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Thanks goooders for mentioning nd's puzzles. I found them shortly before I found Ruud's Assassins. There are still some of nd's puzzles that I've never solved although I never tried them using elimination solving; I must try them again that way.

They can be found at http://www.ndorward.com/blog/?page_id=71 and there are WTs for each puzzle. Have fun with them!

nd#10 was first posted on Ruud's Assassin forum in December 2006. It's included in Ed's Assassin Archive & Ratings Update, page 3, as A New One. nd's other puzzles are only on his website. I think the hardest ones are reckoned to be #6alt, #9 and #10.

I ought to have also replied earlier to this point.

When I first started doing Assassins, having done easier Killers on a different site which I still do, I also used insertion solving. For some time I resisted changing over to elimination solving, although others started using it before I did as can be seen from posted walkthroughs. I was surprised to see, from Ed's excellent Assassin Archive & Rating Update thread, that I was still using insertion solving as late as A27.

It's certainly more satisfying if one can make steady progress rather than chipping away one candidate or one combination at a time. That sort of progress can happen with many puzzles, whether one is using insertion or elimination solving.

Here is a complete walkthrough for Assassin 106 v2:

If just judging by difficulty of techniques involved, this one is not particularly hard. But it's quite tricky with the wrap-around cages and all to deal with the big outies. Note I didn't use a single innie-outie.

(Edited: Complete walkthrough replaced.)

_________________
ADYFNC HJPLI BVSM GgK Oa m

I jumped back a bit to my earliest unfinished puzzle on this site, as a change from working backward through my unfinished puzzles.

Thanks Afmob for a challenging variant! It deserves more than one walkthrough.

You forgot to mention that you also used a "clone" and made very good use of it. It took me a long time until I spotted the "clone". Later you had clearly reached a stage where you were avoiding innies-outies; I felt that one step might have been simpler using one.

At the time when this puzzle appeared I'd got stuck after step 15. When I started again last week I got stuck again after step 32 so I took a break and solved another of my backlog, one from Ruud's site, before trying again and finding how I could use the "clone" in step 33. I'm glad that I persevered as I enjoyed finding the somewhat unusual step 46.


Here is my walkthrough for A106 V2.

Prelims

a) R19C1 wrap-around cage = {19/28/37/46}, no 5
b) R1C34 = {29/38/47/56}, no 1
c) R19C9 wrap-around cage = {49/58/67}, no 1,2,3
d) R4C45 = {29/38/47/56}, no 1
e) R5C23 = {18/27/36/45}, no 9
f) R5C78 = {14/23}
g) R6C56 = {13}
h) R9C67 = {89}
i) 9(3) cage at R2C6 = {126/135/234}, no 7,8,9
j) 10(3) cage at R1C6 = {127/136/145/235}, no 8,9
k) 20(3) cage in N7 = {389/479/569/578}, no 1,2
l) 9(3) cage at R9C2 = {126/135/234}, no 7
m) 26(4) cage in N2 = {2789/3689/4589/4679/5678}, no 1

Steps resulting from Prelims
1a. Naked pair R6C56 = {13}, locked for R6 and N5, clean-up: no 8 in R4C45
1b. Naked pair {89} in R9C67, locked for R9, clean-up: no 1,2 in R1C1, no 4,5 in R1C9

2. 45 rule on C12 3 innies R579C2 = 1 outie R2C3 + 4
2a. Min R579C2 = 6 -> min R2C3 = 2

3. 45 rule on N6 4 innies R4C7 + R6C789 = 27 = {3789/4689/5679}, no 1,2, 9 locked for N6

4. 45 rule on C6789 4 innies R4568C6 = 23 = {1679/3479/3569/3578} (cannot be {1589/2489} which clash with R9C6, cannot be {2579/2678/4568} which don’t contain 1,3), no 2
4a. R6C6 = {13} -> no 1,3 in R8C6
4b. Killer pair 8,9 in R4568C6 and R9C6, locked for C6

5. 9(3) cage at R2C6 = {126/135/234}
5a. 5 of {135} must be in R23C6 (R23C6 cannot be {13} which clashes with R6C6) -> no 5 in R2C7

6. 45 rule on N9 4 innies R79C79 = 17 = {1259/1268/1349/1358/2348} (cannot be {1367/1457/2357/2456} which don’t contain 8,9), no 7, clean-up: no 6 in R1C9
6a. R9C7 = {89} -> no 8,9 in R7C79
6b. R9C9 = {456} -> no 4,5,6 in R7C79

