 = 14(4) <> 9
d) 11(2): R6C3 <> 2

4. R789
a) Outies R89 = 17(4) must have 1 or 2 and it's only possible @ R7C6 -> R7C6 = (12)
b) Naked pair (12) locked in R79C6 for C6
c) 17(4) <> 12{59/68} since (12) only possible @ R7C6
d) Innies N9 = 25(4) <> 2 because R89C7 @ 17(4) can't have two of (689)
e) 2 locked in 8(3) -> 8(3) = {125} locked for N9
f) 12(2) <> 7
g) 13(2): R6C7 <> 8
h) Naked triple (125) locked in R9C689 for R9
i) 5 locked in R9C89 for N9

5. C89 !
a) ! R2C9+R23C8 @ 26(6) <> 1,2 because together with 8(3) = {125} 26(6) would build
a generalized X-Wing for C89 which would leave no 1,2 @ N6
b) 1 locked in 26(6) for R4+N6
c) Hidden pair (12) locked in R1C7+R3C9 for N3 -> R3C9 = (12)
d) 17(3) = {179/269/278} -> R45C9 <> 2,3,4,5
e) Naked pair (12) locked in R38C9 for C9
f) R9C9 = 5

6. C45
a) 1 locked in R56C4 @ 16(4) for C4; R5C3 <> 1
b) 16(4) = 12{49/58/67} <> 3
c) 5(2): R3C5 <> 4
d) Innies C1234 = 12(2): R1C4 <> 7

7. R123
a) Naked pair (12) locked in R3C59 for R3
b) Innies+Outies R1: -13 = R2C5 - R1C19; R2C5 = (12)
-> R1C19 = 14/15(2) = {59/68/69} <> 7 because {78} blocked R1C8 = (78)
c) 17(4) <> 6 because {1367} impossible since (67) only possible @ R1C5
d) 6 locked in R1C19 -> R1C1 <> 5 (step 7b)

8. C123 !
a) ! R7C1 <> 1 because it sees all 1 of N4
b) 1 locked in R8C13 for R8
c) R8C9 = 2, R9C8 = 1, R9C6 = 2, R7C6 = 1, R3C9 = 1, R1C7 = 2 -> R1C8 = 7

9. R123
a) R3C5 = 2 -> R4C5 = 3
b) 6(2) = {15} locked for R1+N1
c) 17(4) = {1349} -> R2C5 = 1, {49} locked for R1+N2
d) 26(6) = 1256{39/48} -> R4C7 = 1, R4C8 = 2; 5 locked for C8+N3; 6 locked for N3
e) 17(3) = {179} -> 7,9 locked for C9+N6

10. C456
a) Innies C6789 = 5(2) = {23} -> R1C6 = 3
b) Innies C1234 = 12(2) = [48/93]
c) 20(3) <> 4 because {479} blocked by R1C5 = (49)
d) 20(3) = 5{69/78} -> 5 locked for C5

11. C456
a) Outies N3 = 14(2) = {68} locked for C6+N2
b) 26(4) @ N2 = {3689} -> {39} locked for C7+N3
b) 23(4) = 57{29/38} -> 5,7 locked for C4; R23C3 = [29/38/83]
c) 26(4) @ N5 must have 6 xor 8 and it's only possible @ R5C7 -> R5C7 = (68)
d) 17(4) @ N8 = {1457} -> R8C6 = 5, {47} locked for C7+N9
e) 26(4) @ N5 = {4679} -> R5C7 = 6, {479} locked for N5

12. R456
a) 21(4) = {3468} -> R7C9 = 6
b) R6C7 = 5
c) 20(3) = 5{69/78} -> R5C5 = 5
d) 16(4) = {1267} because R456C4 <> 4,9 -> R5C3 = 7
e) Hidden pair (12) locked in R56C4 for N5 -> R56C4 = {12}
f) R4C4 = 6, R6C5 = 8 -> R7C5 = 7

13. N78
a) Outies N8 = 7(2) = [16/34/43]
b) 18(3) <> 4,6 because 6{39/48} blocked by Killer pairs (36,46) of Outies N8
c) 18(3) = 8{19/37} -> 8 locked for N7
d) 13(2) = {49} locked for C2+N7
e) 18(3) = {378} -> 3 locked for N7
f) 15(4) must have 2 xor 5 and it's only possible @ R7C1 -> R56C2+R6C1 <> 2

14. Rest is singles.

Rating: 1.25. This assassin could be solved quite quickly if you find the right moves.

Thanks for getting the thread going, Afmob!

This was a difficult puzzle, because there are 2 critical moves (Afmob's steps 5a and 8a = my steps 1a and 8a) that are difficult to spot. If you don't get both of them, you'll have an exceedingly hard time solving this Assassin!

As if to prove me wrong, Gary has just done it using only the first of these two "critical" moves! He used two advanced moves instead. Well done, Gary!

In that sense, it was similar to my Maverick 2, which also had an extremely narrow initial solving path, except the M2 remained difficult, whereas this puzzle is relatively straightforward (once those 2 critical moves have been found...).

I'm glad Afmob rated this puzzle as 1.25, because that's the rating I was going to give it. However, because of the narrow solving path, some people may find it subjectively harder than that, or have difficulty completing the puzzle at all.


Assassin 86 Walkthrough

Prelims

a) 6(2) at R1C2 = {15/24}
b) 9(2) at R1C7 = {18/27/36/45} (no 9)
c) 26(6) at R1C9 = {1(23479/23569/23578/24568/34567)}
d) 26(4) at R2C6 and R4C6 = {2789/3689/4589/4679/5678} (no 1)
e) 5(2) at R3C5 = {14/23}
f) 20(3) at R5C5 = {389/479/569/578} (no 1,2)
g) 11(2) at R6C3 = {29/38/47/56} (no 1)
h) 13(2) at R6C7 and R7C2 = {49/58/67} (no 1..3)
i) 12(2) at R7C8 = {39/48/57} (no 1,2,6)
j) 8(3) at R8C9 = {125/134}; 1 locked for N9

1. Outies C89: R14C7 = 3(2) = {12}, locked for C7
1a! -> no 1,2 in R23C8+R12C9 (CPE)
1b. cleanup: no 1..6 in R1C8

2. Hidden pair (HP) on {12} at R1C7+R3C9
2a. -> R3C9 = {12}
2b. 17(3) at R3C9 = {179/269/278}
2c. -> R45C9 = {6789}

3. R3C9 and R4C7 must contain the same digit, because they both see R1C7
3a. -> this digit (1 or 2) must be constrained to C8 within N9
3c. -> R9C8 = {12}

4. 6(2) at R1C2 and R1C7 form killer pair (KP) on {12}
4a. -> no 1,2 elsewhere in R1

5. 17(4) at R1C4 = {1349/1358/1367/1457/2348/2357/2456} = {(1/2)..}
(Note: {1259/1268} unplaceable)
5a. {12} only available in R2C5
5b. -> R2C5 = {12}

6. 1 in 26(6) at R1C9 (Prelim c) locked in R4C78 for R4 and N6
6a. cleanup: no 4 in R3C5

7. 1 in N5 locked in C4 -> not elsewhere in C4
7a. no 1 in R5C3

8. 1 in N4 locked in R56C12
8a. -> no 1 in R7C1 (CPE)

9. Hidden single (HS) in R7 at R7C6 = 1

10. Innies C6789: R19C6 = 5(2) = [32] (last combo/permutation)

11. Naked single (NS) at R9C8 = 1
11a. -> R3C9 = 1, R4C7 = 1 (both step 3)
11b. -> R1C78 = [27], R34C5 = [23]
11c. -> R2C5 = 1
11c. cleanup: no 4 in R1C23; no 5 in R78C8

12. split 7(2) at R89C9 = [25] (last combo/permutation)
(Note: {34} blocked by 12(2) at R7C8)
12a. cleanup: no 8 in R6C7

13. 7 unavailable for 26(6) at R1C9 (Prelim c) = {1256(39/48)}
13a. -> killer single (KS) at R4C8 = 2
13b. 5 locked in R23C8 for C8 and N3
13c. 6 locked for N3

14. split 16(2) at R45C9 = {79}, locked for C9 and N6
14a. cleanup: no 4,6 in R7C7

15. Naked pair (NP) at R1C23 = {15}, locked for R1 and N1

16. split 13(2) at R1C45 = {49} (last combo), locked for R1 and N2

17. Outies N3: R23C6 = 14(2) = {68} (last combo), locked for C6, N2 and 26(4)
17a. -> R23C7 = 12(2) = {39} (last combo), locked for C7 and N3
17b. cleanup: no 4 in R6C7

18. 9 in C8/N9 locked in 12(2) at R7C8 = {39} (no 4,8), locked for C8 and N9

19. HS in C9/N6 at R6C9 = 3
19a. cleanup: no 8 in R7C3

20. NP at R23C4 = {57}, locked for C4 and 23(4)
20a. -> R23C3 = 11(2) = [29]/{38}
20b. -> R2C3 = {238}, R3C3 = {389}

21. Split 16(3) at R8C6+R89C7 = {457} (no 6,8,9) (last combo)
21a. -> R8C6 = 5; R89C7 = {47}, locked for C7 and N9

22. R67C7 = [58]
22a. -> R5C7 = 6, R7C9 = 6
22b. cleanup: no 7 in R8C2

23. R12C9 = [84]
23a. -> R1C1 = 6

24. HS in R4 at R4C4 = 6

25. HS in C5/N5 at R5C5 = 5
25a. -> split 15(2) at R67C5 = [87] (last combo/permutation)
25b. cleanup: no 4 in R6C3; no 3 in R7C3; no 6 in R8C2

26. R56C8 = [84]

27. HP in N5 at R56C4 = {12} (no 4,9)
27a. -> R5C3 = 7 (cage sum)
27b. cleanup: no 4 in R7C3

28. R45C9 = [79]

29. R456C6 = [947]

30. 19(4) at R7C4 = {1(369/468)} (all other combos unplaceable)
30a. -> KS at R8C3 = 1

31. R1C23 = [15]
31a. cleanup: no 6 in R6C3

32. HS in C3 at R9C3 = 6 (alternatively, outie N8)

33. Innies N7 = 7(2) = [52] (last combo/permutation)
33a. -> R6C3 = 9
33b. cleanup: no 8 in R8C2

Now it's all just singles and cage sums.

This was a nice puzzle based on a number of killer 1/2 pairs, viz;



1.r7c14=1/2 and with 6(2) cage r1c23 1/2 fixed at r1c237 in r1
2. Thus r3c9=1/2.26(6) must contain a 1 and this must be at r4c7/8.3.In r1 3 must be in N2..cannot go elsewhere.R4C5<>2
4.So r4c5=3/4 and r3c5=1/2.
5.Combo analysis on 17(4) cage N2 -> r2c5 also=1/2.
6.r19c6=5 and r1c6 therefore=3/4 so r9c6=1/2
7.r789c6+r7c9=25 and contains a 6.So cannot also contain a 5.If 5 in the 12(2) cage N9 -> r1c7=1->r3c9=2->r9c8=2..contradiction.Thus the 8(3) cage N9={125}
8.Now if r9c6=1 ->r8c9=1->r3c9=2 ->r1c7=1 then cannot place the 4 (see 6.) at r1c6.So r9c6=2 r8c9=2 and now many placements are possible.
9.r1c19={68}
10.r4c3={48} and so r3c1={48}
11.The 33(6) cage N14 doesn't (after placements) contain a 1.So other two missing digits total 11.Combo analysis shows that this 11 pair must go in r23c3.Thus r23c4=12,r23c6=14 (={68} and it's pretty much all over now.

I'ld rate it about 1.25 again really based on time to complete..not very scientific I'll admit.!!Took me about 1.5 hours.

Regards

Gary

I'll agree with most of that. It took me a very long time to spot my step 2a, which is clearly the key move for this puzzle. Congratulations to Ruud for creating a puzzle that required this key move! I didn't spot the other move that Mike identified. It clearly speeds up the solution, particularly when used with his step 3, but doesn't seem to be critical. In Afmob's walkthrough steps 4a and 4b speeded up the solution.Having spent a lot of time before I found step 2a, I know that it would have been very difficult to solve A86 without that step. Therefore any variant would almost certainly need to provide a similar step or it would risk becoming an Unsolvable.

Here is my walkthrough for A86. Not one of my best. I only modified it as required after finding step 2a. As well as taking a long time to find that step, I'd also taken time to find step 19 and a modified version of step 22, both before I found step 2a.

Thanks Mike for the comments, which I've added below, and for corrections to steps 9 and 22; I've also corrected a typo in step 32a.

Mike's comments about some of my steps, in the later message where he analyses Gary's steps, are appreciated!

Prelims

a) R1C23 = {15/24}
b) R1C78 = {18/27/36/45}, no 9
c) R34C5 = {14/23}
d) R67C3 = {29/38/47/56}, no 1
e) R67C7 = {49/58/67}, no 1,2,3
f) R78C2 = {49/58/67}, no 1,2,3
g) R78C8 = {39/48/57}, no 1,2,6
h) R567C5 = {389/479/569/578}, no 1,2
i) 8(3) cage in N9 = 1{25/34}, 1 locked for N9
j) 26(4) cage at R2C6 = {2789/3689/4589/4679/5678}, no 1
k) 26(4) cage at R4C6 = {2789/3689/4589/4679/5678}, no 1
l) 26(6) cage at R1C9 = {123479/123569/123578/124568/134567}, must contain 1

1. 45 rule on C12 2 outies R14C3 = 9 = [18/27]/{45}, no 1,2,3,6,9 in R4C3

2. 45 rule on C89 2 outies R14C7 = 3 = {12}, locked for C7, clean-up: R1C8 = {78}
2a. R1C9 + R2C89 + R3C8 can 'see' R14C7 -> CPE no 1,2 in R1C9 + R2C89 + R3C8
2b. 1 in 26(6) cage locked in R4C78, locked for R4 and N6, clean-up: no 4 in R3C5
2c. R3C9 = {12} (hidden pair R1C7 + R3C9 for N9)
2d. R345C9 = {179/269/278}, no 3,4,5
2e. 2 of {269/278} must be in R345C9 -> no 2 in R45C9

3. Killer pair 1,2 in R1C23 and R1C7, locked for R1
3a. 1 in R789C6 locked in C6, locked for N8

4. 45 rule on C1234 2 innies R19C4 = 12 = {39/48/57}, no 2,6

5. 45 rule on C6789 2 innies R19C6 = 5 = [32/41]

6. 45 rule on R1 2 innies R1C19 = 1 outie R2C5 + 13
6a. Min R1C19 = 14, no 3,4
6b. Max R1C19 = 17 -> max R2C5 = 4

7. 3 in R1 locked in R1C456, locked for N2, clean-up: no 2 in R4C5
7a. 17(4) cage at R1C4 = {1349/1358/1367/2348/2357}
7b. 1,2 only in R2C5 -> R2C5 = {12}
7c. Naked pair {12} in R23C5, locked for C5 and N2
7d. Naked pair {12} in R3C59, locked for R3

8. Hidden killer triple 7,8,9 in R1C19, R1C45 and R1C8 for R1 -> R1C19 must contain one of 7,8,9
8a. R2C6 = {12} -> R1C19 = 14,15 (step 6) = {59/68/69} (cannot be {78} because of step 8), no 7
[Simpler was "cannot be {78} which clashes with R1C8".]

9. 45 rule on R89 2 innies R8C28 = 2 outies R7C46 + 8, max R8C28 = 17 -> max R7C46 = 9, no 9, no 8 in R7C6

10. 6 in N9 locked in R7C79 + R89C7
10a. 45 rule on N9 4 innies R7C79 + R89C7 = 25 = {2689/3679/4678}, no 5, clean-up: no 8 in R6C7

11. 45 rule on N7 4 innies R7C13 + R89C3 = 14 = {1238/1247/1256/1346/2345}, no 9, clean-up: no 2 in R6C3
11a. 18(3) cage in N7 = {189/279/369/378/459/567} (cannot be {468} which clashes with R7C13 + R89C3)

12. 45 rule on N89 5 innies R7C4579 + R8C4 = 33, max R7C4579 = 30 -> min R8C4 = 3

13. 45 rule on N9 2 innies R7C79 = 2 outies R78C6 + 8
13a. Min R78C6 = 5 (cannot be {12} which clashes with R9C6, cannot be {13} which clashes with R19C6) -> min R7C79 = 13, no 2,3 in R7C9

14. 2 in N9 locked in 8(3) cage = {125}, locked for N9, clean-up: no 7 in R78C8

15. Naked triple {125} in R9C689, locked for R9, clean-up: no 7 in R1C4 (step 4)
15a. 18(3) cage in N7 (step 11a) = {189/279/369/378/459/567}
15b. 5 of {459} must be in R8C1 -> no 4 in R8C1

16. Naked triple {125} in R389C9, locked for C9
[Mike: At this point, 5 of both R9 and C9 is locked in 8(3)N9 -> R9C9 = 5.
Another example of my "killer brain" being blind, as well as the very long time I took before I saw step 2a.]

17. 17(4) cage at R1C4 (step 7a) = {1349/1358/2348/2357} (cannot be {1367} because 6,7 only in R1C5), no 6
17a. 6 in R1 locked in R1C19 = {68/69} (step 8a), no 5
[Alternatively Killer pair 4,5 in R1C23 and R1C456, locked for R1]
17b. 17(4) cage at R1C4 = {1349/2348/2357} (cannot be {1358} which clashes with R1C19 which must be {68} when R2C5 = 1)
17c. 7 of {2357} must be in R1C5 -> no 5 in R1C5

18. 17(4) cage at R7C6 = {1349/1358/1367/1457/2348/2357/2456} (cannot be {1259/1268} which clash with R9C6)
18a. Cannot be {1358} because {13} in R78C6 clashes with R19C6 and {38} in R89C7 clashes with R7C79 + R89C7
18b. -> 17(4) cage at R7C6 = {1349/1367/1457/2348/2357/2456}
18c. 8,9 of {1349/2348} must be in R89C7 because R89C7 cannot be {34} (step 10a) -> no 8,9 in R8C6

19. Killer pair 1,2 in R78C6 and R9C6, locked for C6 and N8, clean-up: no 7 in R7C6 (step 9)

20. R7C79 + R89C7 (step 10a) = {3679/4678}
20a. R789C7 cannot be {367} which clashes with R6C7 -> no 9 in R7C9, clean-up: no 4 in R7C7 (step 13a), no 9 in R6C7
20b. R789C7 cannot be {467} which clashes with R6C7 -> no 8 in R7C9
20c. No 6 in R7C6, CPE R7C6 'sees' all cells of R7C79 + R89C7
[That has been there since step 13a, when it would have eliminated 6,7, but I only spotted it here.]

21. 19(4) cage at R7C4 = {1369/1378/1459/1468/1567/2359/2368/2458/2467/3457} (cannot be {1279} because 1,2 only in R8C3)
21a. Only combination without 1,2 is {3457} -> no 6,8 in R8C3

22. 1,2 in N5 locked in R123C4, locked for 16(4) cage -> no 1,2 in R5C3
22a. 16(4) cage at R4C4 = {1249/1258/1267}, no 3

23. R7C79 + R89C7 (step 20) = {3679/4678}
23a. 17(4) cage at R7C6 (step 18b) = {1349/1367/1457/2348/2357/2456}
23b. R89C7 cannot be {67} because R78C6 = {13} clashes with R19C6
23c. -> R89C7 must contain 3 or 4 -> no 4 in R7C9

24. Naked quad {6789} in R1457C9, locked for C9

25. 7 in C9 locked in R457C9, CPE no 7 in R56C8

26. Killer pair 6,7 in R45C9 and R7C9, locked for C9
26a. R1C1 = 6 (hidden single in R1)
[Mike: You could have dispensed with step 25 and had KP on {67} eliminating 6,7 from R56C8, too.
Wow! A CPE killer pair. I’ve never thought of that and don’t remember it ever appearing on the forum.]

27. 26(6) cage at R1C9 = {123479/123569/123578/124568} (cannot be {134567} because R1C9 only contains 8,9)
27a. 1,2 only in R4C78 -> R4C78 = {12}, locked for R4 and N6
27b. R1C9 = {89} -> no 8,9 in R23C8
27c. 7 in C8 locked in R123C8, locked for N3

28. 16(4) cage at R4C4 (step 22a) = {1249/1258/1267}
28a. 1,2 only in R56C4 -> R56C4 = {12}

29. 21(4) cage at R5C8 = {3468/3567} (cannot be {3459} because R7C9 only contains 6,7), no 9

30. 9 in C8 locked in R78C8 -> R78C8 = {39}, locked for C8 and N9, clean-up: no 4 in R6C7

31. 21(4) cage at R5C8 = {3468/3567} -> R6C9 = 3, R2C9 = 4, clean-up: no 8 in R7C3

32. 26(6) cage at R1C9 (step 27) = {124568} (only remaining combination) -> R1C9 = 8, R1C78 = [27], R3C9 = 1, R4C78 = [12], R34C5 = [23], R2C5 = 1, clean-up: no 4 in R1C23, no 6 in R45C9 (step 2d)
32a. Naked pair {56} in R23C8, locked for C8 and N3 -> R9C8 = 1, R9C6 = 2, R89C9 = [25]
32b. Naked pair {79} in R45C9, locked for C9 and N6 -> R7C9 = 6, clean-up: no 5 in R6C3, no 7 in R8C2
32c. Naked pair {48} in R56C8, locked for N6

33. 1,4 locked in 17(4) cage at R7C6 (step 18) = {1457} (only remaining combination), no 3,6,8
33a. Naked pair {47} in R89C7, locked for C7 and 17(4) cage -> R7C7 = 8, R6C7 = 5, R5C7 = 6, clean-up: no 7 in R4C4 (step 22a), no 5 in R8C2
33c. Naked pair {15} in R78C6, locked for C6 and N8

34. R5C7 = 6 -> R456C6 = 20 = {479} (only remaining combination), locked for C6 and N5 -> R1C6 = 3, clean-up: no 4,9 in R5C3 (step 22a)

35. Naked pair {15} in R1C23, locked for R1 and N1
35a. Naked pair {49} in R1C45, locked for N2
35b. Naked pair {68} in R23C6, locked for N2
35c. Naked pair {57} in R23C4, locked for C4 and 23(4) cage, clean-up: no 8 in R5C3 (step 22a)

36. R5C5 = 5 (hidden single in C5), R5C3 = 7, R4C4 = 6 (step 22a), R45C9 = [79], R5C6 = 4, R46C6 = [97], R56C8 = [84], R6C5 = 8, R7C5 = 7 (cage sum), clean-up: no 3,4 in R7C3, no 6 in R8C2

37. 6 in C5 locked in R89C5, 20(4) cage in N8 = {2369/2468}
37a. Only other 8,9 in R8C4 -> R8C4 = {89}

38. R23C4 = {57} = 12 -> R23C3 = 11 = [29]/{38}, no 4, no 9 in R2C3

39. 19(4) cage at R7C4 (step 21) = {1369/1468} (cannot be {1459} because 1,5 only in R8C3) -> R8C3 = 1
39a. R7C4 = {34} -> no 3,4 in R9C3

40. R78C6 = [15], R1C23 = [15], R7C3 = 2, R6C3 = 9

41. Naked pair {38} in R23C3, locked for C3 and N1 -> R4C3 = 4, R9C3 = 6, R4C2 = 5 (cage sum), R4C1 = 8, clean-up: no 8 in R8C2

42. R4C1 = 8 -> R35C1 = 6 = [42], R56C4 = [12], R5C2 = 3, R6C12 = [16], R7C1 = 5

43. Naked pair {49} in R78C2, locked for C2 and N7 -> R23C2 = [27], R2C1 = 9, R9C2 = 8, R23C7 = [39], R23C3 = [83], R23C6 = [68], R23C4 = [75], R23C8 = [56]

44. R8C4 = 8 (hidden single in C4), R7C4 = 4 (step 39)

and the rest is naked singles

Hi folks,

So, another hectic forum week draws to a close . Time to discuss a few moves made in some of the walkthroughs.Yes, we all required this move. It seems to be pretty critical. To prove that, I removed the 26(6)n36 cage, and let SudokuSolver and JSudoku try to solve this modified puzzle. This way, they could readily determine that R14C7 = {12}, but could no longer perform the CPE move eliminating the {12} from R12C9+R23C8. The result was that neither program could now complete the puzzle individually, although manually synchronizing the candidates in JSudoku with those of SudokuSolver then allowed JSudoku (using several chains) to successfully solve the grid. However, although I haven't yet analyzed the steps in detail, it looked like pretty tough going...

Incidentally, I found out that the two chains Gary used to break this puzzle were (in the re-wored form presented below), both capable of being expressed as AICs. To illustrate this, however, I would like to apply them to Andrew's WT, starting from his step 10a, due to ease of following the lead-up steps.

Grid state after Andrew's step 10a:



From this position, Gary's first chain can be applied:

(5)r8c9+r9c89=(5,7)r78c8-(7=8)r1c8,(1)r1c7-(1=2)r3c9-(2)r789c9=(2)r9c8

[Note: Alternative explanation for those unfamiliar with Eureka notation:
(a) R8C9+R9C89 <> {5..} => R78C8 = {5..} (strong link, N9)
(b) -> R78C8 = {7..} (neutral link, combinations 12(2))
(c) -> R1C8 <> 7 (weak link, C8)
(d) -> R1C8 = 8 (strong link, bivalue cell R1C8)
(e) -> R1C7 = 1 (neutral link, combinations 9(2))
(f) -> R3C9 <> 1 (weak link, N3)
(g) -> R3C9 = 2 (strong link, bivalue cell R3C9)
(h) -> R789C9 <> 2 (weak link, C9)
(i) -> R9C8 = 2 (strong link, N9)]

=> if 8(3)n9 does not contain a 5, it must contain a 2 (in r9c8)
-> {134} combo for 8(3)n9 blocked
-> 8(3)n9 = {125}, locked for N9
-> cleanup: no 7 in R78C8

Note: Andrew locked the 2 in 8(3)n9 without using chains by considering the overlapping cages 17(4) at R78C6+R89C7 and the 25(4) N9 innies at R789C7+R7C9. R78C6 must sum to 5 or higher, because {12/13} are both blocked by R19C6. Hence R7C79 must sum to at least 13, removing both of {23} from R7C9 and thus locking the 2 of N9 into the 8(3) cage = {125}. Afmob used a similar approach, but had already reduced R7C6 to {12}. Therefore, Gary's first AIC did not really provide a significant benefit compared to the classical Killer approach used by Andrew and Afmob. I'm basically just including it out of interest, and to show how AICs are actually not that uncommon on this forum, even though they are often not recognized and labelled as such.

New grid position:



From this position, Gary's second chain can be applied:



Note: This second AIC of Gary's provided a useful (although more complex) alternative to the CPE move for N4 eliminating the 1 from R7C1, which Afmob used. Andrew avoided both by considering the overlapping cages 13(2) at R67C7 and the 25(4) N9 innies at R789C7+R7C9. The N9 innies must contain both of {67}, and they cannot both be within R89C7 (which must sum to at most 12). Furthermore, they cannot be split 1:1 between R7C7 and R89C7 because R89C9 would then clash with R6C7. Therefore, 1 of {67} must be in R7C9. This was IMO a critical move in Andrew's WT.

That's all for today, folks. Roll on A87! =P~

3x3::k:6400:6400:2562:2562:3844:1285:1285:6919:6919:4617:6400:6400:2828:3844:2318:6919:6919:4113:4617:4627:6400:2828:3094:2318:6919:3609:4113:4617:4627:4627:4627:3094:3609:3609:3609:4113:5412:3621:3621:4135:4135:4135:3626:3626:5932:5412:5412:3621:3120:4135:6194:3626:5932:5932:1846:5412:3120:3120:5946:6194:6194:5932:3646:1846:5696:5696:5946:5946:5946:3397:3397:3646:5696:5696:2890:2890:5946:2893:2893:3397:3397:

Hi folks,This puzzle proved to be the opposite for me, with progression possible in big leaps and bounds. Hopefully, I haven't made one of those logic errors that result in a lucky fake breakthrough I've checked the WT through already, so it should be OK (unless I was blind in the same place twice...).