7. 17(3) cage at R6C7 = {179/269/278/359/368} (cannot be {458/467} because R7C7 only contains 1,2,3), no 4
7a. R7C7 = {123} -> no 1,2,3 in R7C6
7b. 8,9 can only be in R6C7 -> R6C7 = {89}
7c. Killer single 7 in R4568C6 and R7C6, locked for C6
7d. 2 in C6 only in R123C6, locked for N2, clean-up: no 9 in R1C3

8. Naked pair {89} in R69C7, locked for C7
8a. 9 in N6 locked in R6C789, locked for R6

9. 13(3) cage at R6C3 = {148/157/238/247/256/346} (cannot be {139} because R6C3 doesn’t contain any of 1,3,9), no 9

10. 45 rule on R789 2 outies R6C37 = 3 innies R7C9 + R9C19
10a. Min R79C7 = 9 -> max R79C9 = 8 (step 6) -> max R7C9 + R9C19 = 15 -> max R6C37 = 15 -> no 8 in R6C3

11. 45 rule on N3 4 outies R123C6 + R4C7 = 1 innie R1C9 + 3
11a. R1C9 = {789} -> R123C6 + R4C7 = 10,11,12
11b. Min R123C6 = 7 (cannot be 6 because {123} clashes with R6C6) -> max R4C7 = 5

12. 14(3) cage at R3C7 = {149/158/239/248/257/347/356} (cannot be {167} because R4C7 only contains 3,4,5)
12a. 8,9 of {149/158} must be in R3C8 -> no 1 in R3C8

13. R4C7 + R6C789 (step 3) = {3789/4689/5679}
13a. R4C7 = {345} -> no 4,5 in R6C89

14. 16(3) cage in N4 = {259/268/358/457} (cannot be {169/349} because 1,3,9 only in R5C1, cannot be {178/367} which clash with R6C789), no 1
14a. 9 of {259} must be in R5C1, 2 of {268} must be in R6C12 (R6C12 cannot be {68} which clashes with R6C789) -> no 2 in R5C1

15. 45 rule on N4 2 innies R46C3 = 1 outie R3C1 + 8
15a. Max R46C3 = 16 -> max R3C1 = 8
15b. Min R46C3 = 9 -> min R4C3 = 2

16. 45 rule on C1234 4 innies R2456C4 = 19 = {2359/2368/2458/2467/3457}
16a. 3 of {2359} must be in R2C4 -> no 9 in R2C4
16b. 5 of {2359} must be in R4C4 (R4C4 cannot be 2 or 9 because R456C4 would clash with R4C45, CCC) -> no 9 in R4C4, clean-up: no 2 in R4C5

17. 16(4) cage in N8 = {1249/1258/1267/1456/2347/2356} (cannot be {1348/1357} which clash with R6C5)
17a. Killer pair 1,3 in R6C5 and R789C5, locked for C5

18. 45 rule on N23 3(2+1) innies R1C49 + R3C4 = 1 outie R4C7 + 16
18a. Min R4C7 = 3 -> min R1C49 + R3C4 = 19 -> no 1 in R3C4 (because max R1C49 = 17)
18b. 1 in N2 only in R123C6, locked for C6 -> R6C56 = [13]
18c. 9(3) cage at R2C6 = {126/135/234}
18d. 3 of {234} must be in R2C7 -> no 4 in R2C7

19. 16(4) cage in N8 (step 17) = {2347/2356}, no 8,9, 2,3 locked for N8, 2 also locked for C5
19a. 9(3) cage at R9C2 = {126/135/234}
19b. 4 of {234} must be in R9C4 -> no 4 in R9C23

20. Hidden killer pair 8,9 in R78C4 and 16(4) cage for N8 -> 15(3) cage at R7C4 must contain one of 8,9 in R78C4
20a. 15(3) cage at R7C4 = {159/168/249/258/348} (cannot be {267/357/456} which don’t contain 8 or 9), no 7
20b. 8,9 must be in R78C4 -> no 8,9 in R8C3
20c. 2,3 of {249/348} must be in R8C3 -> no 4 in R8C3

21. 45 rule on R789 4 outies R6C3789 = 2 innies R9C19 + 16
21a. Max R9C19 = 13 -> R6C3789 cannot total 30 -> no 6,7 in R6C3
21b. Min R6C3789 = [29]{67} (because R6C789 must contain 9) = 24 -> min R9C19 = 8, no 1 in R9C1, clean-up: no 9 in R1C1

22. 16(3) cage in N4 (step 14) = {259/268/358/457}
22a. 16(3) cage cannot be {268} => R5C23 = {45} clashes with R6C3
22b. -> 16(3) cage = {259/358/457}, no 6, 5 locked for N4, clean-up: no 4 in R5C23
22c. 3 of {358} must be in R5C1 -> no 8 in R5C1