Rating: 1.0 ? Will be interested to hear what the rest of you think.

Edit: Just seen that SS rates this at 1.88!


Assassin 87 Walkthrough
Prelims

a) 10(2) at R1C3 = {19/28/37/46} (no 5)
b) 15(2) at R12C5 = {69/78}
c) 5(2) at R1C6 = {14/23}
d) 11(2) at R23C4, R9C34 and R9C67 = {29/38/47/56} (no 1)
e) 9(2) at R23C6 = {18/27/36/45} (no 9)
f) 12(2) at R34C5 = {{39/48/57} (no 1,2,6)
g) 14(4) at R3C8 = {1238/1247/1256/1346/2345} (no 9)
h) 24(3) at R6C6 = {789}
i) 7(2) at R78C1 = {16/25/34} (no 7..9)
j) 14(2) at R7C9 = {59/68}
k) 13(4) at R8C7 = {1237/1246/1345} (no 8,9); 1 locked for N9

1. Innies N2: R1C46+R3C5 = 10(3) = {127/136/145/235} (no 8,9)
1a. R1C46 cannot sum to 5 due to R1C7
1b. -> no 5 in R3C5
1c. possible permutations are: [127/217]
(Note: [613] blocked because it would force a 4 into both of R1C37)
1d. -> R3C5 = 7
1e. -> R4C5 = 5
1f. R1C46 = {12}, locked for R1 and N2
1g. cleanup: no 3,4,6,7 in R1C3; no 8 in R12C5; no 4,9 in R23C4; no 8 in R23C6

2. Naked pair (NP) at R12C5 = {69}, locked for C5 and N2
2a. cleanup: no 5 in R23C4; no 3 in R23C6
2b. NP at R23C4 = {38}, locked for C4
2c. NP at R23C6 = {45}, locked for C6
2d. cleanup: no 3,8 in R9C3; no 6,7 in R9C7

3. Innies C6789: R58C6 = 10(2) = {19/28/37} (no 6)
3a. -> R58C6 and R67C6 form killer triple (KT) on {789} in C6
3b. -> no 7,8,9 elsewhere in C6
3c. cleanup: no 2,3,4 in R9C7

4. Innies C1234: R58C4 = 11(2) = {29}/{47}/[65] (no 1)
4a. no 6 in R8C4

5. 13(4) at R8C7 = {1237/1246/1345}
5a. -> must have exactly 2 of {234}
5b. only other place for {234} in N9 is R7C8
5c. -> R7C8 = {234} (no 5..9)

6. Outies N36: R14C6+R7C8 = 9(2+1)
6a. R1C6 = {12} -> R4C6+R7C8 must sum to 7 or 8 = [34/62] (only possible permutations)
6b. -> R4C6 = {36}, R7C8 = {24}

7. Innies N9: R7C78+R9C7 = 18(3) = [729/945] (no 8) (only possible permutations)
7a. 9 locked in R79C7 for C7 and N9
7b. cleanup: no 3 in R9C6; no 5 in R78C9

8. Naked pair (NP) at R78C9 = {68}, locked for C9 and N9

9! Innie/Outie (I/O) diff. C9: R67C8 = R19C9 + 8
9a. Max. R67C8 = 13 -> max. R19C9 = 5
9b. -> R19C9 = [31/32/41]
9c. -> R1C9 = {34}; R9C9 = {12}
9d. Min. R19C9 = 4 -> min. R67C8 = 12
9e. -> R67C8 = [84/94]
9f. -> R7C8 = 4; R6C8 = {89}
9g. -> R79C7 = [95] (step 7)
9h. -> R9C6 = 6 (cage sum)
9i. -> R4C6 = 3
9j. -> R1C6 = 2 (step 6)
9k. -> R1C7 = 3 (cage sum); R1C34 = [91]
9l. -> R19C9 = [41] (step 9b); R12C5 = [69]
9m. -> R6C8 = 9 (step 9.)
9n. cleanup: no 7,8 in R58C6 (step 3); no 2 in R9C4; no 3 in R8C1

10. Hidden single (HS) at R3C9 = 9
10a. -> R24C9 = [52] (only possible permutation)
10b. -> R23C6 = [45]

11. Innie N3: R3C8 = 1
11a. -> R4C78 = [46] (only possible permutation)

12. HS in C8/N6 at R5C8 = 5
12a. -> split 9(2) at R56C7 = {18}, locked for C7

13. 18(4) at R3C2 cannot have both of {79} due to cage sum
13a. -> no 7,9 in R4C23
13b. -> R4C23 = {18}, locked for N4
13c. -> split 9(2) at R3C2+R4C4 = [27] (only possible permutation)
13d. cleanup: no 4 in R9C3; no 4 in R58C4 (step 4)

14. R67C6 = [87]
14a. -> R56C7 = [81]

15. R3C7 = 6; R4C1 = 9 (both naked singles)
15a. split 9(2) at R23C1 = [18/63] (only possible permutations)
15b. -> R3C3 = 4 (HS@R3/N1)

16. Innies N7: R7C23+R9C3 = 16(3)
16a. -> R9C3 can't be 2, because {68} in R7C23 blocked by R7C9
16b. -> R9C34 = [74]
16c. -> split 9(2) at R7C23 = {18/36} (no 2,5)
16d. -> R7C23 and R7C9 form KP on {68}, locked for R7
16e. cleanup: no 1 in R8C1

17. 12(3) at R6C4+R7C34 = [615] (only possible permutation)
17a. -> R7C2 = 8 (step 16c)
17b. -> R4C23 = [18]; R78C9 = [68]
17c. cleanup: no 2,6 in R8C1

18. NP at R79C1 = {23}, locked for C1 and N7
18a. cleanup: no 6 in R2C1 (step 15a)

19. HS in C1 at R5C1 = 6
19a. -> split 7(2) at R6C12 = [43] (only possible permutation)
19b. cleanup: no 3 in R7C1

Now only naked singles left.

That was a fun assassin! Like Mike I'm surprised that SS rated this one so high. My key moves are similar to Mike's one though I used a different reasoning to apply them.

A87 Walkthrough:

1. R89
a) Outies = 11(3) <> 9
b) Outies = 11(3) must have two of (1234) and they are only possible @ R7C15 -> R7C15 <> 5,6,7,8
c) 7(2): R8C1 <> 1,2
d) 14(2): R8C9 <> 5
e) 13(4) = 1{237/246/345} -> 1 locked for N9

2. N2 !
a) Innies = 10(3) <> 8,9
b) Innies = 10(3): R1C4 <> 7 because R3C5 <> 1,2
c) 10(2): R1C3 <> 1,2,3
d) 12(2): R4C5 <> 3,4
e) Outies = 17(2+1): R1C3 <> 4 because R1C7 <= 4
f) ! Outies = 17(2+1): R4C5 <> 7 because R1C37 would be 10(2) which conflicts with 10(2) @ R1C34
g) R1C4 <> 6
h) 12(2): R3C5 <> 5
i) Innies = 10(3) must have one of (567) and they are only possible @ R3C5 -> R3C5 = 7

3. C456
a) Innies N2 = 10(3) = {127} -> {12} locked for R1+N2
b) 12(2) = [75] -> R4C5 = 5
c) 10(2) = [82/91]
d) 15(2) = {69} locked for C5+N2
e) 11(2) @ N2 = {38} locked for C4+N2
f) 9(2) = {45} locked for C6
g) 11(2) @ N7 <> 3,8
h) 11(2) @ N9: R9C7 <> 6,7
i) Innies C1234 = 11(2) <> 1; R8C4 <> 6
j) Innies C6789 = 10(2) <> 6
k) Killer triple (789) locked in Innies C6789 + R67C6 for C6 -> R49C6 <> 7,8,9
l) 11(2) @ N9: R9C7 <> 2,3,4

4. C6789
a) Innies N9 = 18(3): R7C8 = (234) because R79C7 >= 12 and {567} blocked by Killer pair (56) of 14(2)
b) Outies N36 = 9(2+1): R7C8 <> 3 because R14C6 <> 4,5
c) 3 locked in 13(4) = 13{27/45} <> 6
d) 6 locked in 14(2) = {68} locked for C9+N9
e) 9 locked in R79C7 for C7
f) 24(3) = {789}; 8 locked for C6
g) Innies C1234 = 10(2) = {19/37}
h) 11(2) = [29/65]
i) 16(3) = {259/349/457}
j) Outies N36 = 9(2+1) = 2+[16] / 4+[23] -> R4C6 = (36)

5. R789
a) Killer pair (24) locked in Outies R89 + R7C8 for R7
b) 23(4) <> 1 because R7C8 = (24)
c) Hidden Single: R9C9 = 1 @ C9

6. N1
a) Innies+Outies: -2 = R4C1 - R1C3+R3C2
-> R3C2 = (123) because R1C3 = (89)
-> R3C2 = (789) because R1C3+R3C2 >= 9

7. C789 !
a) ! Innies+Outies C9: 9 = R67C8 - R1C9
-> R1C9 <> 5,7,9 because R67C8 <= 13
-> R67C8 = 12/13(2) = [9/8]4 -> R7C8 = 4
b) 13(4) = {1237} locked for N9
c) 24(3) = {789} -> R7C7 = 9; 7 locked for C6
d) Outies N36 = 9(2+1) = 4+[23] -> R1C6 = 2, R4C6 = 3
e) 5(2) = {23} -> R1C7 = 3
f) R1C9 = 4
g) 16(3) = {259} locked for C9, 5 locked for N3
h) 23(4) = {3479} -> R6C8 = 9, {37} locked for N6
i) R4C9 = 2
j) 14(3) = {158} locked for N6

8. R123
a) 10(2) = {19} -> R1C3 = 9, R1C4 = 1
b) 5 locked in R1C12 for N1
c) 14(4) = {1346} -> R3C8 = 1, R4C7 = 4, R4C8 = 6
d) 18(4) = {1278} -> R3C2 = 2, R4C4 = 7, {18} locked for N4
e) 18(3) = 9{18/36} -> R4C1 = 9; R2C1 <> 8

9. N8
a) R9C6 = 6, R7C4 = 5
b) 23(5) = {12389} locked
c) 11(2) @ R9C3 = {47} -> R9C3 = 7, R9C4 = 4
d) 12(3) = {156} -> R6C4 = 6, R7C3 = 1

10. N17
a) Hidden Single: R4C2 = 1 @ N4, R2C1 = 1 @ N1 -> R3C1 = 8
b) 7(2) = [25/34]
c) 22(4) = 69{25/34} because 38{29/56} blocked by Killer pairs (23,35) of 7(2)
d) Hidden Single: R7C2 = 8 @ N7
e) R1C5 = 6
f) Hidden Single: R5C1 = 6 @ C1
g) 21(4) = 68{25/34}; R6C1 <> 5

11. Rest is singles.

Rating: Hard 1.0. I thought about rating it 1.25 but we had enough of them already

Yes, a fun puzzle. Comparing Mike's and Afmob's walkthroughs with mine, there seems to be a general direction that has to be followed although it's definitely not a narrow solving path and not hard to find.

They both got one key move, Mike's step 9 and Afmob's step 7a, which made their solutions more direct than mine. We all got the other key moves although not necessarily using the same logic.

Afmob also had interesting steps 1a, 1b and 5a. I don’t think they were used by Mike and I didn’t spot them. Remainder of this comment deleted, I'd been looking at an incorrect grid state.I immediately spotted the but I'll still make the general comment that ratings shouldn't be influenced by which ones are more common. Mike's rating definitions suggest that typical Assassins, apart from the early ones, will normally be rated 1.25 so there will be more of that rating than anything else.

I'm not sure between hard 1.0 and easier 1.25 but I think I'll rate A87 an easier 1.25 for the way I solved it. However I'm expecting Ed to rate it 1.0 because of the key step that I missed.

Here is my walkthrough for A87 (original step 35 deleted and step 36 renumbered).

Prelims

a) R1C34 = {19/28/37/46}, no 5
b) R12C5 = {69/78}
c) R1C67 = {14/23}
d) R23C4 = {29/38/47/56}, no 1
e) R23C6 = {18/27/36/45}, no 9
f) R34C5 = {39/48/57}, no 1,2,6
g) R78C1 = {16/25/34}, no 7,8,9
h) R78C9 = {59/68}
i) R9C34 = {29/38/47/56}, no 1
j) R9C67 = {29/38/47/56}, no 1
k) 24(3) cage at R6C6 = {789}
l) 14(4) cage at R3C8 = {1238/1247/1256/1346/2345}, no 9
m) 13(4) cage in N9 = {1237/1246/1345}, no 8,9, 1 locked for N9

1. 45 rule on N2 3 innies R1C46 + R3C5 = 10 = {127/136/145/235}, no 8,9, clean-up: no 1,2 in R1C3, no 3,4 in R4C5
1a. Cannot be {136} because [613] would make R1C37 = [44]
1b. Cannot be {145} because R1C46 = {14} clashes with R1C67 = {14}
1c. Cannot be {235} because R1C46 = {23} clashes with R1C67 = {23}
1d. -> R1C46 + R3C5 = {127} -> R1C46 = {12}, locked for R1 and N2, R3C5 = 7, R4C5 = 5, clean-up: R1C3 = {89}, no 8 in R12C5, no 4,9 in R23C4, no 8 in R23C6

2. Naked pair {69} in R12C5, locked for C5 and N2, clean-up: no 5 in R23C4, no 3 in R23C6
2a. Naked pair {38} in R23C4, locked for C4, clean-up: no 3,8 in R9C3
2b. Naked pair {45} in R23C6, locked for C6, clean-up: no 6,7 in R9C7

3. 45 rule on C1234 2 innies R58C4 = 11 = {29/47}/[65], no 1, no 6 in R8C4

4. 45 rule on C6789 2 innies R58C6 = 10 = {19/28/37}, no 6

5. Killer triple 7,8,9 in R58C6 and R67C6, locked for C6, clean-up: no 2,3,4 in R9C7

6. 45 rule on N9 3 innies R7C78 + R9C7 = 18 = {279/378/459} (cannot be {369) which clashes with 13(4) cage, cannot be {468} because 4,6 only in R7C8, cannot be {567} which clashes with R78C9), no 6
6a. 2,3,4 only in R7C8 -> R7C8 = {234}
6b. 8 of {378} must be in R9C7 -> no 8 in R7C7

7. 8 in 24(3) cage locked in R67C6, locked for C6, clean-up: no 2 in R58C6 (step 4)

8. 45 rule on N36 2 outies R4C6 + R7C8 = 1 innie R1C7 + 4
8a. R1C7 = {34} -> R4C6 + R7C8 = 7,8 = [34/62], R4C6 = {36}, R7C8 = {24}, clean-up: no 8 in R9C7 (step 6), no 3 in R9C6

9. R7C78 + R9C7 (step 6) = {279/459}, 9 locked in R79C7 for C7 and N9, clean-up: no 5 in R78C9

10. Naked pair {68} in R78C9, locked for C9 and N9

11. R234C9 = {259/349/457}, no 1

12. 45 rule on N14 2 outies R4C4 + R7C2 = 1 innie R1C3 + 6
12a. Min R1C3 = 8 -> min R4C4 + R7C2 = 14, no 1,2,3,4

13. 14(4) cage at R3C8 = {1238/1256/1346/2345} (cannot be {1247} because R4C6 only contains 3,6), no 7

14. 12(3) at R6C4 = {129/147/156/237/246/345} (cannot be {138} because 3,8 only in R7C3), no 8
14a. R67C4 = {12} would clash with R1C4 -> no 9 in R7C3

15. 4 remaining innies in N5 R46C46 = 24 = {1689/2679/3489/3678}
15a. 1,2,4 of {1689/2679/3489} must be in R6C4 -> no 9 in R6C4

16. 45 rule on N1 2 innies R1C3 + R3C2 = 1 outie R4C1 + 2
16a. Min R1C3 + R3C2 = 9 -> min R4C1 = 7
16b. Max R4C1 = 9 -> max R1C3 + R3C2 = 11, max R3C2 = 3

17. 45 rule on N3 2 innies R1C7 + R3C8 = 1 outie R4C9 + 2
17a. R4C9 = {23479} -> R1C7 + R3C8 = 4,5,6,9,11 = [31/32/41/42/36/45/38], no 3,4 in R3C8

18. 45 rule on N3 4 innies R1C7 + R2C9 + R3C89 = 18 = {1359/2349/2358/2457/3456} (cannot be {1269/1278} because R1C7 only contains 3,4, cannot be {1368/1458/1467} because 1,6,8 only in R3C8, cannot be {2367} because {27} cannot be placed in R23C9)
18a. 1,6,8 of {1359/2358/3456} must be in R3C8, 5 of {2457} cannot be in R3C8 because {27} cannot be placed in R23C9 -> no 5 in R3C8

19. 14(4) cage at R3C8 (step 13) = {1238/1346}, CPE no 1 in R56C8
19a. 3 locked in R4C678, locked for R4

20. 45 rule on N6 3 innies R4C789 = 1 outie R7C8 + 8
20a. R7C8 = {24} -> R4C789 = 10,12 = {127/145/235/129/147/237/246/345} (cannot be {136/138/156} because R4C9 only contains 2,4,7,9), no 8

21. 14(4) cage at R3C8 (step 19) = {1238/1346}
21a. 8 must be in R3C8 -> no 2 in R3C8

22. R1C7 + R3C8 = R4C9 + 2 (step 17)
22a. R4C9 = {2479} -> R1C7 + R3C8 = 4,6,9,11 = [31/36/38] (no valid permutations for R1C7 + R3C8 = 6) -> R1C7 = 3, R4C9 = {279}, R1C6 = 2, R1C4 = 1, R1C3 = 9, R12C5 = [69], R9C6 = 6, R9C7 = 5, R4C6 = 3, clean-up: no 7 in R58C6 (step 4), no 2 in R9C4
22b. R3C9 = 9 (hidden single in R3), R24C9 = 7 = [52], R23C6 = [45]
22c. R7C7 = 9 (hidden single in C7)

23. R4C4 + R7C2 = R1C3 + 6 (step 12), R1C3 = 9 -> R4C4 + R7C2 = 15 = [78/96]
23a. R1C3 + R3C2 = R4C1 + 2 (step 16), R1C3 = 9 -> R4C1 = R3C2 + 7, R4C1 = {89}, R3C2 = {12}

24. Naked pair {68} in R7C29, locked for R7 -> R7C6 = 7, R6C6 = 8, clean-up: no 1 in R8C1, no 4 in R9C3

25. 45 rule on N3 1 remaining innie R3C8 = 1, R3C2 = 2, R4C1 = 9 (step 23a), R4C4 = 7

26. Naked pair {46} in R4C78, locked for R4 and N6
26a. Naked pair {18} in R4C23, locked for N4

27. 45 rule on N8 2 remaining innies R79C4 = 9 = [54], R9C3 = 7, clean-up: no 2 in R8C1
27a. R1C9 = 4 (hidden single in C9)

28. 12(3) cage at R6C4 = {156} (only remaining combination, cannot be {345} because 3,4 only in R7C3) -> R6C4 = 6, R7C3 = 1, R4C23 = [18], clean-up: no 6 in R8C1
[Alternatively R6C4 = 6 comes from remaining innie in N5]

29. R6C8 = 9 (hidden single in R6)

30. 45 rule on N7 1 remaining innie R7C2 = 8, R78C9 = [68]
30a. R9C5 = 8, R9C2 = 9, R9C9 = 1 (hidden singles in R9)

31. Naked pair {37} in R56C9, locked for N6
31a. R7C8 = 4 (cage sum), R4C78 = [46], R6C7 = 1, R5C78 = [85]

32. Naked pair {23} in R79C1, locked for C1 and N7

33. R4C1 = 9 -> R23C1 = 9 = [18], R23C4 = [83], R3C7 = 6, R3C3 = 4

34. Naked pair {57} in R1C12, locked for R1 and N1 -> R1C8 = 8

35. R5C1 = 6 (hidden single in C1)
35a. R5C1 + R7C2 = 14 -> R6C12 = 7 = [43]

and the rest is naked singles

I finally finished Assassin 87.

When I first tried it a few days ago I kept winding up eliminating all the 7s in the bottom right corner. After many hours of frustration I gave up and then came back to it today. Realized that I had drawn the cages incorrectly in my excel spreadsheet

I didn't find it too difficult (once I drew the cages correctly) - and my walkthrough doesn't seem to be significantly different from Mike and Andrew. I'd give it a rating of 1.25 - not bad - but not incredibly easy.

My walkthrough is below. (with edits - thanks Afmob!! and Andrew!!)

Cheers,

Caida

Assassin 87 walkthrough

Preliminaries:

a. 10(2)n12 = {19/28/37/46} (no 5)
b. 15(2)n2 = {69/78} (no 1..5)
c. 5(2)n23 = {14/23} (no 5..9)
d. 11(2)n2 and n78 and n89 = {29/38/47/56} (no 1)
e. 12(2)n25 = {39/48/57} (no 1,2,6)
f. 9(2)n2 = {18/27/36/45} (no 9)
g. 14(4)n356 = {1238/1247/1256/1346/2345} (no 9)
h. 24(3)n589 = {789} (no 1..6)
i. 7(2)n7 = {16/25/34} (no 7..9)
j. 14(2)n9 = {59/68} (no 1..4,7)
k. 13(4)n9 = {1237/1246/1345} (no 8,9) -> 1 locked for n9
l. 9 locked in c5 in 15(2)n2 and 12(2)n25 -> no 9 elsewhere in c5


1. Innies n2: r1c46+r3c5 = 10(3) = {127} (no 3,5,4,6,8,9)
Note: combo [14]{5} blocked by 5(2)n23
combo [613] blocked by 10(2)n12 and 5(2)n23 (would need two 4s in r1)
combo {23}[5] blocked by 5(2)n23
1a. r3c5 = 7; r4c5 = 5
1b. r1c3 = 8,9
1c. r1c7 = 3,4
1d. pair {12} locked in r1 and n2 in r1c46 -> no 1,2 elsewhere in r1 and n2
1e. 15(2)n2 = {69} -> locked for n2 and c5
1f. 9(2)n2 = {45} -> locked for n2 and c6
1g. 11(2)n2 = {38} -> locked for c4
1h. r9c3 no 3,8
1j. r9c7 no 6,7

2. Innies c1234: r58c4 = 11(2) = {29/47}/[65] (no 1)
2a. r8c4 no 6

3. Innies c6789: r58c6 = 10(2) = {19/28/37} (no 6)
3a. killer triple {789} in h10(2) (r58c6) and r67c6 -> no 7,8,9 elsewhere in c6
3b. -> r9c7 no 2,3,4

4. Outies n14: r14c4+r7c2 = 16(2+1) = [169/196/178/295/268/277]
4a. r4c4 no 1,2,4
4b. r7c2 no 1,2,3,4

5. Outies n36: r14c6+r7c8 = 9(2+1) = [126/162/216/135/234]
5a. -> r7c8 no 3,7,8,9
5b. 3 in n9 locked in 13(4)n9 = {1237/1345} (no 6) (contains either 2 or 4 but not both)
5c. -> only other place for 2 and 4 in n9 is r7c8
5d. -> r7c8 no 5,6
5e. 6 in n9 locked in 14(2)n9 = {68} -> locked for n9 and c9
5f. -> r9c6 no 3
5g. 8 in 24(3)n589 locked in c6 -> no 8 elsewhere in c6
5h. r58c6 no 2 (step 3)

6. h9(2+1) (step 5) = [162/234]
6a. -> r4c6 no 1,2

7. 23(4)n69 contains either a 2 or a 4 in n9 = {489/579}[2]/{289/379}[4] -> no 1,6
7a. -> r6c8 no 2,4 (if 23(4) contains both 2 and 4 then r6c8 = 8)

8. 9 in n9 locked in c7 -> no 9 elsewhere in c7

9. 16(3)n36 = {259/349/457} (no 1)
9a. -> r9c9 = 1 (single)

10. Innies r567: r7c159 = 11(3) = {12}[8]/{14}[6]/{23}[6]
10a. -> r7c15 = {1234} (no 5,6,8)
10b. -> r8c1 no 1,2
10c. killer pair {24} in r7 in c15 + c8 -> no 2,4 elsewhere in r7

11. 12(3)n578 = [219/291/417/471/156/165/615/651/237/435] (no 8)
11a. -> r6c4 no 7,9

12. Innies n5: r4c46+r6c46 = 24(4) = [9348/7368/9618/7629/9627]
12a. -> r4c4 no 6
12b. -> r7c2 no 9 (step 4)
12c. -> 18(4)n146 cannot have both 7 and 9
12d. -> r3c2+r4c23 no 7,9

13. Innies n8: r7c46+r9c46 = 22(4) = [6952/5962/5872/1876/5926/5746]
Note: combos [7942/9742] blocked by r7c7
combo [7852] blocked by 11(2)n89 and 24(3)n589
13a. -> r7c4 no 7,9
13b. -> r9c4 no 9
13c. -> r9c3 no 2

14. Outies and Innie c123: r149c4 – r7c3 = 11
14a. -> max r149c4 = 18 -> max r7c3 = 7 (no 9)
14b. 9 in r7 locked in 24(3)n589
14c. -> r6c6 no 9
14d. r6c4 no 2 (step 11)
14e. r6c6 = 8 (step 12)
14f. pair {79} locked for r7 in r7c67 -> no 7,9 elsewhere in r7
14g. r7c4 no 1 (step 13)
14h. r56c9 no 2,4 (step 7)
Andrew pointed out that another way to say this is: 23(4)n69 must now have three odd numbers - so no 2,4 I like this way of looking at the sums but don't often spot these until after the fact - perhaps with more practice I'll be able to use this.

15. 23(4)n69 = {379}[4]/{579}[2]
15a. -> 7,9 locked in n6 in 23(4)n69 -> no 7,9 elsewhere in n6
15b. 14(3)n6 = {158/248} (no 3,6) -> 8 locked in n6 and r5 in 14(3) -> no 8 elsewhere in n6 and r5
Note: combo {356} blocked by 23(4)n69
15c. 6 in n6 locked in 14(4)n356 in r4 -> no 6 elsewhere in 14(4)n356 and r4
15d. single: r4c6 = 3
15c. 14(4)n356 = {1346} (no 2,5,8)
15d. r5c8 no 1,4 (CPE with 14(4)n356)
15e. 14(3)n6 = {158} (combo {248} blocked by r4c9) 1,5,8 locked for n6
15f. r4c9 = 2 (single)
15g. r7c8 = 4 (step 15)

Singles and cage sums are left (finally!!!)

Well I know everything seems to be rated 1.25 these days but I'ld have to rate this one about.....1.25.It was roughly as difficult as many recent ones,I certainly found it no easier.

I needed to use the O-I of c9 and the combos in N9 to show that there was a HS in c9 viz, r9c9=1.In c9 3 then had to be in r5/6 which meant the only option for r8c7=4.The O for N3/6 then -> r14c6 and I was well on my way to solving it.Took about 2 hours...long enough !!!

Regards

Gary

3x3::k:4352:4352:2562:4355:4355:4355:4870:5383:5383:7433:4352:2562:2562:4621:4870:4870:5383:4881:7433:4352:3092:4621:4621:4621:2328:5383:4881:7433:7433:3092:4382:3615:6432:2328:4881:4881:3876:4382:4382:4382:3615:6432:6432:6432:3628:3876:3876:3119:3119:3615:3634:3634:3628:3628:3876:5943:5943:3119:2362:3634:3132:3132:3628:1343:5943:6209:6209:2362:5444:5444:3132:3655:1343:6209:6209:3915:3915:3915:5444:5444:3655:

This assassin had a lot of Killer pairs/triples you could use to solve it. And it's quite stubborn in the end game (my first version was about 30% longer) but if you manage to find the right moves it can be solved in a not too long way.

Edit: Andrew found an elimination in my wt which couldn't be applied at this stage. I fixed this mistake and changed the walkthrough from step 6 on.

A88 Walkthrough:

1. R6789
a) Innies R89 = 11(3) <> 9; R8C58 <> 5,6,7,8 because R8C2 = (68)
b) 23(3) = {689} locked N7, 9 locked for R7
c) Innies R789 = 12(4) = 12{36/45} -> 1,2 locked for R7
d) 9(2): R7C5 <> 3,4
e) Innies+Outies N7: 7 = R8C4 - R7C1 -> R7C1 = (12), R8C4 = (89)
f) Killer pair (12) locked in R7C1 + 5(2) for C1+N7
g) Innies+Outies N9: 2 = R8C6 - R7C9 -> R8C6 <> 1,2,9
h) Innies+Outies : -2 = R5C19 - R6C5
-> R5C19 <> 7,8,9;
-> R6C5 = (6789) and R5C9 <> 5,6 since R5C1 >= 3

2. C123 !
a) 29(4) = {5789} locked between C1+N4 -> R56C1 <> 5,7,8,9
b) R56C1 = 6{3/4} because {34} blocked by Killer pair (34) of 5(2)
-> 6 locked for C1+N4
-> 6 locked in 15(4) = 36{15/24} -> 3 locked for N4
c) 15(4) must have 1 xor 2 and R7C1 = (12) -> R6C2 <> 1,2
d) ! 15(4): R6C2 <> 3 because R567C1 = {246} blocked by Killer pair (24) of 5(2)
e) 3 locked in 15(4) for C1
f) 5(2) = {14} locked for C1+N7
g) 24(4) = {3579} -> R8C4 = 9
h) 15(4) = {2346} -> R6C2 = 4, R7C1 = 2

3. C123
a) 12(2) <> 5,7 since it's blocked by R89C3 = (357)
b) 12(2): R3C3 <> 8,9
c) Innies C12 = 24(4) <> 1 because R9C2 = (357)
d) 1 locked in R56C3 for C3
e) 10(3): R2C4 <> 4,6,7 because R12C3 <> 1
f) 10(3): R2C4 <> 2 because {35}2 blocked by R89C3 = (357)

4. R1234
a) Innies N2 = 10(2) = [19/37]
b) Outies N1 = 23(3+1) and R2C4 = (13)
-> R4C123 = 20/22(3) = 58{7/9} -> 5,8 locked for R4+N4;
c) 5 locked in R4C12 @ 29(4) -> R23C1 <> 5
d) Innies = 9(3) = 2{16/34} -> 2 locked R4+N5
e) 9(2): R3C7 <> 1,4,7

5. C123 !
a) Killer triple (789) locked in 17(4) + R23C1 for N1
b) Innies C12 = 24(4): R5C2 <> 9 since R789C3 >= 17
c) 10(3) = {36/45}1 / {25}3 -> R12C3 must have 1 of (35)
d) ! Killer triple {357} locked in R12C3+R89C3 for C3
e) 12(2) = {48} -> R3C3 = 4, R4C3 = 8
f) 29(4) = {5789} -> 8 locked for N1
g) 17(4) @ N5: R45C4 <> 2,7 because R5C3 <> 3,5
h) ! 2 locked in Innies C1234 = 16(3) = {268} locked for C4

6. N5+R56
a) Hidden Single: R6C4 = 7 @ C4
b) 12(3) = 7{14/23}; R7C4 <> 1
c) Hidden Single: R5C4 = 5 @ C5
e) 14(3) @ R4C5 = {149/239/248}
f) Innies+Outies R6789: -2 = R5C19 - R6C5
-> R6C5 <> 8 because R5C1 = (36)
-> R6C5 = 9; R5C19 = [34/61]
g) 14(3) @ C5 = 9{14/23}; R4C5 <> 3
h) 25(4) = 68{29/47} because 79{18/36} blocked by Killer pair (79) of 17(4)

7. N5
a) Innies R1234 = 9(3): R4C4 <> 4 because 3 only possible there
b) 17(4) = 25{19/37} -> 2 locked for R5+N4
c) 12(3) = {147} -> R6C3 = 1, R7C4 = 4
d) 14(3) @ R6C6 = 5{18/36}
e) 14(3) @ R6C6: R7C6 <> 5 because R6C67 <> 1 and R6C1 = (36) blocks {36}5

8. R789
a) Innies = 12(4) = {1245} -> R7C9 = 5, R7C6 = 1
b) 14(2) = {68} locked for C9+N9
c) 12(3) = {237} -> R8C8 = 2; {37} locked for R7+N9
d) 9(2) = {36} -> R7C5 = 6, R8C5 = 3
e) 14(3) = {158} -> R6C6 = 8, R6C7 = 5
f) 15(3) = {258} locked for R9+N8
g) R8C6 = 7, R2C6 = 9

9. N36
a) 14(4) = 25{16/34} -> R6C9 = 2
b) 19(4) = {1369} -> R4C8 = 6; {139} locked for C9
c) R5C9 = 4, R6C8 = 3, R1C9 = 7
d) 19(3) = 9{28/46}
e) 9(2) = [27/81]
f) 6 locked in 19(3) = {469} -> 4 locked for C7+N3

10. N2
a) 17(3) = 8{36/45} -> 8 locked for R1+N2

11. Rest is singles.

Rating: 1.25. I used some Killer triples

I found this one rather harder than most recent assassins..at least it took me longer to do,about 3 hours or so.Having said that I didn't use any advanced moves mainly a lot of combo work



c1 is where I made first placements given the restrictions imposed by the 29(4) cage..this also -> r4c8
combo work then shows that r5c2=2/7 and r5c23+r6c3={127}
innies on r789=12(4)..very useful
innies-outies c89 also used
combo work on n456 then solved it but quite long-winded..couldn't really find a "neat" move for this one!!



Regards

Gary

It took me until the end of the weekend, working on and off, to solve A88.

Like Gary I had to do a lot of combo work. After the early steps, I initially found it hard to see which combos to work on but it eventually started to flow. Gary must be a quicker solver than I am; it took me much longer than 3 hours.

I guess I'll still rate A88 as 1.25 but definitely one of the hardest of that rating for me.

In Afmob's walkthrough, as well as the steps that were highlighted by !s, I think steps 5g and 5h were also key ones that removed the need for a lot of combo work. Step 5g looked difficult to spot but maybe that's because I work with an Excel spreadsheet and my only helper is Ruud's combination calculator. Looking again at my walkthrough, I did have the equivalent of step 5g in my step 21 but missed Afmob's step 5h which I think would have made my solving path a lot easier and shorter (this note has been edited to be consistent with changes in Afmob's walkthrough).

Here is my walkthrough, thanks Afmob for corrections to typos. I've also done some of my own tidying up, mainly taking account of eliminations that I missed when I was finishing my original solution late last night.

Prelims

a) R34C3 = {39/48/57}, no 1,2,6
b) R34C7 = {18/27/36/45}, no 9
c) R78C5 = {18/27/36/45}, no 9
d) R89C1 = {14/23}
e) R89C9 = {59/68}
f) 10(3) cage at R1C3 = {127/136/145/235}, no 8,9
g) 19(3) cage at R1C7 = {289/379/469/478/568}, no 1
h) 23(3) cage in N7 = {689}, locked for N7
i) 29(4) cage at R2C1 = {5789}, CPE no 5,7,8,9 in R56C1
j) 14(4) cage at R5C9 = {1238/1247/1256/1346/2345}, no 9

1. 45 rule on N7 1 outie R8C4 = 1 innie R7C1 + 7 -> R7C1 = {12}, R8C4 = {89}

2. Killer pair 1,2 in R7C1 and R89C1, locked for C1 and N7

3. R56C1 = {36/46} (cannot be {34} which clashes with R89C1), 6 locked for C1 and N4
3a. Killer pair 3,4 in R56C1 and R89C1, locked for C1
3b. 15(4) cage at R5C1 = {2346} (only remaining combination, cannot be {1356} because R567C1 = {36}1 clashes with R89C1), R7C1 = 2, R8C4 = 9 (step 1), 3,4 locked for N4, clean-up: no 8,9 in R3C3, no 7 in R8C5, no 3 in R89C1, no 5 in R9C9
[Alternatively 45 rule on C1 2 outies R46C2 = 1 outie R1C1, R1C1 must equal R4C4 -> R6C2 = 4 …]
3c. Naked pair {14} in R89C1, locked for C1 and N7
3d. R6C2 = 4 (hidden single in N4)
3e. 9 in N7 locked in R7C23, locked for R7
3f. R34C3 = [39/48] (cannot be {57} which clashes with R89C3)

At this stage there appears, at first sight, to be a CPE because R1234C1 and R4C2 are all {5789}. However R1C1 must equal R4C2 so there is no CPE.

4. 45 rule on N9 1 outie R8C6 = 1 innie R7C9 + 2, no 1,2,4 in R8C6, no 7,8 in R7C9

5. 45 rule on R89 3 innies R8C258 = 11 = {128/236} (cannot be {137/245} because R8C2 only contains 6,8, cannot be {146} which clashes with R8C1), no 4,5,7, 2 locked for R8, clean-up: no 4,5 in R7C5
5a. 6,8 must be in R8C2 -> no 6,8 in R8C58, clean-up: no 1,3 in R7C5

6. 45 rule on R789 3 remaining innies R7C469 = 10 = {136/145}, 1 locked for R7

7. 12(3) cage in N9 = {138/147/237/345} (cannot be {156} which clashes with R89C9, cannot be {246} which clashes with R7C469), no 6

8. 45 rule R1234 3 innies R4C456 = 9 = {126/135/234}, no 7,8,9
8a. Max R4C6 = 6 -> min R5C678 = 19, no 1

9. 45 rule on R6789 1 innie R6C5 = 2 outies R5C19 + 2
9a. Min R5C19 = 4 -> min R6C5 = 6
9b. Max R6C5 = 9 -> max R5C19 = 7, max R5C9 = 4
9c. R6C5 = {6789} -> R5C19 = [31/32/34/61] cannot be 6 -> no 3 in R5C9, no 8 in R6C5
9d. Min R6C5 = 6 -> max R45C5 = 8, no 8,9

10. 45 rule on C12 2 innies R59C2 = 1 outie R7C3 + 1, IOU no 1 in R5C2
10a. Max R7C3 = 9, max R59C2 = 10, min R9C2 = 3 -> max R5C2 = 7
10b. R7C3 = {689} -> R59C2 = 7,9,10 = [25/27/73], no 5 in R5C2
10c. 1 in N4 locked in R56C3, locked for C3

11. 45 rule on C89 2 innies R59C8 = 1 outie R7C7 + 10
11a. Min R7C7 = 3 -> min R59C8 = 13, no 1,2,3
11b. Max R59C8 = 17 -> max R7C7 = 7

12. 45 rule on N2 2 innies R2C46 = 10 = [19/28]/{37/46}, no 5, no 2 in R2C6

13. 10(3) cage at R1C3 = {127/136/235} (cannot be {145} because R12C3 = {45} => R3C3 = 3 clashes with R89C3), no 4, clean-up: no 6 in R2C6 (step 12)
13a. 1 of {127/136} must be in R2C4 -> no 6,7 in R2C4, clean-up: no 3,4 in R2C6 (step 12)
13b. 2 of {235} must be in R12C3 (R12C3 cannot be {35} which clashes with R89C3), no 2 in R2C4, clean-up: no 8 in R2C6 (step 12)

14. R3C3 = 4 (hidden single in C3), R4C3 = 8, clean-up: no 1 in R3C7, no 5 in R4C7
14a. 8 in N7 locked in R78C2, locked for C2

15. 45 rule on N1 2 innies R23C1 = 1 remaining outie R2C4 + 14
15a. R2C4 = {13} -> R23C1 = 15,17 = {78/89}, no 5, 8 locked for N1
15b. 5 in 29(4) cage locked in R4C12, locked for R4 and N4
15c. R4C456 (step 8) = {126/234}, 2 locked for R4 and N5, clean-up: no 7 in R3C7

16. 19(3) cage at R1C7 = {289/379/469/478} (cannot be {568} because R2C6 only contains 7,9), no 5

17. R1C456 = {269/278/368/458/467} (cannot be {179} which clashes with R2C6, cannot be {359} which clashes with R2C46), no 1

18. 17(4) cage at R1C1 = {1259/1367}
18a. 7 of {1367} must be in R1C1 -> no 7 in R123C2

19. Killer pair 7,9 in 17(4) cage at R1C1 and R23C1, locked for N1
[The elimination of 7 from R12C3 could have been done after step 15b using hidden killer pair 3,5 in R12C3 and R89C3.]
19a. 10(3) cage at R1C3 (step 13) = {136/235}, CPE no 3 in R2C2

20. 12(3) cage at R6C3 = {138/147/156/237/246}, cannot be {129} because 2,9 only in R6C3, cannot be {345} because no 3,4,5 in R6C3), no 9
20a. 1 of {138/156} must be in R6C3, 1 of {147} must be in R6C34 -> no 1 in R7C4
20b. 7,8 of {138/237} must be in R6C4 -> no 3 in R6C4

21. 17(4) cage at R4C4 = {1259/1268/1367/1457/2357} (cannot be {1349/1358} because R5C2 only contains 2,7, cannot be {2348/2456} because no 3,4,5,6,8 in R5C23)
21a. 1 of {1259} must be in R4C4, 1 of {1268/1367/1457} must be in R5C3 -> no 1 in R5C4
21b. 2 of {1259/1268} must be in R5C2, 2 of {2357} must be in R5C23 -> no 2 in R4C4
21c. 5 of {1457} must be in R5C4 -> no 4 in R5C4
21d. 5 of {1457} must be in R5C4, 7 of {2357} must be in R5C23 -> no 7 in R5C4

22. R456C5 = {149/239/257/347} (cannot be {167} which clashes with R78C5, cannot be {356} which clashes with 17(4) cage at R4C4), no 6
22a. R6C5 = {79} -> no 7 in R5C5

23. 45 rule on N8 3 innies R7C46 + R8C6 = 12 = {138/147/156/345}
23a. 1 of {156} must be in R7C6 -> no 6 in R7C6
23b. 1 of {138} must be in R7C6, {345} must be {45}3 (cannot be {34}5 which clashes with R7C469) -> no 3 in R7C6

24. R8C6 = R7C9 + 2 (step 4)
24a. 45 rule on N9 4 innies R7C9 + R8C7 + R9C78 = 19 = {1279/1459/1468/2359/2368/2467} (cannot be {1369/1567/2458} which clash with R89C9, cannot be {1378} because no 6 in 12(3) cage, cannot be {3457} because R7C9 = 3 or 5 gives repeated digit in 21(4) cage and R7C9 = 4 => R9C78 = {357} clashes with R9C23)
24b. 2 of {2359/2368} must be in R9C7 -> no 3 in R9C7
24c. 2 of {1279/2467} must be in R9C7 -> no 7 in R9C7
24d. Cannot be {1279} because R89C9 = {68}, 12(3) cage = {345} and R7C789 = {45}1 clashes with R7C6
24e. -> R7C9 + R8C7 + R9C78 = {1459/1468/2359/2368/2467}

25. 12(3) cage in N9 (step 7) = {138/147/237} (cannot be {345} which clashes with R7C9 + R8C7 + R9C78), no 5
25a. 1,2 of {138/237} must be in R8C8 -> no 3 in R8C8

26. 5 in R7 locked in R7C469 = {145}, locked for R7, clean-up: no 5,8 in R8C6 (step 4)
[Alternatively killer quad 6,7,8,9 in R7C235 and R7C78, locked for R7]

27. 3 in R7 locked in R7C78, locked for N9

28. R8C6 = R7C9 + 2 (step 4)
28a. 4 in N9 locked in R7C9 + R8C7 + R9C78 = {1459/1468} (cannot be {2467} because 4 must be in R7C9 giving repeated 6 in 21(4) cage), no 2,7, 1 locked for N9 -> R8C8 = 2, R7C78 = 10 = {37}
28b. Naked pair {37} in R7C78, locked for R7

29. 2 in R9 locked in R9C456 = {258/267}, no 1,3,4
29a. R7C46 + R8C6 (step 23) = {147/345} (cannot be {156} which clashes with R9C456), no 6, clean-up: no 4 in R7C9 (step 4)
29b. 3 in N8 locked in R8C56, locked for R8

30. Killer pair 5,7 in R9C23 and R9C456, locked for R9

31. 12(3) cage at R6C3 (step 20) = {147/156/246}, no 8
31a. 5 of {156} must be in R7C4 -> no 5 in R6C4

32. 14(3) cage at R6C6 = {149/158/248/257} (cannot be {167} which clashes with R6C34, cannot be {239} because R7C6 only contains 1,4,5, cannot be {347} which clashes with R6C1 + R6C34, cannot be {356} which clashes with R6C1), no 3,6
32a. 2 of {257} must be in R6C7 -> no 7 in R6C7

33. 14(4) cage at R5C9 = {1238/1247/1256/2345} (cannot be {1346} which clashes with R6C1), 2 locked in R56C9 for C9 and N6
33a. 4 of {1247} must be in R5C9 with 2 in R6C9 -> no 7 in R6C9
33b. 1 of {1238/1247} must be in R7C9
33c. {1256} = 1[62]5/2{56}1 (cannot be 2{16}5 which clashes with R6C34)
33d. combining steps 33b and 33c -> no 1 in R6C89

34. 14(3) cage at R6C6 (step 32) = {149/158}, no 7

35. 19(3) cage at R1C7 (step 16) = {289/379/469/478}
35a. 7 of {379/478} must be in R2C6 (cannot be R12C7 = {37} which clashes with R7C7) -> no 7 in R12C7

36. 14(4) cage at R5C9 (step 33) = {1247/1256/2345} (cannot be {1238} because R6C89 = {38} => R6C67 = {19} so cannot place 5 in R6), no 8
36a. 2 of {2345} must be in R6C9 (4 is in R5C9) -> no 3 in R6C9

37. 8 in R6 locked in R6C67 -> 14(3) cage at R6C6 (step 34) = {158}
37a. R6C5 = 9 (hidden single in R6), R45C5 = 5 = {14}/[23], no 3 in R4C5, no 5 in R5C5
37b. Killer pair 1,3 in R45C5 and R8C5, locked for C5
37b. R7C4 = 4 (hidden single in R7)

38. R6C5 = R5C19 + 2 (step 9)
38a. R6C5 = 9 -> R5C19 = 7 = [34/61], no 2 in R5C9

39. R6C9 = 2 (hidden single in C9)
39a. 14(4) cage at R5C9 (step 36) = {1247/1256/2345}
39b. 6 of {1256} must be in R6C8, 5 of {2345} must be in R7C9 -> no 5 in R6C8

40. 5 in R6 locked in R6C67 -> R6C67 = {58}, R7C6 = 1, R7C9 = 5, R8C5 = 3, R7C5 = 6, R8C6 = 7, R7C23 = [89], R8C23 = [65], R89C9 = [86], R2C6 = 9, R2C4 = 1 (step 12), clean-up: no 2 in R12C3 (step 19a)
40a. R6C3 = 1 (hidden single in R6), R6C4 = 7 (step 31)

41. Naked pair {36} in R12C3, locked for C3 and N1 -> R9C23 = [37], R5C23 = [72]
41a. R5C23 = 9 -> R45C4 = 8 = [35], R6C67 = [85], clean-up: no 6 in R3C7, no 4 in R4C7, no 2 in R4C5 (step 37a)

42. Naked pair {14} in R45C5, locked for C5 and N5 -> R45C6 = [26], R56C1 = [36], R6C8 = 3, R5C9 = 4 (step 36), R45C5 = [41], R7C78 = [37], R9C6 = 5, R3C6 = 3, R1C6 = 4, clean-up: no 6 in R2C7 (step 16), no 6 in R4C7

43. R4C7 = 7 (hidden single in C7), R3C7 = 2, clean-up: no 8 in R12C7 (step 16)
43a. R12C7 = [64], R12C3 = [36], R89C7 = [19], R9C8 = 4, R89C1 = [41], R5C78 = [89], R4C89 = [61]

44. R4C89 = 7 -> R23C9 = 12 = [39], R1C9 = 7
[Original step 44 deleted, step 44a renumbered.]

45. R1C6 = 6 -> R1C45 = 13 = [85]
[Original step 45 deleted, step 45a renumbered.]

and the rest is naked singles

3x3::k:3840:2817:2817:3587:3587:3587:5382:2823:2823:3840:3594:3595:3595:3587:5382:5382:4368:2823:3840:3594:4884:3595:6934:3351:3351:4368:4368:2587:3594:4884:3614:6934:3104:4129:4129:4129:2587:2587:4884:3614:6934:3104:5674:3371:3371:5165:5165:5165:3614:6934:3104:5674:3380:3371:3894:3894:1848:1848:6934:2619:5674:3380:3646:4415:3894:4929:4929:4675:2619:2619:3380:3646:4415:4415:4929:4675:4675:4675:2382:2382:3646:

I can't say that this assassin was "disturbingly" easy or moderate. I guess I missed something since I used a chain to crack it.

A89 Walkthrough:

1. C1234
a) Innies N14 = 1 = R2C3
b) 7(2): R7C4 <> 6
c) Outies N7 = 13(2) = [49/58]
d) 7(2) = [25/34]
e) Innies = 5(2) = {14/23}

2. N23
a) Innies = 1 = R3C5
b) 14(4) = {2345} locked for N2
c) 14(3) = {167} -> 6,7 locked for C4+N2
d) Naked pair (89) locked in R23C6 for C6
e) 13(2) = [85/94]
f) Innies N3 = 17(3) = 4{58/67} -> 4 locked for C7+N3
g) 9 locked in 17(3) = 9{26/35}
h) 1 locked in 11(3) = 1{28/37}

3. C6789
a) Innies N69 = 3 = R8C7
b) Hidden pair (12) in R49C7 for C7 -> no other candidates
c) 9(2) = [18/27]
d) 16(3) = {169/178/259/268}; R4C89 <> 1,2
e) 10(3) = {16/25}3
f) 12(3) <> 6 because 6{15/24} blocked by Killer pairs (26,56) of 10(3)
g) 6 locked in R789C6 for N8
h) Innies = 9(2): R9C6 <> 1,2,3

4. N589
a) Outies N5 = 7 = R7C5
b) 3 locked in 18(4) for R9
c) 6 locked in 27(5) = 167{49/58}
d) 7 locked in 12(3) = 7{14/23}

5. N369
a) Innies+Outies N9: -6 = R6C8 - R7C7 -> R7C7 = (89), R6C8 = (23)
b) Killer pair (12) locked in 9(2) + 14(3) for N9
c) 13(3) @ N9 = {247/256/346}
d) 14(3) <> 6 because {167} blocked by Killer pair (67) of 13(3) @ N9
e) 6 locked in 13(3) @ N9 = 6{25/34} -> 6 locked for C8
f) 4 locked in 13(3) @ R5C8 = 4{18/27/36}

6. C123
a) 9 locked in R1C123 for N1
b) Innies N1 = 18(3) = {378/468/567}
c) Innies+Outies N1: -4 = R4C2 - R3C3 -> R3C3 <> 3,4; R4C2 = (1234)
d) 11(2) <> {47} since it's a Killer pair of Innies N1
e) Outies C12 = 12(2) = [39/57/84/93]
f) 11(2): R1C2 <> 5,9

7. R123
a) Killer quad (2345) locked in 11(2) + R1C456 for R1
b) 11(3) must have 2 xor 3 and it's only possible @ R2C9 -> R2C9 = (23)
c) 15(3) <> {267} since it's blocked by Killer pair (67) of Innies N1
d) 15(3) must have 6,7,8 xor 9 and R1C1 = (6789) -> R23C1 <> 6,7,8
e) 21(3): R2C7 <> 8 because R1C7 <> 4
f) 8 locked in R1C789 for R1
g) 11(2) = [29/65]
h) Killer pair (25) locked in 15(3) + 11(2) for N1
i) Innies+Outies N1: -4 = R4C2 - R3C3 -> R4C2 = (234)
j) 14(3) = 4{28/37} -> 4 locked for C2

8. C123
a) 14(3): R4C2 <> 3 because {47}3 blocked by Killer pair (47) of 15(3)
b) Innies+Outies N1: -4 = R4C2 - R3C3 -> R3C3 <> 7
c) Outies C12 = 12(2) = [57/93]
d) 20(3) <> 6 because R6C3 = (37); R6C12 <> 3,7
e) 19(3) @ N1 <> 3 because {379} blocked by R6C3 = (37)
f) Innies N7 = 13(3) <> 9 because R789C3 <> 1

9. N36
a) 17(3): R3C9 <> 2,9 because R23C8 <> 6 and Killer pair (35) of 13(3) @ R6C8 blocks {35}9
b) 9 locked in 17(3) for C8
c) Innies N3 = 17(3): R2C7 <> 5 because 21(3) can't have 5 and 8

10. R123 !
a) ! Consider candidates of R3C3 -> R3C9 <> 6
- i) R3C3 = 6 -> R3C9 <> 6
- ii) R3C3 = 8 -> R2C6 = 8 (HS @ N2) -> 21(3) = 8{67} -> R3C9 <> 6
b) 17(3) = {359} locked for N3
c) Innies N3 = {467} -> R3C7 = 4; {67} locked for C7+N3

11. N69
a) 22(3) = {589} -> 5 locked for N6
b) 16(3) = 8{17/26} because R4C8 = (78) -> 8 locked for R4+N6
c) 13(3) @ R5C8 = 4{27/36}
d) 1 locked in 16(3) = {178} -> R4C7 = 1; 7 locked for R4+N6
e) 13(3) @ R5C8 = {346} locked for N6
f) 9(2) = [27] -> R9C7 = 2, R9C8 = 7
g) 13(3) @ R6C8 = {256} -> R6C8 = 2, {56} locked for C8+N9

12. N17
a) Hidden Single: R3C1 = 2 @ R3
b) 15(3) = {249} -> R1C1 = 9, R2C1 = 4
c) 17(3) = {179} -> R8C1 = 7, R9C1 = 1, R9C2 = 9

13. Rest is singles.

Rating: Easy 1.5. I had to use a small chain to crack it

remember starting with heavy work on:
N3: outies r23c6 = {89} combos on innies r123c7 = {67}4 | {48}5 = 4..
N3: -> 17/3 = 9..-> 674,935,128 | 485,917,236 | 485,926,137
innies on C7 -> r489 = {123}
And then working on N6 and N9

Hope you can find some of them below.

I took longer than I should have done because I initially made a silly mistake in step 27. However once I'd sorted that out and extended step 27 the rest of it came fairly smoothly.

I'll rate A89 as a moderate to hard 1.25. I don't think steps 25 and 26 require a higher rating.

Here is my walkthrough. I think the key steps are 25, 26, 27 and 33.