23. Hidden killer quad 6,7,8,9 in R4C12, R4C3, 16(3) cage and R5C23 for N4, R4C12 cannot contain more than one of 6,7,8,9, 16(3) cage contains one of 7,8,9, R5C23 contains one of 6,7,8 -> R4C3 = {6789} and R4C12 must contain one of 6,7,8,9
23a. 12(3) cage at R3C1 cannot contain more than one of 6,7,8,9 which must be in R4C12 -> no 6,7,8 in R3C1

24. Max R7C1 + R8C12 + R9C1 = 27 -> min R7C23 + R8C3 + R9C34 = 18 must contain at least one of 4,7,8 -> R7C23 must contain at least one of 4,7,8
24a. 13(3) cage at R6C3 (step 9) = {148/238/247} (cannot be {157} because R6C3 only contains 2,4, cannot be {256/346} which don’t contain any of 4,7,8 in R7C23), no 5,6
24b. R7C23 = {18/27/38/47}

25. 9 in N7 only in 20(3) cage = {389/479/569}
25a. R7C23 + R8C3 + R9C34 cannot be 18 = {12348/12357/12456} (cannot be {12348/12456} because 4 must be in R7C23 and neither combination contains both of 4,7, cannot be {12357} which clashes with 20(3) cage)
25b. Min R7C23 + R8C3 + R9C34 = 19 -> max R7C1 + R8C12 + R9C1 = 26 -> max R9C1 = 6, clean-up: no 3 in R1C1

26. Hidden killer pair 7,8 in R7C23 and 20(3) cage for N7, R7C23 contains one of 7,8 -> 20(3) cage must contain one of 7,8 -> 20(3) cage (step 25) = {389/479} (cannot be {569} which doesn’t contain 7 or 8), no 5,6

27. 3 in N2 only in R123C4
27a. Hidden killer triple 7,8,9 in R13C4 and 26(4) cage for N2, 26(4) cage contains two of 7,8,9 -> R13C4 must contain one of 7,8,9
27b. 26(4) cage in N2 = {3689/4589/4679/5678}
27c. 26(4) cage = {3689} or R13C4 contains 3 and one of 7,8,9 -> no 6 in R13C4, clean-up: no 5 in R1C3

28. 45 rule on N78 3 innies R9C1 + R79C6 = 1 outie R6C3 + 17
28a. Min R6C3 = 2 -> min R9C1 + R79C6 = 19, max R79C6 = 16 -> min R9C1 = 3, clean-up: no 8 in R1C1

29. 7 in R9 only in R9C58
29a. 45 rule on R9 4 innies R9C1589 = 19 = {1567/2467/3457}
29b. 5,6 of {1567} must be in R9C19, 4,6 of {2467} must be in R9C19 -> no 6 in R9C58

30. 45 rule on R1 4 innies R1C1259 = 24 = {1689/2679/3489/3678/4569/4578} (cannot be {2589} because R1C1 only contains 4,6,7, cannot be {3579} which clashes with R1C34)
30a. 1,2,3 of {1689/2679/3489/3678} must be in R1C2, 9 of {4569} must be in R1C9 -> no 9 in R1C2

31. 45 rule on R1234 3 innies R1C19 + R4C6 = 1 outie R5C9 + 13
31a. Min R1C19 + R4C6 = 15 -> min R5C9 = 2

32. 16(3) cage in N4 (step 22b) = {259/358/457}
32a. {259} => R6C3 = 4
{358} => R5C23 = {27} => R6C3 = 4
{457} => R6C3 = 2
32b. -> no 2,4 in R4C12

33. R4568C6 (step 4) = {3479/3569/3578} -> R458C6 = {479/569/578}
33a. R69C7 = {89}, R9C67 = {89} -> R6C7 = R9C6
33b. 17(3) cage at R6C7 (step 7) = {179/269/278/359/368} -> R7C67 + R9C6 = {179/269/278/359/368}
33c. R7C67 + R9C6 = [629/638/728] (cannot be [539/719] which clash with R458C6) -> R7C6 = {67}, R7C7 = {23}
33d. Killer pair 6,7 in R458C6 and R7C6, locked for C6
33e. Killer pair 6,7 in 16(4) cage and R7C6, locked for N8

34. 9(3) cage at R2C6 = {126/135/234}
34a. 3,6 only in R2C7 -> R2C7 = {36}

35. 14(3) cage at R3C7 (step 12) = {149/158/248/257/347} (cannot be {239} which clashes with R7C7, cannot be {356} because R2C7 “sees” all cells of the 14(3) cage), no 6
35a. 5 of {158/257} must be in R4C7 -> no 5 in R3C78