Prelims

a) R1C23 = {29/38/47/56}, no 1
b) R3C67 = {49/58/67}, no 1,2,3
c) R7C34 = {16/25/34}, no 7,8,9
d) R9C89 = {18/27/36/45}, no 9
e) 21(3) cage at R1C7 = {489/579/678}, no 1,2,3
f) 11(3) cage in N3 = {128/137/146/236/245}, no 9
g) R345C3 = {289/379/469/478/568}, no 1
h) 10(3) cage in N4 = {127/136/145/235}, no 8,9
i) R6C123 = {389/479/569/578}, no 1,2
j) R567C7 = {589/679}, 9 locked for C7, clean-up: no 4 in R3C6
k) 10(3) cage at R7C6 = {127/136/145/235}, no 8,9
l) 19(3) cage at R8C3 = {289/379/469/478/568}, no 1
m) 14(4) cage in N2 = {1238/1247/1256/1346/2345}, no 9

1. 9 in R1 locked in R1C123, locked for N1

2. 21(3) cage at R1C7 = {489/579/678}
2a. 9 of {489/579} must be in R2C6 -> no 4,5 in R2C6

3. 45 rule on N5 2 outies R37C5 = 8 = {17/26/35}, no 4,8,9
3a. 45 rule on N5 3 innies R456C5 = 19 = {289/379/469/478/568}, no 1

4. 45 rule on C12 2 outies R16C3 = 12 = {39/48/57}, no 2,6, clean-up: no 5,9 in R1C2

5. 45 rule on C89 2 outies R49C7 = 3 = {12}, locked for C7, clean-up: R9C8 = {78}
5a. Max R4C7 = 2 -> min R4C89 = 14, no 1,2,3,4

6. R8C7 = 3 (hidden single in C7)
[Alternatively 45 rule on N69 1 innie R8C7 = 3]
6a. R78C6 = 7 = {16/25}, no 4,7

7. 45 rule on N14 1 innie R2C3 = 1, clean-up: no 6 in R7C4
7a. R23C4 = 13 = {49/58/67}, no 2,3

8. 45 rule on N3 2 outies R23C6 = 17 = {89}, locked for C6 and N2, clean-up: R3C7 = {45}, no 4,5 in R23C4 (step 7a)
8a. Naked pair {67} in R23C4, locked for C4 and N2, clean-up: no 1,2 in R7C5 (step 2)

9. 45 rule on N2 1 remaining innie R3C5 = 1, R7C5 = 7 (step 3)
9a. R456C5 (step 3a) = {289/469/568}, no 3

10. Killer quad 2,3,4,5 in R1C23 and R1C456, locked for R1

11. 21(3) cage at R1C7 = {489/579/678}
11a. 4 of {489} must be in R2C7, 8 of {678} must be in R2C6 -> no 8 in R2C7

12. 4 in C7 locked in R23C7, locked for N3
12a. 1 in R1 locked in R1C89
12b. 11(3) cage in N3 = {128/137}, no 5,6
12c. 2,3 only in R2C9 -> R2C9 = {23}
12d. Killer pair 7,8 in R12C7 and 11(3) cage, locked for N3
[Alternatively 9 in N3 locked in 17(3) cage = {269/359}]
12e. 8 in N3 locked in R1C789, locked for R1, clean-up: no 3 in R1C23, no 4,9 in R6C3 (step 4)
12f. 3 in R1 locked in R1C456, locked for N2

13. 45 rule on N7 2 outies R78C4 = 13 = [49/58], clean-up: R7C3 = {23}
13a. 3 in N8 locked in R9C456, locked for R9

14. 45 rule on C1234 2 innies R19C4 = 5 = {23}/[41]

15. 45 rule on C6789 2 innies R19C6 = 9 = [36]/{45}
15a. Killer triple 4,5,6 in R7C4, R78C6 and R9C6, locked for N8

16. 6 in C5 locked in R456C5, locked for N5
16a. R456C5 = {469/568}, no 2

17. 7 in C6 locked in R456C6 = {147/237}, no 5

18. 45 rule on N4 1 outie R3C3 = 1 innie R4C2 + 4, R3C3 = {5678}, R4C2 = {1234}

19. 45 rule on N6 1 outie R7C7 = 1 innie R6C8 + 6, R7C7 = {89}, R6C8 = {23}

20. R789C9 = {149/158/248/257} (cannot be {167} which clashes with R9C78), no 6
20a. Killer pair 1,2 in R789C9 and R9C7, locked for N9
20b. R12C9 cannot be [12] which clashes with R789C9 -> no 8 in R1C8
20c. Killer triple 7,8,9 in R7C7, R789C9 and R9C8, locked for N9

21. R678C8 = {256/346}, 6 locked for C8

22. 4 in N6 locked in 13(3) cage = 4{18/27/36}, no 5,9

23. 45 rule on N7 3 innies R789C3 = 13 = {238/247/256/346}, no 9

24. 45 rule on N3 3 innies R123C7 = 17 = {458/467}
24a. {458} must be [845] (cannot be [854] which clashes with 21(3) cage), no 5 in R2C7

25. 15(3) cage in N7 = {159/168/258/348} (cannot be {249/267/357} which clash with R789C3, cannot be {456} which clashes with R7C4 + R7C8), no 7
25a. 3 in N7 must be in R7C123 -> either 15(3) cage must contain 3 or R789C3 = 3{28/46} -> 15(3) cage cannot be {168}
25b. 15(3) cage = {159/258/348}, no 6

26. 17(3) cage in N7 = {179/269/278/467} (cannot be {458} which clashes with 15(3) cage), no 5
26a. 1 in N7 must be in 15(3) cage or 17(3) cage, if 17(3) not {179} => 15(3) = {159} -> 17(3) cannot be {269}
26b. 17(3) cage = {179/278/467}, 7 locked for N7
26c. 9 of {179} must be in R9C12 (cannot be 9{17} which clashes with R9C78), no 9 in R8C1
26d. R789C3 (step 23) = {238/256/346}

27. 45 rule on N4 3 innies R4C23 + R5C3 = 15 = {249/348} (cannot be {159/267/357} which clash with R345C3, cannot be {168/258/456} because R345C3 = {568} clashes with R789C3), no 1,5,6,7, clean-up: no 5 in R3C3 (step 18)
27a. R345C3 = {289/469/478} (cannot be {379} which clashes with R4C23 + R5C3), no 3
27b. 4 locked in R4C23 + R5C3, locked for N4

28. 1 in N4 locked in 10(3) cage = {127/136}, no 5

29. 5 in N4 locked in R6C123, locked for R6
29a. R6C123 = {569/578}, no 3
[Alternatively this follows from hidden killer pair 6,7 in 10(3) cage and R6C123]

30. R567C7 = {589/679}
30a. 5 of {589} must be in R5C7 -> no 8 in R5C7
30b. 5 of {589} must be in R5C7 and 9 of {679} must be in R7C7 -> no 9 in R5C7

31. R7C3 = 3 (hidden single in C3), R7C4 = 4, R8C4 = 9 (step 13), clean-up: no 5 in R1C6 (step 15), no 1 in R9C4 (step 14)
31a. Naked pair {23} in R19C4, locked for C4
31b. R8C4 = 9 -> R89C3 = {28/46}, no 5

32. Naked triple {158} in R456C4, locked for N4
32a. Naked triple {469} in R456C5, locked for C5 and N5
32b. Naked triple {237} in R456C6, locked for C6 -> R1C6 = 4, R9C6 = 5 (step 15), clean-up: no 7 in R1C23

33. R4C23 + R5C3 (step 27) = {249} (cannot be {348} which clashes with R89C3), locked for N4, clean-up: no 7 in R3C3 (step 18), no 7 in 10(3) cage (step 28), no 6 in R6C123 (step 29a)
33a. 9 locked in R45C3, locked for C3 -> R1C3 = 5, R1C2 = 6, R3C3 = 8, R4C2 = 4 (step 18), R6C3 = 7, R3C6 = 9, R3C7 = 4, R2C6 = 8, R12C7 = [76], R1C1 = 9, R1C89 = [18], R2C9 = 2 (step 12b), R2C5 = 5, R5C7 = 5, R23C4 = [76], R2C12 = [43], R2C8 = 9, R3C12 = [27] (cage sums), R5C2 = 1, R56C4 = [81], R4C4 = 5, clean-up: no 2 in R89C3 (step 31b)

34. Naked pair {58} in R6C12, locked for R6 -> R67C7 = [98], R6C8 = 2 (step 19), R6C6 = 3, R4C7 = 1, R9C78 = [27], R9C4 = 3, R9C5 = 8, R8C5 = 2, R9C2 = 9, R1C45 = [23], clean-up: no 7 in R5C89 (step 22), no 4 in R8C8 (step 21)

35. Naked pair {56} in R78C8, locked for C8 and N9

and the rest is naked singles

3x3:d:k:4352:4352:4352:3843:3843:3843:6406:6406:6406:4352:5642:5642:5642:3843:4622:4622:4622:6406:3858:3858:5642:3605:4374:4374:4622:3353:3353:3858:6428:3605:3605:4895:1312:3617:4130:3353:6428:6428:2342:1831:4895:1312:3617:4130:4130:3885:6428:2342:1831:4895:3890:3890:4130:4661:3885:3885:4408:3385:3385:3890:4924:4661:4661:5951:4408:4408:4408:4419:4924:4924:4924:4423:5951:5951:5951:4419:4419:4419:4423:4423:4423:

I've just finished Bored89-Easy. Nice puzzle!

It is easy but only after one finds the key move. It appears from the earlier messages that some people didn't find it. I must admit that I was also struggling until I spotted step 3a.

I wasn't sure how to rate this puzzle. Step 3a isn't a difficult move but it's hard to spot unless one is looking for that sort of move. Obviously I can't take into account the time "wasted" before that step so I'll rate Bored89-Easy as a 1.25.

Here is my walkthrough. Thanks Afmob for your comments which I've used for editing several steps. Fortunately my error in step 8 didn't affect other steps; that elimination is now made in step 26c.

This is a Killer-X. I've included eliminations along diagonals, for those not using software to do eliminations, because they are easy to overlook.

Prelims

a) R3C56 = {89}, locked for R3 and N2
b) R45C6= {14/23}
c) R45C7 = {59/68}
d) R56C3 = {18/27/36/45}, no 9
e) R56C4 = {16/25} (cannot be {34} which clashes with R45C6)
f) R7C45 = {49/58/67}, no 1,2,3
g) R456C5 = {289/379/469/478/568}, no 1

1. Killer pair 1,2 in R45C6 and R56C4, locked for N5

2. 45 rule on R12 2 outies R3C37 = 7 = {16/25/34}, no 7

3. 45 rule on R89 2 outies R7C37 = 3 = {12}, locked for R7
3a. CPE no 1,2 in R3C37, clean-up: no 5,6 in R3C37 (step 2)
3b. Naked pair {34} in R3C37, locked for R3
3c. CPE no 3,4 in R5C5

4. 15(3) cage at R3C1 = {159/168/258/267/357/456} (cannot be {249/348} because 3,4,8,9 only in R4C1
4a. 8,9 of {159/168} must be in R3C12 -> no 1 in R4C1
4b. 3,4,8,9 of {159/258/357/456} must be in R4C1 -> no 5 in R4C1

5. 13(3) cage at R3C8 = {157/247/256} (cannot be {139/148/238/346} because 3,4,8,9 only in R4C9), no 3,8,9

6. 45 rule on N1 2 outies R2C4 + R4C1 = 9 = [18]/{27/36}/[54], no 9, no 4 in R2C4

7. 45 rule on N3 2 outies R2C6 + R4C9 = 11 = {47/56}, no 1,2,3

8. 45 rule on N7 2 outies R6C1 + R8C4 = 10 = {19/28/37/46}/[55]
[I first made a "doubles possible" error more than a year ago. Since then I've usually managed to avoid that error so I don't know why I made it this time. I think that every time I've noticed "doubles possible" for outies they have been eliminated before the final solution. Maybe sometime there will be a puzzle with this "trap" using the doubles as part of the final solution. ]

9. 45 rule on N9 2 outies R6C9 + R8C6 = 9 = {18/27/36/45}, no 9

10. 45 rule on N4 3 innies R4C13 + R6C1 = 11 = {128/137/146/236/245}, no 9, clean-up: no 1 in R8C4 (step 8)

11. 45 rule on C6789 3 innies R139C6 = 20 = {389/479/569/578}, no 1,2
11a. 3 of {389} must be in R1C6 -> no 3 in R9C6

12. 45 rule on N5 2 innies R4C4 + R6C6 = 14 = {59/68}

13. 7 in N5 locked in R456C5, locked for C5, clean-up: no 6 in R7C4
13a. R456C5 = {379/478}, no 5,6

14. Killer pair 8,9 in R3C5 and R456C5, locked for C5, clean-up: no 4,5 in R7C4

15. 45 rule on C1234 3 innies R179C4 = 16 = {169/178/259/268/349/358/367/457}
15a. 9 of {169/259/349} must be in R7C4 -> no 9 in R9C4

16. Hidden killer pair 1,2 in R45C6 and R8C6 for C6 -> R8C6 = {12}
16a. 45 rule on C789 2 outies R28C6 = 1 innie R6C7 + 5
16b. Max R28C6 = 9 -> max R6C7 = 4
16c. R28C6 = 6,7,8,9 = [51/52/61/62/71/72] (cannot be [42] which clash with R45C6), no 4, clean-up: R6C9 = {78} (step 9), no 7 in R4C9 (step 7)

17. 45 rule on N6 3 innies R4C9 + R6C79 = 15 = {168/267/348/357} (cannot be {456} because R6C9 only contains 7,8, cannot be {258} which clashes with R45C7)
17a. 3 of {348} must be in R6C7 -> no 4 in R6C7

18. R7C7 + R8C6 = {12} = 3 -> R8C78 = 16 = {79}, locked for R8 and N9, clean-up: no 1,3 in R6C1 (step 8)
18a. CPE no 1,2 in R8C9

19. Killer triple 7,8,9 in R4C4 + R6C6, R5C5 and R8C8, locked for D\

20. 15(3) cage at R6C6 = {168/249/258/267/348/357} (cannot be {159} which clashes with R139C6, cannot be {456} because R6C7 only contains 1,2,3)
20a. 9 of {249} must be in R6C6 -> no 9 in R7C6
20b. 3 of {348/357} must be in R6C7 -> no 3 in R7C6

21. 45 rule on N8 3 innies R7C6 + R8C46 = 15 = {168/258/267} (cannot be {348/357/456} because R8C6 only contains 1,2), no 3,4, clean-up: no 6,7 in R6C1 (step 8)
21a. 2 of {258/267} must be in R8C6 -> no 2 in R8C4, clean-up: no 8 in R6C1 (step 8)

22. Hidden killer pair 3,4 in R19C6 and R45C6 for C6 -> R19C6 must contain 3 or 4 -> R139C6 (step 11) = {389/479}, no 5,6, 9 locked for C6, clean-up: no 5 in R4C4 (step 12)

23. 15(3) cage at R6C6 (step 20) = {168/258/267/357}
23a. Hidden killer pair 5,6 in R2C6 and R67C6 for C6 -> R2C6 = {56}, clean-up: no 4 in R4C9 (step 7)

24. 13(3) cage at R3C8 (step 5) = {157/256}, CPE no 5 in R12C9

25. R4C9 + R6C79 (step 17) = {168/267/357}
25a. Killer pair 5,6 in R45C7 and R4C9 + R6C79, locked for N6

26. 45 rule on N2 3 innies R2C46 + R3C4 = 13 = {157/256}, no 3, 5 locked for N2, clean-up: no 6 in R4C1 (step 6)
26a. 6 in {256} must be in R2C6 (R23C4 cannot be {26} which clashes with R56C4) -> no 6 in R23C4, clean-up: no 3 in R4C1 (step 6)
26b. Killer pair 1,2 in R23C4 and R56C4, locked for C4
26c. 5 in C5 locked in R789C5, locked for N8

27. R4C13 + R6C1 (step 10) = {128/245} (cannot be {137} because R6C1 only contains 2,4, cannot be {146/236} because 1,3,6 only in R4C3), no 3,6,7, 2 locked for N4, clean-up: no 2 in R2C4 (step 6), no 7 in R56C3
27a. 1,5 must be in R4C3 -> R4C3 = {15}
27b. 2 locked in R46C1, locked for C1

28. 14(3) cage at R3C4 = {158/167} (cannot be {257} because 2,7 only in R3C4), no 2,9, clean-up: no 5 in R6C6 (step 12)

29. Naked pair {68} in R4C4 + R6C6, locked for N5 and D\, clean-up: no 4 in R46C5 (step 13a), no 1 in R56C4

30. Naked pair {25} in R56C4, locked for C4 and N5, clean-up: no 4 in R4C1 (step 6), no 3 in R45C6

31. Naked pair {14} in R45C6, locked for C6 -> R8C6 = 2, R7C7 = 1, locked for D\, R7C3 = 2, locked for D/ -> R56C4 = [25], 5 locked for D/, R6C9 = 7 (step 9), clean-up: no 4 in R5C3, no 7 in R19C6 (step 11) -> R1C6 = 3

32. Naked pair {89} in R39C6, locked for C6 -> R67C6 = [67], R6C7 = 2 (step 23), R2C6 = 5, R4C9 = 6 (step 7), R4C4 = 8, R3C4 = 1 (step 28), R4C3 = 5, R2C4 = 7, R7C45 = [94], R9C6 = 8, R3C56 = [89], R89C4 = [63], R1C4 = 4, R1C1 = 5, locked for D\, R46C1 = [24], R45C7 = [95], R8C78 = [79], 9 locked for D\ -> R5C5 = 7, 7 locked for D/, R46C5 = [39], clean-up: no 3 in R5C3
32a. R7C12 = 11 = {38}/[65], no 6 in R7C2

33. Naked pair {67} in R3C12, locked for R3 and N1
33a. Naked pair {25} in R3C89, locked for N3

34. R7C3 + R8C4 = 8 -> R8C23 = 9 = {18}, locked for R8 and N7

and the rest is naked singles, remembering eliminations along the diagonals


I'll have a try at the "Hard" version once I've caught up with a couple of other walkthroughs. A fair number of the steps used for "Easy" can still be used because of the way the puzzle wraps itself around N5

Hi folks,Well, finally finished it.

I was actually very close to the breakthrough (step 14) when I stopped after the last session. I now retract my comment above regarding picking off of individual candidates.

All in all, this was a nice puzzle, which looked impossible at the beginning, due to the huge number of candidates still left after the (relatively few) preliminaries. There were also some good X-moves in there. The difficulty level was just right for me. Many thanks to Nasenbaer for a great little puzzle!

As for the rating, I'll go along with Andrew's 1.25.

Edit: Thanks to Andrew for minor addition to step 18b!

Bored 89 Easy Walkthrough

Prelims:

a) 17(2) at R3C5 = {89}, locked for R3 and N2
b) 19(3) at R4C5 = {289/379/469/478/568} (no 1) = {(8/9)..}
c) 5(2) at R4C6 = {14/23} = {(3/4)..}
d) 14(2) at R4C7 = {59/68}
e) 9(2) at R5C3 = {18/27/36/45} (no 9)
f) 7(2) at R5C4 = {16/25} = {(2/6)..}
(Note: {34} blocked by 5(2) at R4C6 (prelim c))
g) 13(2) at R7C4 = {49/58/67} (no 1..3)

1. 19(3) at R4C5 (prelim. b) and R3C5 form killer pair on {89} within C5
1a. -> no 8,9 elsewhere in C5
1b. cleanup: no 4,5 in R7C4

2. Innies N5: R4C4+R6C6 = 14(2) = {59/68} = {(8/9)..}

3. 7 in N5 locked in 19(3) at R4C5 (prelim b) = {379/478} (no 2,5,6) = {(3/4)..}
3a. 7 locked in R456C5 for C5
3b. cleanup: no 6 in R7C4

4. Outies R89: R7C37 = 3(2) = {12}, locked for R7
4a. no 1,2 in R3C37 (CPE)

5. Outies R12: R3C37 = 7(2) = {34} (last combo), locked for R3
5a. no 3,4 in R5C5 (CPE)

6. 13(3) at R3C8 = {157/247/256} (no 3,8,9)
(Note: {139/148/238/346} unplaceable)

7. Outies N3: R2C6+R4C9 = 11(1+1) = {47/56} (no 1..3)

8. Innies C6789: R139C6 = 20(3) = {389/479/569/578} (no 1,2)
8a. 3 of {389} must go in R1C6
8b. -> no 3 in R9C6

9. Hidden killer pair on {12} in C6 at R45C6 and R8C6
9a. -> R8C6 = {12}

10. 19(4) at R7C7 = {1279} (last combo)
10a. -> R8C78 = {79}, locked for R8 and N9
10b. no 1,2 in R8C9 (CPE)

11. R8C8, R5C5 and R4C4+R6C6 (step 2) form killer triple on {789} in D\
11a. -> no 7..9 elsewhere in D\
11b. 8 locked in R4C4+R5C5+R6C6 for N5

12. Outies N9: R6C9+R8C6 = 9(2)
12a. -> R6C9 = {78}

13. Innies N6: R4C9+R6C79 = 15(3) = {168/258/267/348/357}
(Note: {159/249/456} unplaceable)
13a. must have 1 of {123}, only available in R6C7
13b. -> R6C7 = {123}
13c. can only have 1 of {78}, which must go in R6C9
13d. -> no 7 in R4C9
13e. cleanup: no 4 in R2C6 (step 7)

14. R2C3 and 17(4) at R1C1 form hidden killer pair on {89} within N1
14a. -> R2C3 = {89} (no 1..7)
14b. 17(4) at R1C1 = {(8/9)..} = {1259/1268/1358} (no 4,7)
(Note: {1349/2348} both blocked by R3C3)

15. 7 in N1 locked in R3C12 for R3 and 15(3)
15a. 15(3) at R3C1 = {7..} = {267/357} (no 1,4,8,9)
15b. 3 only available in R4C1
15c. -> no 5 in R4C1

16. Outies N1: R2C4+R4C1 = 9(1+1)
16a. -> R2C4 = {367} (no 1,2,4,5)

17. 13(3) at R3C8 (step 6) = {256} (no 1,4) (last combo)
17a. 2 locked in R3C89 for R3 and N3
17b. cleanup: no 7 in R2C6

18. Innies N2: R2C46+R3C4 = 13(3) = [751] (last permutation)
18a. -> R4C19 = [26] (steps 7,16)
18b. cleanup: no 3 in R5C6; no 5 in R3C12 (step 15a); no 6 in R56C4; no 6 in R7C5; no 8 in R45C7; no 7 in R56C3

19. 1 in N5 locked in 5(2) at R4C6 = {14}, locked for C6 and N5

--- NOTE: cleanups omitted from here on for simplicity ---

20. Naked single at R8C6 = 2
20a. -> R7C7 = 1; R7C3 = 2; R6C9 = 7 (outie N9)
20b. -> R6C7 = 2 (innie N6); R56C4 = [25]

21. Naked pair at R45C7 = {59}, locked for C7 and N6
21a. -> R8C78 = [79]
21b. -> Split 13(2) at R4C34 = [58]
21c. -> R5C5 = 7; R67C6 = [67]; R45C7 = [95]; R7C45 = [94]
21d. -> split 12(2) at R46C5 = [39]; R19C6 = [38]
21e. -> R3C56 = [89]; R1C1 = 5

22. Innie N8: R8C4 = 6

Rest is now just singles and simple cage sums

3x3:d:k:4352:4352:4352:3843:3843:3843:6406:6406:6406:4352:5642:5642:5642:3843:4622:4622:4622:6406:3858:3858:5642:3605:4374:4374:4622:3353:3353:3858:6428:3605:3605:3871:3871:3617:4130:3353:6428:6428:2342:4135:3871:3871:3617:4130:4130:3885:6428:2342:4135:4135:3890:3890:4130:4661:3885:3885:4408:3385:3385:3890:4924:4661:4661:5951:4408:4408:4408:4419:4924:4924:4924:4423:5951:5951:5951:4419:4419:4419:4423:4423:4423:

What a tough Killer. There was only little progress you could make with no breakthrough moves at all but by picking off every candidate one by one I was able to solve it.

I think it would be best if we name A89 V2 (Easy) as A89 V1.5 since it fits with the difficulty though I haven't solved it but tried and it seems to be at least as tough as A89 V1.

We cannot expect that Ruud's makes all V2 for us so it's good that other users do this. But right now, I would love to have some easier assassins which aren't of rating 1.25-1.5 since they are the most fun to solve.

A89 V2 (Hard) Walkthrough:

1. N123
a) 17(2) = {89} locked for R3+N2
b) Outies N1 = 9(1+1): R4C1 <> 1,9
c) Outies N3 = 11(1+1) <> 1; R4C9 <> 2,3

2. N789+D\/
a) Outies R89 = 3(2) = {12} locked for R7
b) Outies N9 = 9(1+1) <> 9
c) R3C37+R5C5 <> 1,2 since they see all 1,2 of R7
d) 15(3) @ N7: R6C1 <> 9 because R7C12 >= 7
e) Outies N7 = 10(1+1): R8C4 <> 1

3. R123 + D\/
a) Outies R12 = 7(2) = {34} locked for R3
b) R5C5 <> 3,4 because it sees all 3,4 of R3
c) 15(4): R4C56+R5C6 <> 8,9 because R5C5 >= 5
d) 15(3): R4C1 <> 5 because R3C12 <> 3,4,8
e) Outies N1 = 9(1+1): R2C4 <> 4
f) 13(3) = {157/247/256} <> 8,9 (no {148} because R3C89 <> 4,8)
g) Outies N3 = 11(1+1): R2C6 <> 2,3
h) 22(4): R2C23 <> 1 because R2C4+R3C3 <= 11

4. N45
a) Innies N4 = 11(3) <> 9
b) Innies N5 = 14(2) = {59/68}
c) 15(3) @ N5: R6C7 <> 8,9 because R67C6 >= 8
d) Killer pair (56) of Innies N5 blocks {1356} of 15(4)
e) 15(4): R4C56+R5C6 <> 6 because R5C5 <> 2,3,4

5. N5689 + N7
a) Innies N5689 = 20(2+1): R8C4 <> 2,3 because R4C49 <= 16
b) Outies N7 = 10(1+1): R6C1 <> 7,8
c) 14(3): R4C3 <> 6 because R34C4 <> 3 and R4C4 <> 1,7
d) Innies N6 = 15(3): R6C9 <> 1 because R4C9+R6C7 <= 13
e) Outies N9 = 9(1+1): R8C6 <> 8

6. C789
a) Outies = 20(4): R8C6 <> 6 because (12) only possible there and R6C6 <> 3,4,7
b) Outies N9 = 9(1+1): R6C9 <> 3
c) Killer pair (12) locked in R7C7 + 17(4) for N9
d) Innies N6 = 15(3) = {168/267/348/357} since other combos blocked by Killer pairs (56,58) of 14(2)
e) 16(4) <> {1258/1456/2356} since they are blocked by Killer pairs (56,58) of 14(2)
f) 16(4) <> 5 because (137) is a Killer triple of Innies N6
g) Innies N6 = 15(3): R6C79 <> 4 because 3,8 only possible there
h) Innies N6 = 15(3): R6C7 <> 5 because R46C9 <> 3
i) Outies N9 = 9(1+1): R8C6 <> 5

7. N1
a) 17(4) <> 34{19/28} because R3C3 = (34)
b) 15(3) <> {348} because they are only possible @ R4C1
c) 15(3) <> 4 because {56}4 blocked by Killer pair (56) of 17(4)
d) Outies = 9(1+1): R2C4 <> 5

8. R789 + N6 !
a) Innies N6 = 15(3): R6C79 >= 8 because R4C9 <= 7
b) Outies R789 = 19(4): R6C16 <= 11 because R6C79 >= 8
c) ! Outies R789 = 19(4): R6C1 <> 5,6 because R6C16 would be {56} (step 8b) which would
force R6C79 = [17] -> no combo for Innies N6
d) Outies N7 = 10(1+1): R8C4 <> 4,5
e) Innies N8 = 15(3): R8C6 <> 7 because R7C6+R8C4 >= 9
f) Outies N9 = 9(1+1): R6C9 <> 2
g) 19(4): R8C78 <> 3,4 because 19(4) must have at least 2 of (56789) and they are only possible there
h) Innies N6 = 15(3) must have 1,2 xor 3 and it's only possible @ R6C7 -> R6C7 <> 6,7
i) 15(3) @ N8: R7C6 <> 3 because R6C67 <> 4,7
j) 17(4) @ N7: R8C23 <> 9 because R8C4 >= 6

9. C789
a) Outies = 20(4): R8C6 <> 4 because R267C6 would be >= 18
b) Outies N9 = 9(1+1): R6C9 <> 5
c) 16(4) <> 6 because either 3 in N6 is in 16(4) = 34{18/27} or in
Innies N6 = {357} -> 16(4) <> {1267}
e) 16(4) = 4{129/138/237} -> 4 locked for N6
f) 13(3) = 5{17/26} -> 5 locked between C9+N3 -> R12C9 <> 5
g) Outies N3 = 11(1+1): R2C6 <> 7

10. R789 + N6
a) Innies N8 = 15(3): R7C6 <> 9 because R8C4 >= 6
b) 15(3) @ N8: R7C6 <> 6 because R6C67 <> 4,7 and R6C67 = [81] clashes with Innies N6
c) Outies R789 = 19(4): R6C1 <> 2 because:
- <> 24{58/67} since 4 only possible there
- <> {2359} since (59) only possible @ R6C6
- <> {1279} since R6C79 = [17] clashes with Innies N6
- <> {2368} because R6C7 = 3 forces Innies N6 = {357} -> no 5,7 in Outies R789

d) Outies N9 = 9(1+1): R8C4 <> 8
e) 17(4) @ N7 <> 37{16/25} because (37) is a Killer pair of 19(4)
f) 17(4) @ N7: R8C23 <> 6,7 because R8C4 = (679)
g) 13(2) <> {58} since it's a Killer pair of 15(3) @ N7
h) 23(4) <> 58{19/37/46} since {58} is a Killer pair of 15(3) @ N7
i) 17(4) @ N7 <> {1358} because of Killer pair (58) of 15(3) @ N7
j) 23(4) <> {2489} since (24) is a Killer pair of 17(4) @ N7
k) 15(3) <> 7 because (57) is a Killer pair of 23(4)

11. R789 !
a) ! 17(4) @ N7 <> 3 because R8C4 = (679) and 17(4) = {1349} forces
19(4) = {1279} which clashes with R8C4 = 9
b) Killer pair (58) locked in 15(3) + 17(4) for N7
c) 23(4) = 79{16/34} -> 9 locked for N7
d) 2 locked in 17(4) @ N7 = 2{159/168/456} <> 7
e) Outies N7 = 10(1+1): R6C1 <> 3
f) 15(3) @ N7 must have 1 xor 4 and R6C1 = (14) -> R7C12 <> 4
g) Innies N8 <> 3 because R8C4 = (69)
h) 19(4) = {1279} -> {79} locked for R8+N9
i) Outies N7 = 10(1+1) = [46] -> R6C1 = 4, R8C4 = 6
j) 13(2) = {49} locked for R7+N8
k) 18(3) = 7{38/56} -> R6C9 = 7

12. R789
a) Hidden Single: R7C6 = 7 @ R7
b) Outies N9 = 9(1+1): R8C6 = 2
c) 15(3) @ N8 = 7{26/35}
d) R7C7 = 1, R7C3 = 2
e) Hidden Single: R3C6 = 9 @ C6, R3C5 = 8

13. N456
a) Innies N4 = 11(3) = [25/61]4
b) 9(2) = {18/36}
c) 14(3) = 5{18/27}
d) Innies N5 = 14(2) = [86] -> R4C4 = 8, R6C6 = 6
e) 15(3) @ R6C6 = {267} -> R6C7 = 2
f) Innies N6 = 15(3) = {267} -> R4C9 = 6
g) 13(3) = {256} -> {25} locked for R3+N3
h) 14(3) = {158} -> R3C4 = 1, R4C3 = 5
i) 15(3) = {267} -> R4C1 = 2; {67} locked for N1
j) 15(4) = {1347} -> R5C5 = 7; {134} locked for N5

14. N236
a) 14(2) = [95] -> R4C7 = 9, R5C7 = 5
b) 9 locked in 25(4) @ C9 = 79{18/36} -> 7,9 locked for N3
c) Innies N2 = 13(3) = {157} -> R2C4 = 7, R2C6 = 5
d) Hidden pair (26) in R12C5 for C5 locked for N2
e) Naked pair (34) locked in R1C46 for R1

15. C123
a) Hidden Single: R4C2 = 7 @ R4, R3C2 = 6, R3C1 = 7
b) 15(3) = 4{38/56}: R7C1 <> 5
c) Hidden Single: R1C1 = 5 @ C1, R9C3 = 7 @ C3
d) Hidden Single: R5C3 = 6 @ C3 -> R6C3 = 3
e) R3C3 = 4, R3C7 = 3

16. R123
a) 18(4) = {3456} -> 6 locked for R2+N3
b) R2C5 = 2, R1C5 = 6
c) Hidden Single: R1C2 = 2 @ R1
d) 22(4) = {3478} -> R2C2 = 3, R2C3 = 8

17. N7
a) 17(4) = {1268} -> R8C3 = 1, R8C2 = 8
b) R1C3 = 9, R1C9 = 1

18. Rest is singles without considering diagonals.

Rating: 1.75. I used some heavy combination analysis which could be considered contradiction chain-like though very short

I solved Bored89-Hard last week but only went through Afmob's walkthrough yesterday.

A really challenging puzzle. Thanks Nasenbaer! Changing the cages in N5 took away the useful 5(2) cage in C6 making it a lot harder than the Easy version.

Afmob used some heavy combination analysis. I must admit I couldn't follow the details of some of the sub-steps since I work with an Excel worksheet and Ruud's combination calculator. They are probably easier to see and understand by those using software solvers such as SumoCue and SS.

Some of the key solving involves 4 outies, particularly in C4 and then R6. After that, as Ed pointed out in his discussion of the Easy version, the elimination of 4 from R2C6 is a key move. In my solution for Hard, this came from an easy 45 test, step 32, after the harder work had been done.

My methodical combination and permutation analysis in steps 21, 25 and 29 may at first sight look complicated but it only involved simple clashes. I've given summaries after those three steps for anyone who may want to skip the details.

Since my combination analysis was only moderately heavy, I'll rate this puzzle as Hard 1.5


Here is my walkthrough

This is a Killer-X. I've included eliminations along diagonals, for those not using software to do eliminations, because they are easy to overlook.

Prelims

a) R3C56 = {89}, locked for R3 and N2
b) R45C7 = {59/68}
c) R56C3 = {18/27/36/45}, no 9
d) R7C45 = {49/58/67}, no 1,2,3

1. 45 rule on R12 2 outies R3C37 = 7 = {16/25/34}, no 7

2. 45 rule on R89 2 outies R7C37 = 3 = {12}, locked for R7
2a. CPE no 1,2 in R3C37 and R5C5, clean-up: no 5,6 in R3C37 (step 1)
2b. Naked pair {34} in R3C37, locked for R3
2c. CPE no 3,4 in R5C5

3. 15(4) cage at R4C5 = {1239/1248/1257/1347/1356/2346}
3a. 8,9 of {1239/1248} must be in R5C5 -> no 8,9 in R4C56 + R5C6

4. 45 rule on N1 2 outies R2C4 + R4C1 = 9 = [18]/{27/36/45}, no 1,9 in R4C1

5. 45 rule on N3 2 outies R2C6 + R4C9 = 11 = [29/38]/{47/56}, no 1, no 2,3 in R4C9

6. 45 rule on N7 2 outies R6C1 + R8C4 = 10 = {19/28/37/46}/[55]

7. 45 rule on N9 2 outies R6C9 + R8C6 = 9 = {18/27/36/45}, no 9

8. 45 rule on N4 3 innies R4C13 + R6C1 = 11 = {128/137/146/236/245}, no 9, clean-up: no 1 in R8C4 (step 6)

9. 45 rule on N5 2 innies R4C4 + R6C6 = 14 = {59/68}

10. 13(3) cage at R3C8 = {157/247/256} (cannot be {148} because 4,8 only in R4C9), no 8,9, clean-up: no 2,3 in R2C6 (step 5)

11. 15(3) cage at R3C1 = {168/258/267/357/456} (cannot be {348} because 3,4,8 only in R4C1)
11a. 3,4,8 of {258/357/456} must be in R4C1 -> no 5 in R4C1, clean-up: no 4 in R2C4 (step 4)

12. Hidden killer pair 8,9 in N1, 17(4) cage cannot contain both of 8,9 -> R2C23 must contain at least one of 8,9
12a. 22(4) cage at R2C2 = {1489/2389/2479/3469/3478/3568} (cannot be {1579/1678/2569/2578} because R3C3 only contains 3,4, cannot be {4567} which doesn’t contain 8,9)
12b. 1 of {1489} must be in R2C4 -> no 1 in R2C23

13. 14(3) cage at R3C4 = {149/158/167/239/248/257/356} (cannot be {347} because no 3,4,7 in R4C4)
13a. 6 of {167} must be in R4C4, 3 of {356} must be in R4C3 -> no 6 in R4C3

14. 15(3) cage at R6C6 = {159/168/249/258/267/348/357/456}
14a. 1,2 of {159/249} must be in R6C7 -> no 9 in R6C7
14b. 2 of {258} must be in R6C7, 8 of {348} must be in R6C6 -> no 8 in R6C7

15. 45 rule on N689 2 innies R4C9 + R8C4 = 1 outie R6C6 + 6, min R6C6 = 5 -> min R4C9 + R8C4 = 11, no 2,3 in R8C4, clean-up: no 7,8 in R6C1 (step 6)

16. 45 rule on N69 2 innies R4C9 + R6C7 = 1 outie R8C6 + 6, max R4C9 + R6C7 = 13 -> max R8C6 = 7, clean-up: no 1 in R6C9 (step 7)

17. 45 rule on N6 3 innies R4C9 + R6C79 = 15 = {168/267/348/357} (cannot be {258/456} which clash with R45C7)
17a. 4 of {348} must be in R4C9 -> no 4 in R6C79, clean-up: no 5 in R8C6 (step 7)
[At this stage I noticed that R4C9 + R6C79 and 15(3) cage at R6C6 cannot both be {348} because of clash between R6C9 and R6C6 but either one can be {348} if the other one is {357}.]

18. 16(4) cage in N6 = {1249/1267/1348/2347} (cannot be {1258/1456/2356} which clash with R45C7, cannot be {1357} which clashes with R4C9 + R6C79), no 5

19. 45 rule on C789 4 outies R2678C6 = 20 = {1469/1478/1568/2459/2468/2567/3458/3467} (cannot be {1289} which clashes with R3C6, cannot be {1379/2369} because 15(3) cage at R6C6 cannot be = [933], cannot be {2378} because no 4 in R6C7 to make combination with R67C6 = [83])
19a. 1,2 of {1469/1568/2468/2567} must be in R8C6, 6 of {3467} must be in R6C6 -> no 6 in R8C6, clean-up: no 3 in R6C9 (step 7)

20. R4C9 + R6C79 (step 17) = {168/267/348/357}
20a. 3 of {357} must be in R6C7 -> no 5 in R6C7

Consider the combinations of step 19 in more detail. Most of the following could have been done in step 19 but one depends on step 20 so it’s all together here.

21. 45 rule on N78 2 innies R78C6 = 1 outie R6C1 + 5, min R78C6 = 6
21a. R2678C6 (step 19) = {1469/1478/1568/2459/2468/2567/3458/3467}
21b. {1469} cannot be 4{69}1 because R67C6 must total less than 15, cannot be [6941] because min R78C6 = 6 -> cannot be {1469}
21c. {1478} cannot be 4{78}1 because R67C6 must total less than 15, cannot be [7841] because min R78C6 = 6 -> cannot be {1478}
21d. {1568} = 5{68}1 / 6{58}1
21e. {2459} = 4{59}2 / [5942]
21f. {2468} = 4{68}2 / [6842]
21g. {2567} = [5672/6572] (cannot be 7{56}2 because no 4 in R6C7)
21h. {3458} = 4{58}3 / [5843] (cannot be [5834] because no 4 in R6C7)
21i. 6 of {3467} must be in R6C6 = [4673] (cannot be [7643] because no 5 in R6C7, cannot be [7634] because 15(3) cage at R6C6 cannot be [663])

Summary of step 21, R2C678C6 = {1568/2459/2468/2567/3458/3467}, R2C6 = {456}, R67C6 = {58/59/68}/[57/67/84/94], no 3, R8C6 = {123}, clean-up: no 4 in R4C9 (step 5), no 2,5 in R6C9 (step 7)

22. 15(3) cage at R6C6 (step 14) = {159/168/249/258/267/348/357} (cannot be {456} because R67C6 cannot be {45} from combinations in step 21)
22a. 1,2,3 only in R6C7 -> R6C7 = {123}

23. R4C9 + R6C79 (step 17) = {168/267/357}
23a. {168} must be [618] -> R67C6 (summary of step 21) = {58/59}/[57/67/68/84/94] (cannot be [86] which clashes with R6C9), no 6 in R7C6

24. Max R7C7 + R8C6 = 5 -> min R8C78 = 14, no 1,2,3,4
24a. 19(4) cage at R7C7 = {1279/1369/1378/2359/2368}

25. R4C9 + R6C79 (step 23) = {168/267/357} -> R6C79 = [18/26/27/37]
25a. 45 rule on R789 4 outies R6C1679 = 19 = {1279/1378/1468/2368/2467/3457} (cannot be {1459/2359} because R6C9 only contains 6,7,8, cannot be {1369/1567/2458} which don’t match with R6C79)
25b. {1279} = [1927]
25c. {1378} = [1837]
25d. {1468} = [4618]
25e. {2368} = [3826]
25f. {2467} = [4627]
25g. {3457} = [4537]

Summary of step 25, R6C1 = {134}, R6C67 = [53/61/62/82/83/92], clean-up: no 4,5,8 in R8C4 (step 6)

26. R6C67 (step 25) = [53/61/62/82/83/92] -> R7C6 = {4578}, no 9

27. R4C13 + R6C1 (step 8) = {128/137/146/236/245}
27a. 6 of {146} must be in R4C1, 4 of {245} must be in R6C1 -> no 4 in R4C1, clean-up: no 5 in R2C4 (step 4)

28. 13(3) cage at R3C8 (step 10) = {157/256}, CPE no 5 in R12C9

29. 45 rule on C123 4 outies R2348C4 = 22 = {1579/1678/2389/2569/2578/3568}
29a. {1579} = [1759/7159]
29b. {1678} = [6187/7186]
29c. {2389} = [3289]
29d. {2569} = [2569/2659]
29e. {2578} = [2587]
29f. {3568} = [3586]

Summary of step 29 R34C4 = [15/18/28/56/58/65/75], no 9, clean-up: no 5 in R6C6 (step 9)

30. R34C4 (step 29) = [15/18/28/56/58/65/75] -> R4C3 = {123458}, no 7

31. 17(4) cage at R7C3 = {1259/1268/1349/1367/1457/2357/2456} (cannot be {1358/2348} because R8C4 only contains 6,7,9)
31a. 9 of {1259/1349) must be in R8C4 -> no 9 in R8C23

32. 45 rule on N2 3 innies R2C46 + R3C4 = 13 = {157/256} (cannot be {247} because R23C4 cannot be {27}, cannot be {346} because R23C4 cannot be [36], both from step 29), no 3,4, 5 locked for N2, clean-up: no 2 in R3C4 (step 29c), no 6 in R4C1 (step 4), no 7 in R4C9 (step 5)
32a. 2 of {256} must be in R2C4 -> no 6 in R2C4, clean-up: no 3 in R4C1 (step 4)

33. Killer pair 5,6 in R45C7 and R4C9, locked for N6, clean-up: no 3 in R6C1 (step 25e), no 7 in R8C4 (step 6), no 3 in R8C6 (step 7)

34. 19(4) cage at R7C7 (step 24a) = {1279} (only remaining combination)
34a. Naked pair {79} in R8C78, locked for R8 and N9 -> R8C4 = 6, R6C1 = 4 (step 6), clean-up: no 5 in R56C3, no 8 in R6C6 (step 9), no 7 in R7C45

35. R6C1 = 4 -> R7C12 = 11 = {38/56}, no 7,9
35a. R7C45 = {49} (cannot be {58} which clashes with R7C12), locked for R7 and N8

36. R7C6 = 7 (hidden single in R7), R6C67 = 8 = [62], R4C4 = 8 (step 9), 6,8 locked for D\, R2C6 = 5, R4C9 = 6 (step 5), R7C7 = 1, locked for D\, R8C6 = 2, R7C3 = 2, locked for D/, R6C9 = 7 (step 7), clean-up: no 1 in R2C4 (step 4), no 3,7 in R5C3, no 8 in R5C7
[While checking my walkthrough I noticed that the clean-up makes R2C4 + R4C1 into naked pair {27} -> CPE no 2,7 in R2C1. These are both eliminated in the next step.]

37. R2C6 = 5 -> R23C4 = [71] (step 32), R4C1 = 2 (step 4), R4C3 = 5 (step 27), R45C7 = [95], R8C78 = [79], 9 locked for D\, R5C5 = 7, locked for D\ and D/

38. R3C6 = 9 (hidden single in C6), R3C5 = 8, R9C6 = 8 (hidden single in C6)
38a. 1 in C6 locked in R45C6, locked for N5

39. R5C4 = 2 (hidden single in R5), R6C45 = 14 = {59}, locked for R6

40. R4C9 = 6 -> R3C89 = {25} (step 28), locked for R3 and N3

41. R4C2 = 7 (hidden single in R4) -> R3C12 = [76]
41a. R9C3 = 7 (hidden single in C3)

42. Naked pair {34} in R1C46, locked for R1 and N2 -> R1C1 = 5, locked for D\

43. R7C3 = 2, R8C4 = 6 -> 17(4) cage at R7C3 (step 31) = {1268/2456}, no 3
43a. 4 of {2456} must be in R8C3 -> no 4 in R8C2

44. R5C3 = 6 (hidden single in C3), R6C3 = 3, R3C3 = 4, locked for D\, R3C7 = 3, locked for D/

45. R2C6 = 5, R3C7 = 3 -> R2C78 = 10 = {46}, locked for R2 and N3 -> R12C5 = [62], R1C7 = 8, R2C2 = 3, locked for D\, R9C9 = 2, R2C3 = 8 (step 12a), R8C3 = 1, R1C3 = 9, R12C9 = [19], 1 locked for D/, R1C2 = 2, R1C8 = 7, R2C1 = 1, R4C56 = [34], 4 locked for D/

and the rest is naked singles

3x3::k:1536:1536:4866:4866:3076:4357:4357:4615:4615:4105:1536:4866:3596:3076:5902:4357:4615:4369:4105:3859:3859:3596:3076:5902:2328:2328:4369:4105:3859:5149:3596:3615:5902:3873:2328:4369:3364:3364:5149:5149:3615:3873:3873:2347:2347:4397:4398:5149:5680:3615:2098:3873:4916:3893:4397:4398:4398:5680:4922:2098:4916:4916:3893:4397:3904:1601:5680:4922:2098:4421:3398:3893:3904:3904:1601:1601:4922:4421:4421:3398:3398:

Seems my plea didn't get heard .

I used some forcing chains and one (or two) contradiction chain(s) to crack this monster. As always I tried to eliminate candidates by using Killer pairs/triples and this assassin offered some chances to do this.

A90 Walkthrough:

1. C456
a) 23(3) = {689} locked for C6
b) Innies C6 = 14(3) = 7{25/34}
c) 22(3) = 9{58/67} -> 9 locked for C4
d) Innies C4 = 9(3) <> 7,8
e) 14(3) @ N2 <> 5{27/36} since they are blocked by Killer pairs (56,57) of 22(3)

2. C123
a) 6(3) @ N1 = {123} locked for N1
b) 6(3) @ N7 = {123} locked between R9+N7 -> R9C12 <> 1,2,3
c) Outies C12 = 9(2): R3C3 <> 9; R7C3 <> 6,7,8,9
d) Innies C1 = 12(3) <> 8,9 because (123) only possible @ R1C1
e) 13(2): R5C2 <> 4,5
f) 16(3): R4C1 <> 8,9 because R23C1 >= 9
g) 15(3) @ N1: R4C2 <> 7,8,9 because R3C23 >= 9
h) 15(3) @ N7: R8C2 <> 7,8,9 because R9C12 >= 9
i) 17(3) @ R6C2: R67C2 <> 1,2 because R7C3 <= 5
j) Outies N7 = 10(2+1) <> 9; R6C1 <> 7,8 because R6C2+R9C4 >= 4
k) 17(3) @ C1 <> 4 since 4{58/67} blocked by Killer pair (45,46) of Innies C1
l) Hidden Killer pair (89) in 16(3) for C1 since 17(3) can't have both
-> 16(3) <> 7{36/45}

3. C789
a) Outies C89 = 10(2) <> 5; R7C7 <> 2,3
b) Outies N9 = 19(2+1): R6C89 <> 1,2 because R9C6 <= 7
c) Outies N3 = 16(2+1): R4C9 <> 1,2 because R1C9+R4C8 <= 13

4. R789
a) Innies+Outies R9: 6 = R8C2378 - R9C5 -> R9C5 <> 2,3
b) Consider placement of (123) in 15(3) @ N7 -> R78C1 <> 1,2,3:
- i) 15(3) has one of (123) -> 15(3) with R89C3 builds naked triple (123) in N7 -> R78C1 <> 1,2,3
- ii) 15(3) = {456} -> R7C3+R89C3 = {123} -> R78C1 <> 1,2,3
c) 17(3) @ C1 must have one of 1,2,3 and it's only possible @ R6C1 -> R6C1 <> 5,6
d) Outies N7 = 10(2+1): R6C2 <> 3 because R6C1+R9C4 <= 6
e) 17(3) @ R6C2: R7C2 <> 3 because R6C2+R7C3 <= 13

5. C123 !
a) Hidden triple (123) in R146C1 for C1 -> R4C1 = (123)
b) Outies N1 = 11(2+1): R4C2 <> 1 because R1C4+R4C1 <= 9
c) 19(3) <> 2 because {289} blocked by Killer pair (89) of 16(3)
d) Outies C123 = 9(3): R5C4 <> 6 because R1C4 <> 1,2
e) Killer pair (89) locked in 16(3) + 19(3) for N1
f) Outies C12 = 9(2): R7C3 <> 1
g) Hidden killer pair (89) in 19(3) + 20(4) for C3
-> 20(4) <> {1289/2567/3467}
h) Consider placement of (23) in Innies C12 = 23(4) -> 15(3) @ N7 <> 8, R9C1 <> 7
- i) Innies have none of (23) -> R3467C2 = {4568} -> R9C2 = (79) -> R9C1 @ 15(3) @ N7 <> 7
- ii) Innies have one of (23) -> Innies+R12C2 build Naked triple for C2 -> 15(3) @ N7 = {456} <> 7,8
i) Innies C12 = 23(4) = {2579/2678/3578/4568} because:
- <> {2489} since 17(3) @ C2 can't have 8 and 9
- <> {3569} since it clashes with 15(3) @ N7 = {456} (step 5h)
- <> {3479} because R4C2 = 3 forces 15(3) @ N1 = [753] -> Innies = [7349]
-> 17(3) @ C2 can't have 4 and 9

j) ! Outies C1 = 22(5) = 19{237/246/345} because {13468} can only be {13}8{46}
which forces 13(2) = [58] and 15(3) = {456} with R9C1 = 5 -> Two 5s in C1
-> 9 locked for C2

6. C123 !
a) 13(2) <> 5
b) 8 locked in 17(3) @ C2 = 8{27/36/45}
c) 20(4) = {1568/2378/2459/3458} since other combos blocked by Killer pairs (46,47,69,79) of 13(2)
d) ! Consider placement of (123) in 15(3) @ N7 -> R7C2 <> 6,7
- i) 15(3) has one of (123) -> 15(3) + R89C3 builds Naked triple for N7 -> 17(3) @ C2 = {458}
- ii) 15(3) = {456} -> 17(3) @ C1 = 7{19/28} with 7 locked for N7 -> R7C2 = 8
e) ! 15(3) @ N7 <> 9 since 17(3) @ C1 can't have 6 and 7

7. C123
a) Hidden Single: R5C2 = 9 @ C2 -> R5C1 = 4
b) 15(3) @ N7 = {267/357/456} <> 1
c) 1 locked in R12C2 for N1
d) 1 locked in 6(3) @ N7 for C3; R9C4 <> 1
e) Outies C123 = 9(3): R5C4 <> 5 because R19C4 >= 5
f) Outies C123 = 9(3) must have 4,5 xor 6 and it's only possible @ R1C4 -> R1C4 <> 3
g) 20(4) = 8{156/237} -> 8 locked for C3+N4
h) 19(3) = {469} -> 9 locked for N1
i) Hidden Single: R7C2 = 8 @ C2
j) 17(3) @ C2 = 8{27/36/45} -> R7C3 <> 5
k) Outies C123 = 9(3) = 2{16/34} because R1C4 = (46) -> 2 locked for C4
l) Outies C12 = 9(2): R3C3 <> 4

8. C6789
a) 1 locked in 8(3) for N8 -> R6C6 <> 1
b) 9(2) <> 5
c) Outies C89 = 10(2) <> 2
d) 15(4) <> 9 because (123) is a Killer triple of 9(2)
e) 15(4) <> {1347} since (137) is a Killer triple of 9(2)

9. C123
a) Hidden Killer pair (57) in 20(4) + R3C3 for C3 -> R3C3 <> 6
b) Outies C12 = 9(2): R7C3 <> 3
c) 17(3) @ C2: R6C2 <> 6
d) Killer pair (57) locked in 20(4) + R6C2 for N4

10. C456 !
a) Innies+Outies N2: 4 = R4C46 - R1C46
-> R4C4 <> 4 because R1C4 = R4C6 (HS @ C4) would be 6 -> equation impossible (R1C6 = 0)
b) 4 locked in R123C4 for N2
c) 14(3) @ C4: R4C4 <> 6 because {17}6 blocked by Killer pair (17) of 12(3)
d) ! 14(3) @ C4: R4C4 <> 8 because 14(3) would be {15}8 -> 12(3) = {237} -> no candidate for R1C6
e) 23(3): R4C6 <> 9 because R1C4 + R23C6 = {468} is blocked by Killer triple (468) of 14(3) @ N2
f) 9 locked in 23(3) for N2
g) Innies+Outies N2: 4 = R4C46 - R1C46 -> R1C6 <> 2 because sum of R4C46 is always odd
h) 2 locked in 12(3) = {237} locked for C5+N2
i) R1C6 = 5

11. C456
a) 19(3) = 6{49/58} -> 6 locked for C5+N8
b) 14(3) @ C5 = 1{49/58} -> 1 locked for N5
c) Innies C4 = {234} -> R1C4 = 4
d) 8(3) = {134} locked for C6
e) 20(4) = {2378} -> 7 locked for C3+N4
f) 17(3) @ N2 = 5[39/84/93]

12. C123
a) 17(3) @ C2 = {458} -> R6C2 = 5, R7C3 = 4
b) 15(3) @ N7 = 7{26/35} -> R9C2 = 7
c) Hidden pair (78) in R23C1 for N1
d) 16(3) = {178} -> R4C1 = 1

13. C789
a) R9C6 = 2
b) 17(3) @ N8 = 2{69/78}; R8C7 <> 8
c) 15(4) = {1257} -> R6C5 = 7, {125} locked for C7+N8
d) 9(3) = 2{16/34} because (15) only possible @ R3C8 -> R3C8 = 2
e) 9(2) = {36} locked for R5+N6
f) 9(3) = {234} -> R3C7 = 3, R4C8 = 4
g) 17(3) @ R1C6 = {458} -> R1C7 = 8, R2C7 = 4
h) 17(3) @ R2C9 = {179} locked C9; 1 locked for N3
i) 17(3) @ N7 = {269} -> {69} locked for N9

14. N7
a) R9C4 = 3, R9C3 = 1, R8C3 = 2
b) 15(3) @ N7 = {357} -> R8C2 = 3, R9C1 = 5

15. Rest is singles.

Rating: Hard 1.75. I tried to avoid contradiction chains by using forcing chains but I couldn't resist using very short ones (step 5j and maybe 10d).

By the way, if your software can't solve it than see it as a chance to show you can do better .

I-O combos on N1 together with constraints from the 6(3) cage N1 and r159c4=9 -> r4c1=4
The 14(3) cage c4 thus contains a 1 and the I-O N2 then ->r4c6=5
So r4c4=5/7,r4c6=6/8.
Also r59c6=[27] and only by a contradiction move could I easily resolve this combo(r5c69=72).
With this move assassin took only about 2.5 hours.Without it?????

Like everyone else I found A90 a really tough Assassin.Afmob also used chains. My solution used fairly heavy combination and permutation analysis. I only finished A74 Brick Wall fairly recently (I'll post a message and possibly a walkthrough once I've looked at Afmob's and Para's walkthroughs for it) so it seemed natural to use the same sort of techniques although not to anywhere near the same extent. For that reason I agree with Afmob's rating of Hard 1.75.

Maybe the reason that SudokuSolver gives a lower rating is that it's Richard's solver and he's very good at combination and permutation analysis.