36. 10(3) cage at R1C6 = {127/145/235} (cannot be {136} which clashes with R2C7), no 6
36a. R1C1259 (step 30) = {1689/2679/3489/3678/4569} (cannot be {4578} which clashes with 10(3) cage at R1C6)
36b. 1,2,3 of {1689/2679/3489/3678} must be in R1C2 -> no 7,8 in R1C2

37. R79C79 (step 6) = {1259/1268/1349/1358/2348}
37a. 1 of {1259/1268/1349/1358} must be in R7C9, 2 of {2348} must be in R7C7 (R79C7 cannot be [38] which clashes with R7C67 + R9C6) -> no 2 in R7C9

38. Killer triple 3,4,6 in 20(3) cage, R9C1 and R9C23 (because 3,6 of 9(3) cage must be in R9C23), locked for N7

39. 13(3) cage at R6C3 (step 24a) = {148/247} -> R6C3 = 4, clean-up: no 7 in R1C4
39a. 16(3) cage in N4 (step 32) = {259/358}, no 7
39b. 3,9 only in R5C1 -> R5C1 = {39}, 5 locked in R6C12, locked for R6

40. Killer triple 1,2,3 in R7C23, R7C7 and R7C9, locked for R7, 3 also locked for N9
40a. R79C79 (step 6) = {1349/1358/2348}, no 6, clean-up: no 7 in R1C9

41. R6C37 = R7C9 + R9C19 (step 10), R6C3 = 4, R6C7 = {89} -> R7C9 + R9C19 = 12,13
41a. Max R79C9 = 8 -> min R9C1 = 4, clean-up: no 7 in R1C1
41b. Naked pair {46} in R19C1, locked for C1
41c. R9C1589 (step 29a) = {1567/2467/3457}
41d. 1,2,3,7 only in R9C58 -> no 4,5 in R9C58

42. 16(4) cage in N8 (step 19) = {2347/2356}
42a. 2,3 only in R89C5 -> R89C5 = {23}

43. R9C8 = 7 (hidden single in R9)
43a. 1 in R9 locked in 9(3) cage at R9C2 = {126/135}, no 4

44. 45 rule on N4 1 remaining innie R4C3 = 1 outie R3C1 + 4, no 1 in R3C1, no 8 in R4C3

45. 20(3) cage in N9 (step 26) = {389/479}
45a. 4 of {479} must be in R8C2 -> no 7 in R8C2
45b. 8 of {389} must be in R78C1 (R78C1 cannot be {39} which clashes with R5C1) -> no 8 in R8C2

46. 45 rule on R6789 3 innies R6C4 + R9C19 = 1 outie R5C1 + 9
46a. 4 in R9 only in R9C19 = [45/64] = 9,10
46b. R5C1 = {39} cannot be the same as R6C4 = {2678} -> R9C19 cannot total 9
46c. R9C19 = 10 = [64], R1C1 = 4, R1C9 = 9, R9C5 = 2 (step 41c), R8C5 = 3, clean-up: no 2,7 in R1C3

47. R8C2 = 4 (hidden single in N7), R78C1 (step 45) = {79}, locked for C1 and N7, R5C1 = 3, clean-up: no 6 in R5C23, no 2 in R5C78, no 2 in R6C12 (step 39a), no 2 in R7C23 (step 39)

48. Naked pair {58} in R6C12, locked for R6 and N4 -> R4C1 = 1, R6C7 = 9, R6C89 = [67], R6C4 = 2, clean-up: no 9 in R4C5

49. Naked pair {18} in R7C23, locked for R7 and N7 -> R7C9 = 3, R7C7 = 2, R9C67 = [98], R7C6 = 6 (step 33c), clean-up: no 5 in 16(4) cage in N8 (step 19)
49a. R8C6 = 7, R7C5 = 4, R7C4 = 5, R9C4 = 1, R8C34 = [28], R1C4 = 3, R1C3 = 8, R5C23 = [27], R7C23 = [81], R6C12 = [85], R9C23 = [35]

50. 13(3) cage in N6 = {238} (only remaining combination) -> R45C9 = [28], R4C8 = 3
50a. Naked pair {14} in R5C78, locked for R5 and N6 -> R4C7 = 5, R5C6 = 5

51. 45 rule on N1 2 remaining innies R3C13 = 5 -> R3C3 = 3, R3C1 = 2, R4C2 = 9 (cage sum), R4C3 = 6, R3C4 = 9 (cage sum), R2C13 = [59], R5C45 = [69]

52. R4C7 = 5 -> R3C78 = 9 = [18]

and the rest is naked singles.