Here is my walkthrough for A90

Prelims

a) R5C12 = {49/58/67}, no 1,2,3
b) R5C89 = {18/27/36/45}, no 9
c) 6(3) cage in N1 = {123}, locked for N1
d) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
e) R234C6 = {689}, locked for C6
f) 9(3) cage at R3C7 = {126/135/234},no 7,8,9
g) R678C4 = {589/679}, 9 locked for C4
h) R678C6 = {125/134}, 1 locked for C6
i) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
j) R789C5 = {289/379/469/478/568}, no 1
k) 6(3) cage at R8C3 = {123}, CPE no 1,2,3 in R9C12

1. Min R23C1 = 9 -> max R4C1 = 7
1a. Min R3C23 = 9 -> max R4C2 = 6
1b. Min R9C12 = 9 -> max R8C2 = 6

2. 45 rule on C1 3 innies R159C1 = 12 = {147/156/246/345} (cannot be {129/138/237} because 1,2,3 only in R1C1), no 8,9, clean-up: no 4,5 in R5C2

3. R234C1 = {169/178/259/268/349/358} (cannot be {367/457} which clash with R159C1)
3a. 1,2,3 must be in R4C1 -> R4C1 = {123}

4. R678C1 = {179/269/278/359/368} (cannot be {458/467} which clash with R159C1), no 4

5. 45 rule on C4 3 innies R159C4 = 9 = {126/135/234},no 7,8

6. 45 rule on C12 2 outies R37C3 = 9 = {45}/[63/72/81], no 9, no 6,7,8 in R7C3

7. 45 rule on C89 2 outies R37C7 = 10 = [19/28/37]/{46}, no 5, no 2,3 in R7C7

8. 45 rule on N7 3 outies R6C12 + R9C4 = 10 -> max R6C12 = 9, no 9

9. 45 rule on N7 2 innies R7C23 = 2 outies R6C1 + R9C4 + 7
9a. Max R7C23 = 14 -> max R6C1 + R9C4 = 7, no 7,8 in R6C1
9b. Min R6C1 + R9C4 = 2 -> min R7C23 = 9, max R7C3 = 5 -> min R7C2 = 4

10. R678C1 (step 4) = {179/269/278/359/368}
10a. 1 of {179} must be in R6C1 -> no 1 in R78C1

11. 17(3) cage at R6C2 = {179/269/278/359/368/458/467}
11a. 1,2 of {179/269/278} must be in R7C3 -> no 1,2 in R6C2

12. 45 rule on N9 3 outies R6C89 + R9C6 = 19, max R9C6 = 7 -> min R6C89 = 12, no 1,2

13. R789C5 = {289/379/469/478/568}
13a. Hidden killer pair 8,9 in R78C4 and R789C5 -> R78C4 cannot have both of 8,9 -> no 5 in R6C4

14. 45 rule on N1 3 outies R1C4 + R4C12 = 11, max R1C4 = 6 -> min R4C12 = 5, max R4C1 = 3 -> no 1 in R4C2

15. 45 rule on N3 2 outies R1C6 + R4C9 = 2 innies R3C78 + 7
15a. Min R3C78 = 3 -> min R1C6 + R4C9 = 10, max R1C6 = 7 -> min R4C9 = 3

16. 45 rule on C12 4 innies R3467C2 = 23 = {2489/2579/2678/3479/3578/4568} (cannot be {3569} because killer triple 1,2,3 in R12C2 and R46C2 => R8C2 = 4, R9C2 = {78} which leaves no combinations for 15(3) cage at R8C2)
16a. If R3467C2 = {2489/2579/2678/3479/3578} => killer triple 1,2,3 in R12C2 and R46C2, locked for C2 => 15(3) cage can only be {456} => max R7C3 = 3 => min R67C2 = 14
-> no 3 in R6C2, clean-up: no 6 in R6C1 (step 8)
16b. For these combinations of R3467C2, R7C12 + R8C1 = {789}, R78C1 cannot be {89} => R7C2 cannot be 4,5,6,7
-> no 7 in R7C2
16c. 4 of {2489/3479} must be in R3C2 (cannot make valid combinations for 17(3) with 4 in R6C2; step 16a has already eliminated 4,5 from R7C23 for these combinations)
16d. Cannot be {2489} because no valid combination for 17(3) with R67C2 = [89]
16d. If R3467C2 = {4568} => 15(3) cage = [159/249/267/357]
16e. Combining steps 16a and 16d -> no 7 in R9C1, no 8 in R9C2
16f. 8 of {2678} must be in R67C2 (R67C2 cannot be {67} because max R7C3 = 3, step 16a), 8 of {4568} must be in R67C2 (15(3) cage at R3C2 can only be {456} for {4568} in R3467C2) -> no 8 in R3C2
16g. R3467C2 = {2579/2678/3479/3578/4568}
16h. If R3467C2 = {2579/2678/3479/3578} => R7C12 + R8C1 = {789} (step 16b), if R3467C2 = {4568} => R8C2 = {123} => killer triple 1,2,3 in R8C2 + R89C3 for N7 -> no 2,3 in R78C1
16i. 9 of {2579} cannot be in R3C2 because 17(3) cage at R6C2 cannot be [755], 4 of {3479} must be in R3C2 (step 16c) -> no 9 in R3C2

17. Hidden triple {123} in R146C1 -> R6C1 = {123}

18. R159C1 (step 2) = {147/156/246/345}
18a. R1C1 = 1 => R12C2 = {23} => R8C2 = 1 => R9C12 = [59] (step 16d)
-> no {147} in R159C1
18b. R159C1 = {156/246/345}, no 7, clean-up: no 6 in R5C2
18c. R234C1 (step 3) = {169/178/268/349/358} (cannot be {259} which clashes with R159C1
18d. R678C1 (step 4) = {179/269/278/359} (cannot be {368} which clashes with R159C1)

19. R3467C2 (step 16g) = {2678/3479/3578/4568} (cannot be {2579} which clashes with R678C1)
19a. If R3467C2 = {2678/3479/3578} => no 4,5,6 in R7C2 (step 16b)
19b. {4568} must have {458} in 17(3) cage at R6C2 because 1,2,3 of N7 locked in R8C2 (step 16d) and R89C3)
19c. -> no 6 in R7C2

20. R3467C2 (step 16g) = {2678/3479/3578/4568}
20a. If {2678} => R5C12 = [49]
20aa. If [6278] => R3C3 = 7, R456C3 = {568} => R12C3 = {49} -> no valid combination for 19(3) cage at R1C3
20ab. If [7268] => R456C3 = {578} -> no valid combination for 20(4) cage at R4C3
20b. If {3479} => R5C12 = [58], R3467C2 = [4379], R3C3 = 8, R456C3 = {469}, R12C3 = {57} -> no valid combination for 19(3) cage at R1C3
20c. If {3578} => R5C12 = [49]
20ca. If [5378] => R3C3 = 7, R456C3 = {568} => R12C3 = {49} -> no valid combination for 19(3) cage at R1C3
20cb. If [7358] => R456C3 = {678} -> no valid combination for 20(4) cage at R4C3
20cc. If [7385] => R3C3 = 5, R456C3 = {567} clashes with R3C3
20d. -> R3467C2 = {4568}, locked for C2, clean-up: no 5 in R5C1

21. Naked triple {123} in R8C23 + R9C3, locked for N7, clean-up: no 6,7,8 in R3C3 (step 6)
21a. Naked pair {45} in R37C3, locked for C3

22. 15(3) cage at R3C2 = {456}, 6 locked in R34C2, locked for C2

23. 19(3) cage at R1C3 = {289/379/469/478/568}
23a. 2,3,4,5 must be in R1C4 -> R1C4 = {2345}

24. R234C1 (step 18c) = {169/178/268/349/358}
24a. If {169} => R12C3 = {78}, R3C23 = {45}, R4C2 = 6 -> cannot place 6 in C3 -> R234C1 cannot be {169}
24b. If {178} => R12C3 = {69}, R1C4 = 4
24c. If {268} => R12C3 = {79}, R1C4 = 3
24d. If {349} => R3C23 = [65], R12C3 = {78}, R1C4 = 4
24e. If {358} => R3C23 = [64], R12C3 = {79}, R1C4 = 3
24f. -> R1C4 = {34}, R234C1 = {178/268/349/358}, R12C3 = {69/78/79}

25. R159C4 (step 5) = {135/234} (cannot be {126} because R1C4 only contains 3,4), no 6, 3 locked for C4
25a. 5 of {135} must be in R5C4 -> no 1 in R5C4

26. Hidden killer pairs 6,7 and 8,9 in R12C3 and R456C3 -> R456C3 must contain one of 6,7 and one of 8,9
26a. 20(4) cage at R4C3 = {1568/2378/2468} (cannot be {1379} which clashes with R5C2, cannot be {1469/2369} which clash with R5C12, cannot be {1478} because 4 in R5C4 clashes R12C3 = {69} => R1C4 = 4), no 9

27. R5C2 = 9 (hidden single in N4), R5C1 = 4, R9C2 = 7, clean-up: no 5 in R5C89
27a. R8C2 + R9C1 = [26/35] (step 16d), no 1
27b. Max R9C6 = 5 -> min R6C89 = 14 (step 12), no 3,4

28. 4 in N1 locked in R3C23, locked for R3, clean-up: no 6 in R7C7 (step 7)
28a. 4 in N7 locked in R7C23, locked for R7, clean-up: no 6 in R3C7 (step 7)

29. 20(4) cage at R4C3 (step 26a) = {1568/2378}, 8 locked in R456C3, locked for C3 and N4 -> R6C2 = 5, R7C23 = [84], R4C2 = 6, R3C23 = [45], clean-up: no 2 in R3C7 (step 7)
29a. Min R6C89 = 15 -> max R9C6 = 4 (step 12)

30. 20(4) cage at R4C3 (step 29) = {2378}, no 1,5, 7 locked in R456C3, locked for C3

31. Naked pair {69} in R12C3, locked for N1, R1C4 = 4 (step 23), R59C4 = {23} (step 5)
31a. Naked pair {23} in R59C4, locked for C4

32. R23C1 = {78} -> R4C1 = 1 (step 18c)

33. 1 in C4 locked in R23C4, locked for N2
33a. 1 in N8 locked in R78C6, locked for C6
33b. 6 in C6 locked in R23C6, locked for N2

34. R234C4 = {158} (only remaining combination), no 7, locked for C4

35. R123C5 = {237} (only remaining combination), locked for C5 and N2 -> R1C6 = 5, clean-up: no 2 in R678C6 (Prelim h)
35a. R12C7 = 12 = {39}/[84], no 1,2,6,7, no 8 in R2C7

36. Naked triple {134} in R678C6, locked for C6 -> R9C6 = 2, R9C4 = 3, R89C3 = [21], R8C2 = 3, R5C4 = 2, R5C6 = 7
36a. R89C7 = 15 = {69}/[78], no 1,4,5, no 8 in R8C7
36b. 2 in C7 locked in R46C7, locked for N6
36c. R5C6 = 7 -> R456C7 = 8 = {125}, locked for C7 and N6 -> R3C7 = 3, R4C8 = 4, R3C8 = 2 (cage sum), R3C5 = 7, R23C1 = [78], R234C4 = [815], R456C7 = [251], clean-up: no 8 in R5C89, no 9 in R12C7 (step 35a)
36d. R12C7 = [84], clean-up: no 7 in R8C7 (step 36a)

37. Naked pair {36} in R5C89, locked for R5 and N6 -> R5C3 = 8, R5C5 = 1
37a. Naked pair {37} in R46C3, locked for N4 -> R6C1 = 2, R1C1 = 3, R12C5 = [23], R12C2 = [12]

38. Naked pair {89} in R4C56, locked for R4 and N5 -> R4C9 = 7, R46C3 = [37], R6C456 = [643], R78C6 = [14]
38a. R23C9 = 10 = [19] -> R1C9 = 6, R12C8 = [75], R12C3 = [96], R234C6 = [968], R4C5 = 9, R5C89 = [63], R6C89 = [98], R7C78 = [73], R89C8 = [18], R78C9 = [25], R9C9 = 4, R78C4 = [97]

39. R6C1 = 2 -> R78C1 = 15 = [69]

and the rest is naked singles

3x3::k:2560:2560:3586:2307:3588:4101:2310:2311:2311:4617:3586:3586:2307:3588:4101:2310:2310:6929:4617:4617:3860:3860:3588:3607:3607:6929:6929:3611:4617:3860:4638:4638:4638:3607:6929:3363:3611:3109:3109:3109:4638:5929:5929:5929:3363:3611:4654:3887:4912:4912:4912:3635:4916:3363:4654:4654:3887:3887:4912:3635:3635:4916:4916:4654:5184:5184:3650:3650:3650:3141:3141:4916:2888:2888:5184:4939:4939:4939:3141:2383:2383:

This was a fun assassin since I got to use Killer triples and Killer quads. It took me more time than it should have to solve it since I didn't see step 7a which is a basic move.

A91 Walkthrough:

1. R123
a) 16(2) = {79} locked for C6+N2
b) 9(2) @ N2 <> 2
c) Innies N2 = 6(2) = {15/24}
d) Killer pair (45) locked in 14(3) + Innies N2 for N2
e) Innies N3 = 27(4) <> 1,2
f) 9(2) @ N3 <> 3,6 since (36) is a Killer pair of 9(3)

2. C789
a) 23(3) = {689} locked for R5, 9 locked for N6
b) 27(4) = 9{378/468/567} -> 9 locked for N3
c) Innies C89 = 13(3): R28C8 <> 6,7,8,9 because R5C8 = (689)
d) Outies C789 = 14(3) must have 6 xor 8 and R5C6 = (68) -> R7C6 <> 6,8
e) 1 locked in R9C789 for N9
f) Outies N9 = 9(2+1) <> 8

3. R6789
a) Innies R9 = 6(2) = [42/51]
b) Innies R89 = 5(2) = [14/23/32]
c) 9(2) <> {45} since it's blocked by R9C3 = (45)
d) 20(3) = {479/569/578} because R9C3 = (45) -> R8C23 <> 3,4,5
e) 12(3) <> {345} because R9C7 = (12)
f) 12(3) must have 6,7,8 xor 9 and it's only possible @ R8C7 -> R8C7 = (6789)
g) Innies N7 = 14(4) <> 9
h) Outies N7 = 19(2+1) -> R7C4 <> 1
i) Innies = 10(2) <> 5; R6C1 <> 1
j) 19(3): R9C45 <> 3 because R9C6 <> 7,9

4. C123
a) Innies C12 = 19(3) <> 1; R2C2 <> 2 because R5C2 <> 8,9
b) Outies C123 = 12(3) <> 8 because {138} blocked by Killer pair (13) of 9(2) @ C4
c) Innies+Outies N1: -3 = R4C2 - R3C3 -> R4C2 <> 7,8,9; R3C3 <> 1,2,3
d) Innies+Outies N7: 4 = R6C2 - R7C3 -> R6C2 = (56789); R7C3 <> 6,7,8

5. N9 !
a) Innies+Outies: -5 = R6C8 - R7C7 -> R6C8 = (1234); R7C7 = (6789)
b) 19(4) must have 2 of (56789) and they are only possible @ R7C89 -> R7C89 <> 2,3,4
c) 4 locked in R8C89 for R8
d) ! 19(4) can only have one of (6789) because of Killer quad (6789) in R78C7 and 9(2)
-> 19(4) = 5{149/239/248/347} -> 5 locked R7+N9

6. R789
a) 5 locked in 14(3) @ N8 = 5{18/27/36} for N8
b) 15(3): R6C3 <> 1 because R7C34 <= 13
c) Innies+Outies N7: 4 = R6C2 - R7C3 -> R6C2 <> 9

7. N58 !
a) Innies+Outies N5: -8 = R7C5 - R5C46 -> R7C5 <> 8,9 because R5C46 <= 15
b) ! 14(3) @ N8 <> 2,7 since {257} is a Killer triple of Innies N8

8. R789
a) Killer pair (13) locked in 14(3) + Innies R89 for R8
b) 12(3) = {129/147/246} <> 8
c) 9(2) <> 2,7 since (27) is a Killer pair of 12(3)
d) Killer pair (16) locked in 9(2) + 12(3) for N9
e) 11(2) <> {38} because it's a Killer pair of 9(2)
f) 3 locked in Innies N7 = 14(4) = 13{28/46} <> 7
g) Innies+Outies N9: -5 = R6C8 - R7C7 -> R6C8 <> 1

9. C789 !
a) ! Killer quad (6789) locked in 14(3) @ N3 + R578C7 for C7
b) 9(3) = 3{15/24} -> 3 locked for N3
c) 9(2) <> 4,5 since (45) is a Killer pair of 9(3)
d) Innies+Outies N3: R3C7 = R4C8 <> 3
e) R6C8 <> 4 since it sees all 4 of N9
f) Innies+Outies N9: -5 = R6C8 - R7C7 -> R7C7 <> 9

10. C789
a) Innies C89 = 13(3) <> 9 because R8C8 = (24)
b) Hidden Single: R5C7 = 9 @ N6
c) 12(3) = 4{17/26} -> R8C8 = 4
d) 19(4) = {2359} -> 9 locked for R7; {23} locked between N6 and C9 -> 13(3) <> 2,3
e) 13(3) = 1{48/57} -> 1 locked for C9+N6
f) Both 9(2): R19C8 <> 8

11. R789
a) Innies R89 = 5(4) = {23} locked for R8
b) 14(3) @ R8 = {158} locked for R8+N8
c) 19(3) = 9{37/46} -> 9 locked for R9
d) 11(2) <> 2
e) Killer pair (45) locked in 11(2) + R9C3 for R9+N7
f) 2 locked in Innies N7 = 14(4) = {1238}
h) 19(3) = {379} -> R9C6 = 3; 7 locked for R9+N8
i) Hidden Single: R9C9 = 8 @ R9 -> R9C8 = 1
j) 14(3) @ N9 = 7{25/34} -> R7C7 = 7; R6C7 = (35)

12. C456
a) Outies C789 = 14(3) = {248} because R7C6 = (24) -> R5C6 = 8; {24} locked for C6
b) Innies N2 = 6(2) = {24} locked for R3+N2
c) Outies C123 = 12(3) = {246} -> R7C4 = 6; {24} locked for C4
d) 9(2) = {18} locked for C4+N2
e) 12(3) must have 2 xor 4 because R5C4 = (24) -> R5C23 <> 2,4

13. R123
a) 9(2) @ N3 = {27} locked for R1+N3
b) 9(3) = {135} locked for N3
c) 1 locked in R3C12 for N1
d) 10(2) = {46} locked for R1+N2
e) 14(3) @ N1 = 2{39/57} -> R2C3 = 2
f) R1C6 = 9, R2C6 = 7
g) 14(3) @ N1 = {239} -> R1C3 = 3, R2C2 = 9

14. N45
a) 15(3) @ N7 = {168} -> R6C3 = 8, R7C3 = 1
b) 15(3) @ N1 = 6{27/45} because R3C3 = (57) -> R4C3 = 6
c) 18(4) @ N5 = {1359} because 24{39/57} blocked by R5C4 = (24)

15. Rest is singles.

Rating: Hard 1.25. I used some Killer triples and Killer quads

Assassin 91 took me a long time to solve. The killers and hidden killers were fairly easy to see but some of the other steps weren't. It took me several sessions to spot step 36a, my first key move.

Therefore although my steps weren't hard ones, I'll rate A91 as a lower range 1.5.

My other key moves were steps 46 and 49, the latter another killer after which the rest of the puzzle was straightforward. Maybe the later stages might have been a bit shorter if I'd thought to re-apply step 21, which became R5C4 = R7C5, after step 37.

I missed Afmob's step 8a, which I felt I ought to have seen even though it involves a cage split between C1 and C9. I don't know how much difference it would have made to my solving path; it wasn't marked as a key move.

Here is my walkthrough.

Prelims

a) R1C12 = {19/28/37/46}, no 5
b) R12C4 = {18/27/36/45}, no 9
c) R12C6 = {79}, locked for C6 and N2, clean-up: no 2 in R12C4
d) R1C89 = {18/27/36/45}, no 9
e) R9C12 = {29/38/47/56}, no 1
f) R9C89 = {18/27/36/45}, no 9
g) 9(3) cage in N3 = {126/135/234}, no 7,8,9
h) R5C678 = {689}, locked for R5, 9 locked in R5C78 for N6
i) 20(3) cage in N7 = {389/479/569/578}, no 1,2
j) R9C456 = {289/379/469/478/568}, no 1
k) 27(4) cage at R2C9 = {3789/4689/5679}, no 1,2, 9 locked in R2C9 + R3C89 for N3

1. 1 in R9 locked in R9C789, locked for N9

2. 45 rule on R89 2 innies R8C19 = 5 = [14]/{23}

3. 45 rule on R9 2 innies R9C37 = 6 = [42/51]
3a. R9C89 = {18/27/36} (cannot be {45} which clashes with R9C3), no 4,5
3b. 20(3) cage in N7 = {479/569/578} (cannot be {389} because R9C3 only contains 4,5), no 3
3c. R9C3 = {45} -> no 4,5 in R8C23

4. 45 rule on C12 3 innies R258C2 = 19 = {289/379/469/478/568}, no 1
4a. 2 of {289} must be in R5C2 -> no 2 in R2C2
4b. 5 of {568} must be in R5C2 -> no 5 in R2C2

5. 45 rule on N1 1 innie R3C3 = 1 outie R4C2 + 3, no 1,2,3 in R3C3, no 7,8,9 in R4C2

6. 45 rule on N2 2 innies R3C46 = 6 = {15/24}
6a. R12C4 = {18/36} (cannot be {45} which clashes with R3C46), no 4,5

7. 45 rule on N3 1 innie R3C7 = 1 outie R4C8, no 1,2 in R3C7

8. R1C89 = {18/27/45} (cannot be {36} which clashes with 9(3) cage in N3), no 3,6

9. 45 rule on N7 1 outie R6C2 = 1 innie R7C3 + 4, R6C2 = {56789}, R7C3 = {12345}

10. 45 rule on N9 1 innie R7C7 = 1 outie R6C8 + 5, R6C8 = {1234}, R7C7 = {6789}

11. 19(4) cage at R6C8 = {1279/1369/1378/1459/1468/2359/2368/2458/2467/3457} (cannot be {1567} because R6C8 and R8C9 only contain 1,2,3,4)
11a. 1,2,3,4 must be in R6C8 + R8C9 -> no 2,3,4 in R7C89
11b. 4 in N9 locked in R8C789, locked for R8

12. 45 rule on R6789 2 innies R6C19 = 10 = {28/37/46}/[91], no 5, no 1 in R6C1

13. 45 rule on C789 3 outies R357C6 = 14 = {158/248/356}
13a. R5C6 = {68} -> no 6,8 in R7C6
13b. Min R7C67 = 7 -> max R6C7 = 7

14. 45 rule on C123 3 outies R357C4 = 12 = {129/147/156/237/246/345} (cannot be {138} which clashes with R12C4), no 8
14a. 2 of {237} must be in R3C4
14b. 6,9 of {129/246} must be in R7C4
14c. -> no 2 in R7C4

15. 45 rule on C89 3 innies R258C8 = 13 = {139/148/238/256/346} (cannot be {157/247} because R5C8 only contains 6,8,9), no 7
15a. R5C8 = {689} -> no 6,8,9 in R28C8

16. 12(3) cage in N9 = {129/138/147/156/237/246} (cannot be {345} because R9C7 only contains 1,2)
16a. 6,7,8,9 must be in R8C7 -> R8C7 = {6789}

17. Killer quint 5,6,7,8,9 in R7C7, R7C89, R8C7 and R9C89, locked for N9
17a. 5 in N9 locked in R7C89, locked for R7, clean-up: no 9 in R6C2 (step 9)

18. 5 locked in R7C89
18a. 19(4) cage at R6C8 (step 11) = {1459/2359/2458/3457}, no 6
18b. CPE no 4 in R6C8, clean-up: no 9 in R7C7 (step 10)

19. 5 in R8 locked in R8C456, locked for N8
19a. R8C456 = 5{18/27/36}, no 9

20. 15(3) cage at R6C3 = {159/168/249/267/348/357} (cannot be {258} because no 2,5,8 in R7C4, cannot be {456} which clashes with R9C3)
20a. 1 of {159/168} must be in R7C3 -> no 1 in R6C3 + R7C4
20b. 5,8 of {348/357} must be in R6C3 -> no 3 in R6C3

21. 45 rule on N5 2 innies R5C46 = 1 outie R7C5 + 8
21a. Max R5C46 = 15 -> max R7C5 = 7
21b. R5C46 cannot total 14 -> no 6 in R7C5

22. 45 rule on N8 3 innies R7C456 = 12 = {129/147/237/246}

23. 15(3) cage at R6C3 (step 20) = {159/168/249/267/348/357}
23a. 5 of {357} must be in R6C3
23b. 6 of {267} must be in R6C3 (cannot be 7[26] which clashes with R7C456 = 6{24})
23c. -> no 7 in R6C3
23d. 2,9 of {249} must be in R6C3 (cannot be 4[29] which clashes with R7C456 = 9{12})
23e. 8 of {348} must be in R6C3
23f. -> no 4 in R6C3

24. 14(3) at R3C6 = {158/248/257/347/356} (cannot be {167} which clashes with R5C7, R7C7 and R8C7)
24a. Killer quad 6,7,8,9 in R34C7, R5C7, R7C7 and R8C7, locked for C7

25. 9(3) cage in N3 = {135/234}, 3 locked for N3, clean-up: no 3 in R4C8 (step 7)
25a. R1C89 (step 8) = {18/27} (cannot be {45} which clashes with 9(3) cage), no 4,5
25b. R1C12 = {19/37/46} (cannot be {28} which clashes with R1C89), no 2,8

26. 14(3) cage at R6C7 = {158/248/257/347/356} (cannot be {167} because 6,7 only in R7C7)
26a. 5 of {158} must be in R6C7 -> no 1 in R6C7

27. 14(3) at R3C6 (step 24) = {158/248/257/347/356}
27a. 3 of {356} must be in R4C7 -> no 6 in R4C7
27b. 8 of {158/248} must be in R3C7 (R3C67 cannot be {15/24} which clash with R3C46, overlapping cages) -> no 8 in R4C7
27c. 4 of {347} must be in R3C6, 8 of {248} must be in R3C7 (step 27b) -> no 4 in R3C7, clean-up: no 4 in R4C8 (step 7)

28. 15(3) cage at R3C3 = {159/168/249/258/267/348/357/456}
28a. 9 of {159/249} must be in R3C3 (R3C34 cannot be {15/24} which clash with R3C46, overlapping cages) -> no 9 in R4C3

29. Hidden killer quad 6,7,8,9 in R7C12, R8C23 and R9C12 for N7 -> R7C12 must contain one of 6,7,8,9
29a. 18(4) cage at R6C2 = {1269/1278/1359/1368/1458/1467/2358/2367/2457/3456} (cannot be {2349} because R6C2 only contains 5,6,7,8)
29b. R6C2 = R7C3 + 4 (step 9)
29c. 18(4) cage at R6C2 cannot be {1269/1359/1458/2367} which clash with R7C3)
-> 18(4) cage = {1278/1368/1467/2358/2457/3456}, no 9
[I then realised that 45 rule on N7 4 innies = 14 eliminates 9 from R7C12 but it doesn’t give the permutations for the 18(4) cage which were used later.]

30. R6C2 = R7C3 + 4 (step 9)
30a. 15(3) cage at R6C3 (step 20) = {168/249/348/357} (cannot be {159/267} which clash with R6C2)
30b. 8 of {168} must be in R6C3 -> no 6 in R6C3
30c. 3 of {348} must be in R7C3 (cannot be [843] which clashes with R6C2), 3 of {357} must be in R7C3 -> no 3 in R7C4

31. R6C2 = R7C3 + 4 (step 9)
31a. 18(4) cage at R6C2 (step 29c) = {1278/1368/1467/2358/2457} (cannot be {3456} which clashes with 15(3) cage at R6C3)

32. 45 rule on N2369 2 outies R57C6 = 1 innie R3C4 + 8, max R57C6 = 12 -> max R3C4 = 4, clean-up: no 1 in R3C6 (step 6)

33. 15(3) cage at R3C3 (step 28) = {159/168/249/258/267/348/456} (cannot be {357} because R3C4 only contains 1,2,4)
33a. 1 of {159/168} must be in R3C3 -> no 1 in R4C3
33b. 9 of {249} must be in R3C3, 4 of {348/456} must be in R3C4 -> no 4 in R3C3, clean-up: no 1 in R4C2 (step 5)

34. 45 rule on C1234 4 innies R4689C4 = 24 = {2589/2679/3579/4569/4578} (cannot be {1689/3489/3678} which clash with R12C4), no 1

35. R357C4 (step 14) = {129/147/237/246} (cannot be {156} which clashes with R4689C4, cannot be {345} because 3,5 only in R5C4), no 5
35a. R4689C4 (step 34) = {2589/3579/4569/4578} (cannot be {2679} which clashes with R357C4)
[Alternatively 5 in C4 locked in R4689C4 = {2589/3579/4569/4578}]

36. 15(3) cage at R6C3 (step 30a) = {168/249/348/357}
36a. R7C456 (step 22) = {129/147/246} (cannot be {237} which clashes with 15(3) cage), no 3 in R7C56

37. R357C6 (step 13) = {158/248} -> R5C6 = 8
37a. Naked pair {69} in R5C78, locked for N6, clean-up: no 6 in R3C7 (step 7)

38. R8C456 = 5{18/36} (cannot be {257} which clashes with R7C456), no 2,7

39. 14(3) cage at R6C7 (step 26) = {158/248/257/347} (cannot be {356} because 3,5 only in R6C7), no 6, clean-up: no 1 in R6C8 (step 10)

40. Hidden pair {69} in R58C7 for C7 -> R8C7 = {69}

41. 12(3) cage in N9 (step 16) = {129/246}, no 3, 2 locked for N9, clean-up: no 7 in R9C89
41a. 7 in N9 locked in R7C789, locked for R7

42. R7C456 (step 36a) = {129/246}, 2 locked for R7 and N8, clean-up: no 6 in R6C2 (step 9)
42a. 6,9 must be in R7C4 -> R7C4 = {69}

43. 7 in N8 locked in R9C456, locked for R9, clean-up: no 4 in R9C12
43a. R9C456 = {379/478}, no 6
43b. R9C6 = {34} -> no 3,4 in R9C45

44. 15(3) cage at R6C3 (step 30a) = {168/249} (cannot be {348} because R7C4 only contains 6,9), no 3,5, clean-up: no 7 in R6C2 (step 9)
44a. 2 of {249} must be in R6C3 -> no 9 in R6C3

45. 18(4) cage at R6C2 (step 31a) = {1368/2358}, no 4
45a. 3 locked in R7C12, locked for N7, clean-up: no 8 in R9C12
45b. CPE no 8 in R8C2
45c. 4 in N7 locked in R79C3, locked for C3

46. Either R6C2 = 5 or R7C12 must contain 6 (step 45) -> no 5 in R9C2, clean-up: no 6 in R9C1

47. 20(3) cage in N7 (step 3b) = {479/578} (cannot be {569} which clashes with R8C7), no 6
[This also comes from 7 locked in R8C23]

48. 9 in N4 locked in R46C1, locked for C1, clean-up: no 1 in R1C2, no 2 in R9C2
48a. R456C1 = {149/239}, no 5,6,7,8

49. Killer pair 1,2 in R456C1 and R8C1, locked for C1 -> R9C1 = 5, R9C2 = 6, R9C3 = 4, R7C3 = 1, R6C2 = 5 (step 9), R8C1 = 2, R8C89 = [43], R9C6 = 3, R6C8 = 2, R7C7 = 7 (step 10), R6C3 = 8, R7C4 = 6 (step 44), clean-up: no 4 in R1C1, no 9 in R1C2, no 3 in R12C4, no 3 in R456C1 (step 48a), no 7 in R4C8 (step 7)

50. R89C7 = [62] (hidden singles in N9) -> R5C78 = [96]

51. Naked pair {18} in R9C89, locked for R9 and N9

52. R1C9 = 2 (hidden single in C9), R1C8 = 7, R12C6 = [97], clean-up: no 3 in R1C12
52a. R1C12 = [64]

53. 9(3) cage in N3 = {135} (only remaining combination), locked for N3 -> R3C7 = 8, R4C8 = 8 (step 7), R3C8 = 9, R7C89 = [59], R9C89 = [18], R2C8 = 3, R2C12 = [89], R7C12 = [38], R8C23 = [79], R3C1 = 7, R3C3 = 5, R12C3 = [32], R2C3 = 1, R45C3 = [67], R12C4 = [81], R12C7 = [15], R1C5 = 5, R8C456 = [581], R4C2 = 2 (step 5), R5C2 = 3

54. R3C4 = 4 (step 33), R3C6 = 2, R23C5 = [63], R23C9 = [46], R7C56 = [24], R46C6 = [56], R46C7 = [43], R5C4 = 2

55. R6C6 + R7C5 = 8 -> R6C45 = 11 = [74]

and the rest is naked singles

3x3:d:k:3072:3072:3072:4867:4867:4867:3590:3590:3590:3849:3849:4875:4875:4875:2574:2574:2574:2065:3849:4115:4115:3093:3093:3093:5912:4633:2065:4123:4115:3869:2334:2334:2334:5912:4633:2065:4123:4389:3869:3367:3367:5929:5912:4633:4908:4123:4389:3869:3367:5929:5929:4403:4148:4908:3894:4389:1592:1592:1592:4403:4403:4148:4908:3894:4160:4160:4160:1859:1859:1859:4148:4167:3894:4681:4681:4681:4172:4172:4172:4167:4167:

Nice cage pattern! My unpolished walkthrough was quite long with lots of small steps but I realized that the breakthrough move (step 6b,6c) could be applied quite early. Therefore I can understand if one rates this Killer 1.5 since those steps are not easy to see.

M3 Walkthrough:

1. N56
a) 7 locked in 13(3) = 7{15/24}
b) Both 23(3) = {689} locked for C7/N5
c) 9(3) = 3{15/24} -> 3 locked for R4
d) 17(3) must have 6,8 or 9 and it's only possible @ R7C6 -> R7C6 = (689)
e) Naked triple (689) locked in R567C6 for C6

2. R789
a) 6(3) = {123} locked for R7
b) 7(3) = {124} locked for R8
c) 16(3) @ N7 = 3{58/67} -> 3 locked for R8
d) Innies+outies R9 : 5 = R8C9 - R9C1 -> R8C9 <> 5, R9C1 = (1234)
e) Innies+Outies R89: -2 = R7C1 - R8C8 -> R7C1 <> 8,9; R8C8 <> 5
f) 3 locked in R9C789 for R9
g) Innies+Outies R9: 5 = R8C9 - R9C1 -> R8C9 <> 8
h) Naked quad (1234) locked in R7C45+R8C56 for N8
i) 3 locked in R7C45 for R7

3. R789
a) 4 locked in R8C56 for R8
b) 18(3) <> {567} because it's blocked by R9C6 = (57)
c) Killer triple (124) locked in R7C3 + R9C1 + 18(3) for N7
d) 4 locked in R9C123 for R9
e) 16(3) = {178/259/358/367} because R9C6 = (57); R9C57 <> 5,7

4. C89
a) 8(3) = 1{25/34} -> 1 locked for C9
b) Innies+Outies C9 : -2 = R9C8 - R1C9 -> R1C9 <> 2,6; R9C8 <> 8,9
c) Innies+Outies C89: 1 = R1C7 - R2C8 -> R1C7 <> 1, R2C8 <> 5,7

5. R123+D/
a) Innies+Outies N2: 5 = R2C3 - R2C6 -> R2C3 = (6789), R2C6 <> 5,7
b) Innies+Outies N1: -2 = R4C2 - R2C3 -> R4C2 = (4567)
c) Innies+Outies R2: -1 = R3C1 - R2C9 -> R2C9 <> 1; R3C1 = (1234)
d) 9 locked in R1C9+R3C7 @ D/ for N3
e) Innies+Outies N3: -13 = R2C6+R4C9 - R3C78
-> R2C6+R4C9 >= 2 therefore R3C78 >= 15 -> R3C78 = (678)
-> R3C78 <= 17 so R2C6+R4C9 <= 4 -> R2C6+R4C9 <> 4,5
f) Innies+Outies R123: -10 = R4C29 - R3C78 -> R4C2 <> 7
g) Innies+Outies N1 : -2 = R4C2 - R2C3 -> R2C3 <> 9
h) 15(3): R2C12 <> 1 because R3C1 <= 4

6. N2 !
a) 1 locked in 10(3) = 1{27/36/45}
b) ! 10(3): R2C78 <> 3 since 1{36} leaves no combo for Outies = 15(3)
c) ! 10(3) <> 4,5 because 1{45} is blocked by Killer pair (45) of 8(3)

7. C789
a) Innies+Outies C89: 1 = R1C7 - R2C8 -> R1C7 <> 4,5
b) 4,5 locked in 17(3) @ C7 = {458} -> R7C6 = 8
c) Hidden Single: R6C5 = 8 @ N5
d) 7 locked in R12C7 for N3

8. R789+D/
a) 16(3) @ R9C5 = {259/367} <> 1
b) 18(3) <> 2,7 since {279} is blocked by Killer pair (27) of 16(3) @ R9C5
c) 9 locked in R9C45 for R9
d) 2 locked in R9C1+R7C3 for D/

9. R123
a) 10(3): R2C7 <> 2 because 7 only possible there
b) 10(3): Hidden Killer pair (23) @ R1C6 -> R1C6 <> 1
c) 1 locked in 12(3) @ N2 for R3
d) Hidden Single: R4C9 = 1 @ C9
e) 1 locked in 10(3) for N3
f) 14(3) = 7{25/34} since other combos blocked by Killer pairs (23,24,35) of 8(3)
-> R1C7 = 7, R1C8 <> 5
g) 10(3) = {136} -> R1C6 = 3, R1C7 = 1, R1C8 = 6
h) 18(3) = {378} -> R3C8 = 8, R4C8 = 7, R5C8 = 3

10. N56
a) 23(3) = {689} -> R3C7 = 9, {68} locked for N6
b) 19(3) = {469} -> R7C9 = 6, {49} locked for C9+N6
c) 9(3) = {234} -> R4C6 = 4, 2 locked for R4+N5

11. N12
a) 16(3) = 7{36/45} -> 7 locked for R3+N1
b) 12(3) @ N2 = {156} locked for R3+N2

12. N18
a) 7(3) = {124} -> R8C5 = 4, R8C6 = 1, R8C7 = 2
b) Hidden Single: R7C3 = 1 @ R7
c) R2C3 = 8
d) 15(3) = {249} locked for N1, 9 locked for R2
e) R9C1 = 2
f) Hidden Single: R2C2 = 2 @ N1

13. Rest is singles without considering diagonals.

Rating:1.25 since there is only one key move (combo analysis) and M3 can be solved in a short way

My walkthrough


"45" on N124 -> r7c2 = r2c6 + 6 r7c2 = 7/8/9, r2c6 = 1/2/3
"45" on N2 -> r2c3 = r2c6 + 5 r2c3 = 6/7/8
"45" on N1 -> r2c3 = r4c2 + 2 r4c2 = 4/5/6
"45" on R2 -> r3c19r4c9 = 7, r2c9 <>1
"45" on R23 -> r3c78 = r4c29 + 10 max r4c29 = 7 min r3c78 = 15 r3c8 = 6/7/8/9
r4c9 = 123-> r23c9 = {4/5}
-> 10(3) <> 145 = 1{27}/1{36}/2{35}/2{17}/3{15}/3{24}
"45" on N3 -> r3c78 = r2c6 + r4c9 + 13 r2c6&r4c9 = {11}/{12}/{13/22}
R3c78 = {69/78}/{79}/{89}
if r2c6=2 -> r2c3= 7 r4c2 = 5 r2c78 = {35} r4c9 = 12 no solution for 8(3)
if r2c6=1 -> r2c3= 6 r47c2 = [47] r2c78 = {27} <> 45 KP r23c9
-> r3c78 {9(6/8)} -> r4c9<>2, r3c23 = [57] -> r3c456 = {246},
-> r3c78 = {89} r3c19 = [31]-> 8/3 = [413] but N1 15(3) [483] conflict
-> r2c36 = [83], r47c2 = [69] -> r4c9 = 1 -> r23c9 = {25} r3c1 = 1/4, r3c78 = {89}
r5c7 = 6, r2c78 = [16]
straightforward from here


Edit: lingo changed from Djapes to your's (I hope) and the elimination tightened up a bit.

A nice puzzle. The spiral was very obvious when I was colouring the cages in my worksheet. A nice touch although it doesn't, and probably can't, contribute to the solution of the puzzle.

Maybe I found myself too influenced by the introductory comment about innies-outies, which are certainly a key part of this puzzle, so I took a long time to spot a key clash. I also missed a few of the relationships used by Afmob and HATMAN and therefore missed one of Afmob's two key moves.

Unlike Mike, although my walkthrough is a long one, I found this puzzle definitely easier than A91 and didn't get stuck like I did for that one. I'll therefore rate M3 as a Hard 1.25.

Here is my walkthrough, edited thanks to feedback from Afmob.

I've removed {357} from the combinations in step 20. I originally included it because I’d been careless with my eliminations in step 5, deleting 3 from R8 but not from the rest of N7.

An interesting point is that {357} would clash with R8C234 = {358/367} even if 3 hadn’t been eliminated from R8C4 in step 2 and from R789C1 in step 5.


This is a Killer-X

Prelims

a) R1C456 = {289/379/469/478/568}, no 1
b) R2C345 = {289/379/469/478/568}, no 1
c) R2C678 = {127/136/145/235}, no 8,9
d) R234C9 = 1{25/34}, 1 locked for C9
e) R345C7 = {689}, locked for C7
f) R4C456 = {126/135/234}, no 7,8,9
g) 23(3) cage in N5 = {689}, locked for N5
h) R7C345 = {123}, locked for R7
i) R8C567 = {124}, locked for R8

1. R4C456 = {135/234}, 3 locked for R4 and N5

2. Naked quad {1234} in R7C45 and R8C56, locked for N8
2a. 3 in N8 locked in R7C45, locked for R7
2b. 4 in N8 locked in R8C56, locked for R8

3. 17(3) cage at R6C7 = {179/278/359/458/467} (cannot be {269/368} because R7C7 only contains 4,5,7)
3a. 6,8,9 of {179/278/467} must be in R7C6 -> no 7 in R7C6
3b. 8,9 of {359/458} must be in R7C6 -> no 5 in R7C6

4. Naked triple {689} in R567C6, locked for C6

5. R8C234 = {358/367}, no 9, 3 locked for R8 and N7

6. R9C567 = {178/259/358/367/457} (cannot be {169/268/349} because R9C6 only contains 5,7)
6a. 1,2,3,4 must be in R9C7 -> R9C7 = {1234}

7. 45 rule on R2 1 innie R2C9 = 1 outie R3C1 + 1, R2C9 = {2345}, R3C1 = {1234}

8. 45 rule on R9 1 outie R8C9 = 1 innie R9C1 + 5, R8C9 = {679}, R9C1 = {124}

9. 9 on D/ locked in R1C9 + R3C7, locked for N3

10. 45 rule on C1 1 outie R2C2 = 1 innie R1C1 + 1, no 9 in R1C1, no 1 in R2C2

11. 45 rule on C9 1 innie R1C9 = 1 outie R9C8 + 2, no 2 in R1C9, no 8,9 in R9C8

12. 45 rule on N1 1 innie R2C3 = 1 outie R4C2 + 2, no 2,5 in R2C3, no 8,9 in R4C2

13. 15(3) cage at R2C1 = {159/168/249/258/267/348/357/456}
13a. 1 of {159/168} must be in R3C1 -> no 1 in R2C1

14. 45 rule on N2 1 outie R2C3 = 1 innie R2C6 + 5, no 3,4 in R2C3, no 5,7 in R2C6, no 1,2 in R4C2 (step 12)

15. 45 rule on N3 2 innies R3C78 = 2 outies R2C6 + R4C9 +13
15a. Max R3C78 = 17 -> max R2C6 + R4C9 = 4, R2C6 = {123}, R4C9 = {12}, clean-up: no 9 in R2C3 (step 14), no 7 in R4C2 (step 12)
15b. Min R2C6 + R4C9 = 2 -> min R3C78 = 15, min R3C8 = 6

16. Killer pair 1,2 in R4C456 and R4C9, locked for R4

17. 45 rule on N4 1 outie R7C2 = 1 innie R4C2 + 3, no 4,5,6 in R7C2

18. 45 rule on R89 1 innie R8C8 = 1 outie R7C1 + 2, no 8,9 in R7C1, no 5 in R8C8

19. 45 rule on R8 3 innies R8C189 = 22 = {589/679}
19a. 5 of {589} must be in R8C1 -> no 8 in R8C1

20. R789C1 = {159/249/267/456}
20a. 4 of {456} must be in R9C1 -> no 4 in R7C1, clean-up: no 6 in R8C8 (step 19)
20b. 4 in N7 locked in R9C123, locked for R9, clean-up: no 6 in R1C9 (step 11)

21. R9C567 (step 6) = {178/259/358/367}
21a. R9C6 = {57} -> no 5,7 in R9C5

22. Hidden killer pair 5,7 in R89C4 and R9C6 for N8 -> R89C4 must contain 5 or 7
22a. R56C4 cannot be {57} -> no 1 in R5C5

23. 45 rule on C89 1 outie R1C7 = 1 innie R2C8 + 1, no 1 in R1C7, no 5,7 in R2C8

24. 1 in R2 locked in R2C678 = {127/136/145}
24a. 6 of {136} locked in R2C8 -> no 3 in R2C8, clean-up: no 4 in R1C7 (step 23)
24b. 5,7 of {127/145} must be in R2C7 -> no 2,4 in R2C7

25. R678C8 = {169/178/259/268/349/358/367/457}
25a. 1,2,3 of {169/178/259/268/349/358/367} must be in R6C8 -> no 6,8,9 in R6C8
25b. 9 of {169/259} must be in R8C8 -> no 9 in R7C8
25c. 1 of {178} must be in R6C8, 7 of {367/457} must be in R8C8 -> no 7 in R6C8

26. 16(3) cage at R3C2 = {169/259/268/349/358/367/457} (cannot be {178} because R4C2 only contains 4,5,6)
26a. 6 of {169/268/367} -> no 6 in R3C23

27. R345C8 = {189/279/369/378/468/567} (cannot be {459} because R3C8 only contains 6,7,8)
27a. 1,2,3 of {189/279/369} must be in R5C8 -> no 9 in R5C8

28. 4 in C7 locked in R67C7
28a. 17(3) cage at R6C7 (step 3) = {458/467}, no 1,2,3,9

29. 9 in C6 locked in R56C6, locked for N5
29a. 9 in N8 locked in R9C56, locked for R9

30. R9C234 = {189/279/459/468} (cannot be {567} which clashes with R9C6)
30a. 9 of {279/459} must be in R9C4 -> no 5,7 in R9C4

31. Naked triple {689} in R7C6 + R9C45, locked for N8

32. R8C234 (step 5) = {358/367}
32a. R8C4 = {57} -> no 5,7 in R8C23

33. R1C456 = {289/379/469/478/568}
33a. 2,5 of {289/568} must be in R1C6 -> no 2,5 in R1C45

34. R1C789 = {158/239/248/257/347} (cannot be {149} because no 1,4,9 in R1C7, cannot be {167} because 1,6 only in R1C8, cannot be {356} which clashes with R23C9), no 6

35. 45 rule on N4 3 innies R456C2 = 14 = {149/167/248/257/356} (cannot be {158/347} because R567C2 would be {18}8/{37}7, cannot be {239} because R4C2 only contains 4,5,6)
35a. 4 of {149/248} must be in R4C2 -> no 4 in R56C2

36. R789C1 (step 20) = {159/267/456}
36a. 45 rule on C1 3 innies R123C1 = 14 = {149/158/239/248/347} (cannot be {167/257/356} which clash with R789C1), no 6, clean-up: no 7 in R2C2 (step 10)

37. R2C678 (step 24) = {127/136} (cannot be {145} which clashes with R234C9), no 4,5

38. Hidden killer pair 4,5 in R1C789 and R23C9 for N3 -> R1C789 must contain 4 or 5
38a. R1C789 = {158/248/257/347}, no 9, clean-up: no 7 in R9C8 (step 11)

39. R3C7 = 9 (hidden single in N3)
39a. Naked pair {68} in R45C7, locked for N6
39b. 6 on D/ must be in R2C8 or R8C2, CPE no 6 in R2C2, clean-up: no 5 in R1C1 (step 10)
39c. 8 on D/ must be in R1C9 or R8C2, CPE no 8 in R1C2

40. R345C8 (step 27) = {189/279/369/378/567} (cannot be {468} because 6,8 only in R3C8), no 4

41. R567C9 = {289/379/469/478} (cannot be {568} because 6,8 only in R7C9), no 5
41a. 6 of {469} must be in R7C9 -> no 4 in R7C9

42. 16(3) cage at R3C2 (step 26) = {358/367/457} (cannot be {268} because that would make R2C3 + R3C23 8{28}), no 1,2
42a. 4 of {457} must be in R4C2 (cannot be {47}5 because that would make R2C3 + R3C23 7{47}) -> no 4 in R3C23

43. 6 in N3 locked in R23C8, locked for C8, clean-up: no 8 in R1C9 (step 11)

44. R1C789 (step 38a) = {248/257/347} (cannot be {158} because 1,8 only in R1C8), no 1

45. 1 in R1 locked in R1C123, locked for N1, clean-up: no 2 in R2C9 (step 7)
45a. R1C123 = {129/138/156} (cannot be {147} which clashes with R1C789), no 4,7

46. R1C456 = {289/379/469/568} (cannot be {478} which clashes with R1C789)
46a. 4 of {469} must be in R1C6 -> no 4 in R1C45

47. R234C9 = {125/134}
47a. 5 of {125} must be in R2C9 -> no 5 in R3C9

48. R2C345 = {289/469/478/568} (cannot be {379} which clashes with R2C678), no 3

49. R8C2 = 8 (hidden single on D/), R8C34 = 8 = [35], clean-up: no 5 in R4C2 (step 17), no 7 in R2C3 (step 12), no 2 in R2C6 (step 14), no 6 in R7C1 (step 18)

50. R2C8 = 6 (hidden single on D/), R2C67 = 4 = {13}, locked for R2, R2C3 = 8, R4C2 = 6 (step 12), R45C7 = [86], R7C2 = 9 (step 17), R2C6 = 3 (step 14), R2C7 = 1, R89C7 = [23], clean-up: no 3 in R1C12 (step 45a)

51. R4C9 = 1 (hidden single in C9), R9C8 = 1 (hidden single in C8), clean-up: no 5 in R4C56 (step 1)

52. R7C3 = 1 (hidden single in N7), locked for D/

53. R1C9 = 3 (hidden single on D/), R1C78 = 11 = [74], R23C9 = [52], R3C1 = 4 (step 7), R2C2 = 2, locked for D\, R1C1 = 1 (that seems to have been a hidden single on D\ since step 51), R1C23 = [56], R1C6 = 2, R4C6 = 4, R4C45 = [32], R7C45 = [23], R56C4 = [17], R5C5 = 5, locked for D\, R9C1 = 2, R8C56 = [41], R3C23 = [37], 7 locked for D\, R56C2 = [71], R9C23 = [45], R9C4 = 9 (step 30), R1C45 = [89], R3C4 = 6, R2C45 = [47], R3C56 = [15], R2C1 = 9, R4C1 = 5, R78C1 = [76], R3C8 = 8, R78C8 = [59], 9 locked for D\, R8C9 = 7, R67C7 = [54], R4C3 = 9, R4C8 = 7, R9C6 = 7

54. Naked pair {68} in R6C56, locked for R6 and N5

and the rest is naked singles and a cage sum

3x3:d:k:3072:3072:3072:6403:6403:6403:4102:4102:4102:5385:2058:5643:5643:6403:5902:5902:1296:3089:5385:2058:5643:5643:6403:5902:5902:1296:3089:5385:4636:4636:5150:5150:5150:4129:4129:3089:3620:3620:4636:5150:6440:5150:4129:5163:5163:4397:3620:5679:5679:6440:4914:4914:5163:5685:4397:4397:5679:5679:6440:4914:4914:5685:5685:4397:1856:4929:3906:6440:3906:3141:3910:5685:1856:4929:4929:3906:3906:3906:3141:3141:3910:

That was a demanding Killer. The moves might be of rating 1.5 but it took me really long to find them so I rate it higher than Nasenbaer suggested.

By the way, I think we can rest the Mavericks for a while because 2 in one week is more than enough since the gap between M1 and M2 was one month even though there is no Assassin this week.

M4 Walkthrough:

1. R789a) 15(5) = {12345} locked for N8
b) Innies R89 = 22(3) = 9{58/67} -> 9 locked for R8
c) 15(2): R9C9 <> 6
d) Innies+Outies N7: -2 = R6C1 - R7C3 -> R6C1 <> 8,9; R7C3 <> 1,2
e) Innies+Outies N9: 4 = R6C9 - R7C7 -> R6C9 = (56789), R7C7 = (12345)

2. R456+N569
a) Killer quad (1234) locked in 20(5) + 25(4) for N5 since 20(5) has 3 of (1234)
b) Innies N69 = 5(2+1) = [212/131] -> R4C9 = (12), R6C7 = (13), R7C7 = (12); 1 locked for C7
c) Innies+Outies N9: 4 = R6C9 - R7C7 -> R6C9 = (56)
d) Innies N6 = 9(3) = 1{26/35} -> 1 locked for N6
e) 20(3) <> 6 because {569} blocked by R6C9 = (56)
f) 1 locked in 19(4) = 1{279/369/378} <> 5 since R67C7 <> 5,6,7
g) 12(3) @ N9: R9C8 <> 8,9 because R89C7 <> 1
h) 12(3) @ N6 <> 5 because R4C9 = (12) and R6C9 = (56) blocks {156}
i) 12(3) @ N9 <> 9 because {129} blocked by R7C7 = (12)

3. R123
a) Outies R1 = 8(2) <> 4,8,9
b) Outies = 9(2) = [72/81]

4. C123
a) Innies N4 = 13(3): R6C13 <> 6,7,8,9 because R4C1 >= 7
b) Innies+Outies N7 : -2 = R6C1 - R7C3 -> R7C3 <> 8,9

5. N146 !
a) ! Using Outies R123 = 9(2): Innies N46 = R6C1379 = 13(4) = 14{26/35} because R6C9 = (56)
-> 1,4 locked for R6; 4 locked for N4
-> R6C13 <> 5
b) 4 locked in Innies N4 = 4{18/27} <> 3

6. N347
a) Innies N47 = 15(2+1): R7C3 <> 4 since R4C1+R6C3 would be <= 10
b) Innies+Outies N7: -2 = R6C1 - R7C3 -> R6C1 <> 2; R7C3 <> 5,7
c) 12(3) <> 6 because 2 in R4C9 forces 6 in R6C9 (Innies N6 = [135/216])

7. N7+D/ !
a) Hidden Killer triple (789) in 17(4) since 19(3) can't have more than two of (789)
-> 17(4) <> {2456}
b) ! 19(3) <> 5,6 because 19(3) must have two of (789) since 17(4) can't have more than one of (789)
c) 17(4) <> {1367/2357} because R6C1 = (14) and R7C3 = (36) blocks {1367}
d) 17(4) = 1{259/268/349/457} since Killer pair (38) of 19(3) blocks <> 38{15/24}
-> 1 locked between C1+N7 -> R9C1 <> 1
e) 7(2): R8C2 <> 6
f) Consider canidates of R7C3 -> 17(4) <> 6,8:
- i) R7C3 = 3 -> 19(3) = 8{29/47} -> 17(4) <> {1268}
- ii) R7C3 = 6 -> 17(4) <> {1268}
g) 8 locked in 19(3) = 8{29/47} <> 3
h) 6 locked in R7C3+R9C1 for D/

8. R789
a) 6 locked in R678C9 for C9 -> 22(4) @ C9 = 6{178/259/349/358/457}; R7C8 <> 6
b) R8C37 <> 8 since together with R8C8 = (678) they would leave no combo for Innies R89 = 22(3)
c) 8 locked in 19(3) for R9
d) 15(2): R8C8 <> 7
e) Killer pair (68) locked in Innies R89 + R8C8 for R8
f) 19(3): R9C23 <> 2 because R8C3 <> 8,9
g) 12(3) <> {237} since it's a Killer triple of 22(4) @ N9

9. C123
a) 21(3) <> 5 because R8C1 = (579) blocks {579}
b) 21(3) = 8{49/67} -> 8 locked for C1
c) 12(3) <> {156/237} since they are Killer triples of 8(2)
d) 12(3) <> 6 because {246} blocked by Killer pair (46) of 21(3)

10. R789 !
a) Innies N9 = 18(4) <> {1359} since there is no combo with {359} for 22(4) @ N9
b) ! 12(3) <> 2 since {246} is a Killer triple of Innies N9
c) 2 locked in R7C789 for R7
d) 17(4) = 14{39/57} -> 4 locked between C1+N7 -> R9C1 <> 4
e) 7(2): R8C2 <> 3
f) Hidden Killer pair (89) in 22(4) @ N9 -> 22(4) <> {4567}
g) Innies N7 = 19(4) = {1369/1567/3457} because R7C3 = (36)
h) ! Hidden Killer triple (123) in R7C123 for R7 since R7C7 and R7C89 @ 22(4) must each have one of (123)
-> Innies N7 = 19(4) = 57{16/34} -> 5,7 locked for N7

11. N47+D/
a) 19(3) = {289} -> R8C3 = 2; 9 locked for R9
b) Innies N4 = 13(3) = {148} -> R4C1 = 8; 1 locked for R6+N4
c) Naked pair (36) locked in R7C3+R9C1 for N7+D/

12. C789
a) Innies N6 = 9(3) = [135] -> R4C9 = 1, R6C7 = 3, R6C9 = 5
b) 15(2) = [87] -> R9C9 = 7, R8C8 = 8
c) 22(4) = {2569} -> {269} locked for N9
d) 12(3) @ N9 = {345} -> R9C8 = 3; {45} locked for C7
e) 5(2) = {14} locked for C8+N3
f) 19(4) = {1369} -> R7C7 = 1; {69} locked for C6

13. C123+D/
a) 7(2) = [16] -> R9C1 = 6, R8C2 = 1
b) 21(3) = {489} -> {49} locked for C1+N1
c) 12(3) = {138} -> R1C1 = 3, R1C2 = 8, R1C3 = 1
d) 8(2) = {26} locked for C2+N1
e) 22(4) @ N1 = 57{19/28/46} -> R3C3 = 5, R2C3 = 7

14. Rest is singles without considering diagonals.

Rating: 1.75. One forcing chain, Hidden Killer Triples and some combo analysis were the most difficult moves I used which where hard to spot.

Many thanks to Nasenbaer for the latest challenging puzzle.

As Afmob said, it was a very demanding killer and the moves were very hard to find. On Tuesday and Wednesday I think I only found 6 or 7 moves each day but I never ground to a complete halt. Then today I found steps 33 and 34, after which it was fairly straightforward even though the first placement didn't come until step 43.

I didn't find this one quite as difficult as Maverick 1, which most people rated as a Hard 1.5, so I'll also rate Maverick 4 as a Hard 1.5. I didn't feel that my combination analysis justified a higher rating; it was fairly routine after the heavy analysis used for some recent puzzles.

I'll be interested to see how Afmob solved it. My walkthrough looks a lot longer.

Here is my walkthrough. Some of the key moves were steps 11a, which I added today, 26, 33, 34 and the simpler 36.Now that I've finished the puzzle I must disagree with that. The diagonals were very helpful from step 42 onward.

Thanks Afmob for the comments. I've corrected steps 17 and 26b and simplified step 41. I've also re-phrased step 10b and added a couple of clean-ups for step 43 which allowed me to simplify the remaining steps.

This is a Killer-X. I've included eliminations on the diagonals because it's easy to overlook them.

Prelims

a) R23C2 = {17/26/35}, no 4,8,9
b) R23C8 = {14/23}
c) R8C2 + R9C1 = {16/25/34}, no 7,8,9
d) R8C8 + R9C9 = {69/78}
e) R234C1 = {489/579/678}, no 1,2,3
f) 20(3) cage in N6 = {389/479/569/578}, no 1,2
g) 19(3) cage in N7 = {289/379/469/478/568}, no 1
h) 15(5) cage in N8 = {12345}, locked for N8

1. 45 rule on R1 2 outies R23C5 = 8 = {17/26/35}, no 4,8,9

2. 45 rule on R123 2 outies R4C19 = 9 = {45}/[63/72/81], no 9, no 6,7,8 in R4C9

3. 45 rule on R89 3 innies R8C159 = 22 = {589/679}, 9 locked for R8, clean-up: no 6 in R9C9

4. 45 rule on N3 2 innies R23C7 = 1 outie R4C9 + 12, min R23C7 = 13, no 1,2,3

5. 45 rule on N7 1 innie R7C3 = 1 outie R6C1 + 2, no 8,9 in R6C1, no 1,2 in R7C3

6. 45 rule on N9 1 outie R6C9 = 1 innie R7C7 + 4, no 1,2,3,4 in R6C9, no 6,7,8,9 in R7C7

7. 45 rule on C12 2 innies R49C2 = 1 outie R1C3 + 11
7a. Min R49C2 = 12, no 1,2
7b. Max R49C2 = 17 -> max R1C3 = 6

8. 45 rule on C89 2 innies R49C8 = 1 outie R1C7
8a. Max R49C8 = 9, no 9
8b. Min R49C8 = 3 -> min R1C7 = 3

9. 45 rule on N5 2 outies R78C5 = 2 innies R6C46
9a. Min R78C5 = 13 -> min R6C46 = 13, no 1,2,3

10. 45 rule on C789 4 innies R2367C7 = 17
10a. Min R23C7 = 13 (step 4) -> max R67C7 = 4 -> R67C7 = {12/13}, 1 locked for C7, clean-up: no 8,9 in R6C9 (step 6)
10b. Min R67C7 = 3 -> max R23C7 = 14 -> no 3,4,5 in R4C9 (step 4), clean-up: no 4,5,6 in R4C1 (step 2)
10c. Max R67C7 = 4 -> min R67C6 = 15, no 4,5

11. 45 rule on N6 3 innies R4C9 + R6C79 = 9 = {126/135} (cannot be {234} because no 2,3,4 in R6C9), no 7, 1 locked in R4C9 + R6C7 for N6, clean-up: no 3 in R7C7 (step 6)
11a. 2 of {126} must be in R4C9 (cannot be [126] which would give R7C7 = 2 (step 6) when R6C7 clashes with R7C7) -> no 2 in R6C7

12. 12(3) cage in N9 = {138/147/156/237/246/345} (cannot be {129} which clashes with R7C7), no 9
12a. 1 of {138} must be in R9C8 -> no 8 in R9C8
12b. 7 of {237} must be in R89C7 (cannot be {23}7 which clashes with R67C7) -> no 7 in R9C8

13. 45 rule on N58 4 outies R67C37 = 11
13a. R67C7 = 3,4 (steps 10b and 10c) -> R67C3 = 7,8, no 8,9, no 6,7 in R6C3, clean-up: no 6,7 in R6C1 (step 5)

14. 45 rule on N1 2 innies R23C3 = 1 outie R4C1 + 4, min R4C1 = 7 -> min R23C3 = 11, no 1

15. R234C9 = {129/138/147/237/246} (cannot be {156} which clashes with R6C9, cannot be {345} because R4C9 only contains 1,2), no 5

16. 20(3) cage in N6 = {389/479/578} (cannot be {569} which clashes with R6C9), no 6

17. 16(3) cage in N6 = {268/349/358/457} (cannot be {259/367} which clash with 20(3) cage and with R4C9 + R6C79)
17a. 6 of {268} must be in R4C78 (cannot be {28}6 which clashes with R4C19) -> no 6 in R5C7

18. R67C3 = 7,8 -> R67C4 = 14,15, no 4 in R6C4

19. R1C123 = {129/138/147/246/345} (cannot be {156/237} which clash with R23C2), if {246/345} R23C2 = {17} -> R1C123 + R23C2 must contain one of 7,8,9
19a. R234C1 = {489/579/678} -> R23C1 must contain one of 7,8,9
19b. Hidden killer triple 7,8,9 in R1C123 + R23C2, R23C1 and R23C3 for N1 -> R23C3 must contain one of 7,8,9
19c. R4C1 = {78} -> R23C3 = 11,12 (step 14), no 6 in R23C3

20. 45 rule on N9 4 innies R7C789 + R8C9 = 18 = {1269/1278/2349/2358/2457} (cannot be {1368/1467/2367} which clash with 15(2) cage, cannot be {1359/1458} which clash with 22(4) cage at R6C9 which would be 5{359}/5{458}, cannot be {3456} because R7C7 only contains 1,2), 2 locked for R7 and N9

21. 12(3) cage in N9 (step 12) = {138/147/156/345}
21a. 1 of {156} must be in R9C8 -> no 6 in R9C8

22. 45 rule on N7 4 innies R7C123 + R8C1 = 19 = {1369/1378/1468/1567/3457} (cannot be {1459} which clashes with 7(2) cage)
22a. 3 of {1369} must be in R7C12 (3 cannot be in R7C3 which would make 17(4) cage at R6C1 1{169} -> 6 of {1369} must be at R7C3 and 9 at R8C1 -> no 9 in R7C12

23. 19(3) cage in N7 = {289/379/469/478} (cannot be {568} which clashes with R7C123 + R8C1), no 5

24. R23C3 = 11,12 (step 14) -> R23C4 = 10,11
24a. 45 rule on C123 4 outies R2367C4 = 25 = {1789/2689/3589/3679/4579/4678}
24b. 5 of {3589/4579} must be in R6C4 (cannot make R23C4 = 10,11 including 5) -> no 5 in R23C4

25. 45 rule on N3 4 innies R23C79 = 24 = {1689/2589/2679/3579/3678/4569/4578} (cannot be {3489} which clashes with R23C8)
25a. 4 of {4569} must be in R23C9 because no {156} in R234C9 (step 15)
25b. 4 of {4578} must be in R23C9 (only way to make R234C9 total 12)
25c. -> no 4 in R23C7

26. R4C19 (step 2) = [72/81]
26a. 45 rule on N4 3 innies R4C1 + R6C13 = 13 = {148/157/238/247}
26b. Cannot be 7{15} which clashes with R4C9 + R6C79 = [216]
26c. Cannot be 8{23} which clashes with R4C9 + R6C79 = [135]
26d. -> R4C1 + R6C13 = {148/247}, no 3,5, 4 locked for R6 and N4, clean-up: no 5,7 in R7C3 (step 5)

27. R67C3 (step 13a) = 7,8 = [16/26/43], no 4 in R7C3, clean-up: no 2 in R6C1 (step 5)

28. R7C123 + R8C1 (step 22) = {1369/1567/3457} (cannot be {1378/1468} which would make 17(4) cage at R6C1 1{178}/4{148}), no 8
28a. 6 of {1567} must be in R7C3 -> no 6 in R7C12 + R8C1

29. 8 in N7 locked in 19(3) cage = {289/478}, no 3,6

30. R23C3 must contain one of 7,8,9 (step 19b)
30a. 45 rule on C123 4 innies R2367C3 = 19 = {1369/1468/1567/2368/2467/3457} (cannot be {1279/1378} which contain two of 7,8,9, cannot be {2458} because R7C3 only contains 3,6, cannot be {1459/2359} which aren’t consistent with R67C3 = [16/26/43])
30b. 2 of {2368/2467} must be in R6C3 -> no 2 in R23C3

31. 45 rule on N1 4 innies R23C13 = 25 = {3589/4579/4678} (cannot be {3679} which clashes with R23C2)
31a. 9 of {3589/4579} must be in R23C1 -> no 9 in R23C3

32. R1C123 (step 19) = {129/138/147/246} (cannot be {345} which clashes with R23C13), no 5

33. R67C37 = 11 (step 13)
33a. R67C3 (step 27) = [16/26/43]
33b. If R67C3 = [26] => R67C7 = 3 = [12]
33c. If R67C3 = [43] => R6C1 = 1 (step 26d)
33d. -> 1 in R6 locked in R6C137, no 1 in R6C5

34. R67C3 (step 27) = [16/26/43]
34a. R7C123 + R8C1 (step 28) = {1369/1567/3457}
34b. 6 of {1369/1567} must be in R7C3 -> R7C37 cannot be [61] => R67C7 = [12]
34c. -> no 1 in R6C3

35. R2367C3 (step 30a) = {2368/2467/3457}
35a. 19(3) cage (step 29) = {289/478}
35b. 4 of {478} must be in R89C3 (because R89C3 = {78} would clash with R23C3) -> no 4 in R9C2

36. Killer pair {24} in R6C3 and R89C3, locked for C3

37. R2367C3 (step 35) = {2368/3457} (cannot be {2467} because 2,4,6 only in R67C3), 3 locked for C3
37a. R23C3 = {38/57}

38. R1C123 (step 32) = {129/138/147/246}
38a. R1C3 = {16} -> no 1,6 in R1C12

39. R23C3 = {38/57} (step 37a)
39a. R23C13 (step 31) = {3589/4579} (cannot be {4678} which clashes with R23C3), 9 locked in R23C1, locked for C1 and N1, 5 locked for N1, clean-up: no 3 in R23C2
39b. R23C1 = {49/59}, no 6,7,8

40. Hidden killer quad 1,3,5,6 in R1C3, R23C3, R45C3 and R7C3 for C3 -> R45C3 must contain one of 1,5,6
40a. 18(3) cage in N4 = {189/369/567} (cannot be {378} which clashes with R4C1)
40b. R45C3 cannot be {56} -> no 7 in R4C2

41. 17(4) cage at R6C1 = {1457} (only remaining combination), no 3, 5,7 locked for N7, clean-up: no 2 in 7(2) cage, no 4 in R89C3 (step 29)
[Step 41 simplified at Afmob’s suggestion. I originally used the remaining combinations for R7C123 + R8C3.]

42. Killer pair 3,6 in R7C3 and 7(2) cage, locked for D/, clean-up: no 2 in R3C8

43. R6C3 = 4 (hidden single in C3), R7C3 = 3 (step 34), R6C1 = 1, R6C7 = 3, R7C7 = 1 (hidden single in C7, locked for D\), clean-up: no 7 in R3C2, no 8 in R23C3 (step 37a), no 4 in 7(2) cage in N7
43a. R9C1 = 6, R8C2 = 1, locked for D/, clean-up: no 7 in R2C2, no 4 in R3C8

44. R1C3 = 1 (hidden single in C3)
44a. Naked pair {26} in R23C2, locked for C2 and N1
44b. Naked pair {57} in R23C3, locked for C3, N1 and 22(4) cage
44c. Naked pair {49} in R23C1, locked for C1 and N1
44d. Naked pair {38} in R1C12, locked for R1
44e. Naked pair {57} in R78C1, locked for C1 and N7 -> R7C2 = 4, R4C1 = 8, R1C12 = [38], 3 locked for D\, R5C1 = 2, R9C2 = 9, R4C9 = 1 (step 2), R6C9 = 5 (step 11), R6C2 = 7, clean-up: no 6 in R8C8

45. Naked pair {89} in R6C48, locked for R6 -> R6C56 = [26], 6 locked for D\, R7C6 = 9 (cage sum), R23C2 = [26], R23C8 = [41], 4 locked for D/, R23C1 = [94], clean-up: no 6,7 in R2C5

46. Naked pair {78} in R8C8 + R9C9, locked for N9 and D\ -> R3C3 = 5, locked for D\, R5C5 = 9, locked for D/, R2C3 = 7, R45C3 = [96], R4C2 = 3 (step 40a), R5C2 = 5, R4C4 = 4, R6C4 = 8, locked for D/, R3C7 = 7, R1C9 = 2, R3C5 = 3, R2C5 = 5 (step 1)

and the rest is naked singles



In my previous message, I mentioned that I'd used 20 different "45" tests which are all included above. In addition I eventually looked at another 5 of them which never led to any candidate eliminations, although some produced combination eliminations.

This walkthrough was posted before I went through Afmob's walkthrough. Some comments on that and Mike's walkthrough are given in my later message including pointing out a couple of 45s that I missed, one of which I ought to have seen and the other was a less obvious one.

So, if my counting is correct, that's at least 27 45s in this puzzle! That must be some sort of record.

Hi folks,

Well, I finally did it, even if some of my moves were maybe a bit "OTT" (i.e., "over the top")!

Thanks to Nasenbaer for an (ultimately!) rewarding challenge! Contrary to his statement above, I even managed to make some use of the diagonals!

Afmob and Andrew will probably have a good laugh at this one, when they see what techniques I was resorting to! I suspect I've missed something important, but at least my approach should make for some interesting reading if nothing else! I hope so.

As to the rating, it definitely deserves a 1.75 from the point-of-view of the techniques I was using. However, if they were indeed OTT, Andrew's rating of a "hard 1.5" may prove to be more accurate.

In the meantime, happy reading!

Edit: Many thanks to Afmob for pointing out two things I missed!

M4 Walkthrough

Prelims:

a) 21(3) at R2C1 = {489/579/678} (no 1..3)
b) 8(2) at R2C2 = {17/26/35} (no 4,8,9)
c) 5(2) at R2C8 = {14/23}
d) 20(3) at R5C8 = {389/479/569/578} (no 1,2)
e) 7(2) at R8C2 = {16/25/34} (no 7..9)
f) 19(3) at R8C3 = {289/379/469/478/568} (no 1)
g) 15(5) at R8C4 = {12345}, locked for N8
h) 15(2) at R8C8 = {69/78}

1. Innies R89: R8C159 = 22(3) = {589/679} (no 1..4)
1a. 9 locked for R8
1b. cleanup: no 6 in R9C9

2. Outies R1: R23C5 = 8(2) = {17/26/35} (no 4,8,9)

3. Outies R123: R4C19 = 9(2) = [45/54/63/72/81]
3a. -> no 9; no 6..8 in R4C9

4. I/O diff. N7: R7C3 = R6C1 + 2
4a. -> no 1,2 in R7C3; no 8,9 in R6C1

5. I/O diff. N9: R6C9 = R7C7 + 4
5a. -> no 6..9 in R7C7; no 1..4 in R6C9

6. I/O diff. N3: R23C7 = R4C9 + 12
6a. -> min R23C7 = 13
6b. -> no 1..3 in R23C7

7. I/O diff. C12: R49C2 = R1C3 + 11
7a. min. R1C3 = 1 -> min. R49C2 = 12
7b. -> no 1,2 in R49C2
7c. max. R49C2 = 17 -> max. R1C3 = 6
7d. -> no 7..9 in R1C3

8. I/O diff. C89: R49C8 = R1C7
8a. min. R49C8 = 3 -> min. R1C7 = 3
8b. -> no 1,2 in R1C7
8c. max. R1C7 = 9 -> max. R49C8 = 9
8d. -> no 9 in R49C8

9. Innies N6: R4C9+R6C79 = 9(3) = {126/135} (no 4,7..9)
(Note: not {234}, because none of these digits in R6C9)
9a. 1 locked for N6
9b. {5/6} must go in R6C9
9c. -> no 5,6 in R4C9+R6C7
9d. cleanup: R7C7 = {12} (step 5); no 4,5 in R4C1 (step 3)

10. 12(3) at R8C7 = {138/147/156/237/246/345} (no 9)
(Note: {129} blocked by R7C7)

11. 20(3) at R5C8 = {389/479/578} (no 6)
(Note: {569} blocked by R6C9)

12. Innies N69: R4C9+R67C7 = 5(1+2) = [131/212]
12a. -> no 3 in R4C9; no 2 in R6C7
12b. R4C9+R6C79 (step 9) = [216/135]
12c. cleanup: no 6 in R4C1 (step 3)
Afmob pointed out that I could have added that 1 is locked in R67C7 for C7 here.

13. 12(3) at R2C9 = {129/138/147/237} (no 5,6)
(Note: not {345}, because none of these digits in R4C9;
{156} blocked by R6C9; {246} blocked by h9(3)n6 (step 12b))

14. I/O diff. N5: R78C5 = R6C46
14a. min. R78C5 = 13 -> min. R6C46 = 13
14b. -> no 1..3 in R6C46
(Note: could stretch the logic here to also eliminate 4 from R6C46, but that's done in next step)

15. Outies N5789: R6C1379 = 13(4) = {1246/1345} (no 7..9)
(Note: not {1237}, because none of these digits in R6C9)
15a. 1,4 locked for R6
15b. 4 locked in R6C13 for N4
15b. possible permutations h13(4): [4216/1435/4135]
(Note: [2416] blocked by R7C3 (step 4); [3415/4315] blocked by h9(3)n6 (step 12b))
15b. -> R6C1 = {14}; R6C3 = {124}
15c. cleanup: R7C3 = {36} (step 4)

16. 17(4) at R6C1 = {1259/1349/1457} (no 6,8) = {(7/9)..}
(Note: not {2357}, because none of these digits in R6C1;
{1358/1367/2456} blocked by R7C3 (step 4);
{1268} blocked because it would force R7C3 to 3 and thus leave no combos for 7(2)n7;
{2348} blocked because it would force R7C3 to 6 and thus leave no combos for 7(2)n7)
16a. no 1 in R9C1 (CPE)
16b. cleanup: no 6 in R8C2

17.Hidden killer pair on {79} within N7 as follows:
17a. 17(4) at R6C1 must have exactly 1 of {79} within N7 (step 16)
17b. -> 19(3) at R8C3 (only other place for {79} in N7) must also have exactly 1 of {79}
17c. -> {379/568} combos both blocked
17d. Furthermore, 8 of N7 locked in 19(3) = {8..}
17e. -> 19(3) at R8C3 = {289/478} (no 3,5,6)

18. 6 in N7 locked in D/ -> not elsewhere in D/
18a. 6 in C9 locked in R678C9
18b. -> no 6 in R7C8
18c. 22(4) at R6C9 = {6..} = {1678/2569/3469/3568/4567} (no eliminations yet)

19. 21(3) at R2C1 = {489/678} (no 5)
(Note: {579} blocked by R8C1)
19a. 8 locked for C1

20. Grouped AIC removes combos {138/147} from 12(3) at R8C7:
(6)r9c78=(6)r9c1,(1)r8c2-(1)r7c12=(1)r7c789
This can be explained in verbose form as follows:
20a. Either R9C78 contains a 6 or...
20b. ...R9C78 does not contain a 6
20c. => R9C1 = 6 (strong link, R9); R8C2 = 1 (neutral link, 7(2))
20d. -> R7C12 does not contain a 1 (weak link, N7)
20e. => R7C789 contains a 1 (strong link, R7)
20f. -> no 1 in 12(3) at R8C7
20g. Thus, if 12(3) at R8C7 does not contain a 6, it cannot contain a 1
20h. -> {138/147} combos blocked
20i. -> 12(3) at R8C7 (step 10) = {156/237/246/345} (no 8)

21. Distribution of {13} across N79:
21a. 7(2) at R8C2 cannot contain both of {13}
21b. -> R7C123 (only other place for {13} in N7) must contain at least 1 of {13}
21c. 12(3) at R8C7 cannot contain both of {13}
21d. -> R7C789 (only other place for {13} in N9) must contain at least 1 of {13}
21e. from steps 21b and 21d, R7C123 and R7C789 must each contain exactly 1 of {13}
21f. -> 7(2) at R8C2 and 12(3) at R8C7 must also each contain exactly 1 of {13}
21g. -> 7(2) at R8C2 = {16/34} (no 2,5) = {(3/6)..}
21h. 12(3) at R8C7 (step 20i) = {(1/3)..} = {156/237/345} (no eliminations)

22. 7(2) at R8C2 (step 21g) and R7C3 form killer pair on {36}
22a. -> no 3 elsewhere in N7 and D/
22b. cleanup: no 2 in R3C8

23. Grouped Turbot Fish removes 1 from R7C89:
(1)r789c7=(1)r6c7-(1)r6c1=(1)r7c12
This can be explained in verbose form as follows:
23a. Either R789C7 contains a 1 or...
23b. ...R789C7 does not contain a 1
23c. => R6C7 = 1 (strong link, C7)
23d. -> R6C1 <> 1 (weak link, R6)
23e. => R7C12 = 1 (strong link, 17(4))
23f. Thus, either R789C7 or R7C12 (or both) must contain a 1
23g. -> no 1 in R7C89 (common peers)

24. 1 now unavailable to 22(4) at R6C9 (step 18c) = {2569/3469/3568/4567}
24a. Hidden killer pair on {89} blocks {4567} combo, as follows:
24b. Only places for {89} in N9 are 15(2) and 22(4), neither of which can contain both
24c. -> each of 15(2) at R8C8 and 22(4) at R6C9 must contain exactly 1 of {89}
24d. -> {4567} combo blocked
24e. -> 22(4) at R6C9 = {2569/3469/3568} (no 7) = {(2/3}..}
Afmob pointed out here that step 23 was not really necessary, because even without it, 22(4) at R6C9 = {1678/2569/3469/3568} = {(2/3/7)..} (within N9), thus also blocking the {237} combo for 12(3) in the next step and thus likewise breaking the puzzle.

25. 12(3) at R8C7 (step 21h) = {156/345} (no 2,7)
(Note: {237} blocked by 22(4) at R6C9 (step 24e))
25a. 5 locked for N9

26. 7 in N9 locked in 15(2) at R8C8 = {78} (no 6,9), locked for N9 and D\
26a. cleanup: no 1 in R3C2

27. 9 in R9 locked in R9C23 for N7
27a. 19(3) at R8C3 = {9..} = {289} (no 4,7) (last combo)
27b. 2 locked in R89C3 for C3 and N7

28. Hidden single (HS) in R9 at R9C9 = 7
28a. -> R8C38 = [28]

29. Naked pair (NP) at R6C13 = {14}, locked for R6 and N4
29a. -> R6C7 = 3
29b. -> R46C9 (step 12b) = [15]
29c. -> R7C7 = 1 (step 5); R4C1 = 8 (step 3, but also obtainable via cage split of N4 innies)

30. 6 in C9 locked in N9 -> not elsewhere in N9
30a. 12(3) at R8C7 = {345} (last combo)
30b. -> R9C8 = 3; R89C7 = {45}, locked for C7 and N9
30c. cleanup: no 2 in R2C8

31. HS in R9 at R9C1 = 6
31a. -> R8C2 = 1; R7C3 = 3
31b. -> R6C1 = 1 (step 4)
31c. -> R6C3 = 4
31d. cleanup: no 7 in R23C1 (step 19)

32. R23C8 = [41]
32a. -> R23C1 = [94]

33. 12(3) at R1C1 = [381/561]
33a. -> R1C1 = {35}; R1C2 = {68}; R1C3 = 1
33b. cleanup: no 7 in R3C2

Only singles and simple cage sums left now.

Good to see that you posted your walkthrough, Mike. As Afmob said we had three different solving paths.

Some interesting steps although it did at times seem to have been hard work. Step 21 looks as if it ought to contain the term "hidden killer pair" in some sub-steps.

Having gone through all three walkthroughs again today, I wondered whether I was right with my rating but then remembered the reason I gave with my walkthrough; I found Maverick 1 harder to solve than this one, particularly in how long they took.

Afmob and Mike both found a couple of important 45s that I missed. They both had innies for N69 which was more direct than how I got that result; that's a 45 that I shouldn't have missed. They also both got the less obvious R6C1379. I particularly liked the way Afmob used N46 to get that. Another good move that only Afmob had was the killer quad in N5 (step 2a).

My walkthrough seems to have made more use of sets of 4 innies and I think I was the only one of us three to use 4 outies for N58.

Thanks again Nasenbaer! A challenging puzzle but at the same time allowing plenty of scope for different solving paths.We'll all agree with that. I certainly wouldn't want the same walkthrough thrice. However I think it's acceptable to have two very similar walkthroughs if they show different logic or thought patterns to achieve the similar results.