Assassin 2

[mhparker]

Hi folks,

Hey, I'm the first to post a WT for this one! Come on guys, where are you all?

The question is: Was this the puzzle where Ruud developed his love of 3-cell cages?

Estimated rating: 0.75. Unfortunately, I messed it up a bit and strayed from the optimum route near the start. Clearly, I can't do 0.75-rated puzzles properly any more...

Anyhow, here's my (non-optimal) WT:


Assassin 2 Walkthrough

Prelims:

a) 21(3) at R1C6 = {489/579/678} (no 1..3)
b) 11(3) at R2C7, R5C1 and R7C5 = {128/137/146/236/245} (no 9)
c) 9(3) at R3C1, R3C6 and R7C5 = {126/135/234} (no 7..9)
d) 20(3) at R3C3, R6C1, R8C4 and R8C6 = {389/479/569/578} (no 1,2)

1. Innie/Outie (I/O) diff. C789: R19C7 = R37C6 + 14
1a. -> R37C6 = {12}, locked for C6; R19C7 = {89}, locked for C7

2. Outies C89: R258C7 = 7(3) = {124}, locked for C7

3. 9(3) at R3C6 = {135} (last combo)
3a. -> R3C6 = 1; R34C7 = {35}, locked for C7

4. Naked single (NS) at R7C6 = 2

5. Outies R12: R3C258 = 22(3) = {589/679} (no 1..4)
5a. 9 locked for R3

6. Innies N3: R13C7+R3C9 = 17(3) = [836/854/935/953]
6a. -> R3C9 = {3..6} (no 2,7,8)

7. Hidden single (HS) in R3 at R3C1 = 2
7a. -> split 7(2) at R4C12 = {16/34} (no 5)

8. Outies N12: R1C7+R4C3 = 17(2) = {89} (no 3..7)
8a. no 8,9 in R1C3 (CPE)

9. Innies N1: R13C3 = 12(2) = [48]/{57} (no 1,3,6; no 4 in R3C3)

10. 11(3) at R5C1 = {128/245} (no 3,6,7)
(Note: {137/146/236} all blocked by R4C12 (step 7a))
10a. 2 locked for R5 and N4

11. 12(3) at R5C7 = {138/345} (no 6,7,9)
(Note: {147/156} both blocked by 11(3) at R5C1 (step 10))
11a. 3 locked for R5 and N6
11b. can only have 1 of {14}, which must go in R5C7
11c. -> no 1,4 in R5C89

12. R34C7 = [35]
12a. -> no 4 in R3C9 (step 6)

13. HS in R3 at R3C4 = 4
13a. -> R34C3 = [79] (last permutation)
13b. -> R1C3 = 5 (step 9)

14. 12(3) at R5C7 = {138} (last combo)
14a. -> R5C7 = 1; R5C89 = {38}, 8 locked for R5 and N6

15. 11(3) at R5C1 (step 10) = {245} (last combo), locked for R5 and N4
15a. cleanup: no 3 in R4C12 (step 7a)

16. Naked pair (NP) at R4C12 = {16}, locked for R4 and N4

17. 15(3) at R3C9 = {267} (no 4,5) (last combo)
17a. -> R3C9 = 6; R4C89 = {27}, locked for R4 and N6
17b. -> R1C7 = 8 (step 6)

18. R679 = [679]

19. NS at R3C8 = 5
19a. -> split 6(2) at R2C78 = {24}, locked for R2 and N3

20. NP at R6C89 = {49}, locked for R6
20a. -> R7C9 = 1 (cage sum)

21. HS in C4 at R6C4 = 1
21a. -> split 11(2) at R4C6+R5C5 = [47] (last combo/permutation)

22. HS in C4 at R1C4 = 2
22a. -> R2C4 = 8 (cage sum)

23. R3C25 = [89]
23a. split 7(2) at R2C23 = {16} (last combo), locked for R2 and N1
23b. split 8(2) at R12C5 = [35]

24. R4C45 = [38]
24a. -> R5C4 = 6 (cage sum)

25. 16(3) at R5C6 = [925]

26. R12C6 = [67]

27. 17(3) at R1C8 = [179] (last combo/permutation)

28. NS at R2C1 = 3

29. 20(3) = {389/578} (no 4,6)
29a. 7 of {578} must go in R6C2
29b. -> R6C1 = 8

Now all singles and simple cage sums to end.

[mhparker]

Hi folks, it's me again...

Clearly, I can't do 0.75-rated puzzles properly any more...

Fortunately, this one should be a tad more difficult...

Assassin 2X (A2X) (Est. rating: 1.75)



3x3:d:k:4352:43523842:461235893335:4352:4618:461846124367:43674626:46183860:46123095:43674626:4626361425923354259625962592:54173626337341435417:5417:440333804151:4143:41434403:4403:62054415:4151:415131306205:62054415:4415390626283399

Note: It's a Killer-X, where no repeated digits are allowed on either diagonal.

Yeah, looks pretty straightforward, I know...

[Caida]

I managed to start A2X pretty well - even got a couple numbers placed. I have most of n5 complete with 3 numbers placed and the others are reduced to pairs

But I have now ground to a halt.

Does the fact that it is a Killer-X help at all with solving it? I'm not seeing it lead to anything so far.

Would it help to do the original A2?

Cheers,

Caida

[mhparker]

Hi Caida,

Thanks for giving it a go. Here are some answers to your questions.

I managed to start A2X pretty well...But I have now ground to a halt.

Yes, it's a toughie. Unlike several recent Assassin V1's, which consist of finding one (or at most, two) key move(s), apart from which the rest is plain sailing, this is more like a traditional V2, which (whilst having easier sections) generally involves more of a fight to dig away at the candidates. This puzzle does contain at least one key move, however, that will make your life easier if you find it/them.

Does the fact that it is a Killer-X help at all with solving it? I'm not seeing it lead to anything so far.

Yes, but they are further down the road.

Would it help to do the original A2?

No, because it doesn't require a move similar to that/those needed to unlock this puzzle.

BTW, I have increased the estimated rating for the A2X to 1.75, which I now suspect may be nearer to the mark.


In the meantime, maybe this is more like the puzzle you're looking for?:


Assassin 2X Lite (A2X-Lite) (Est. rating: 1.25)



3x3:d:k:4096:409620504613:46133591:4096:5130:51303588:4613:4879:48792066:5130:4884:48844631:4631:4879:46342066:488425904631:4634:463436202590541731144397:4397:46555417:5417389243974655:46551587492549273127:46743908:4925:49254927:4927:4674:467439082119

Note: It's a Killer-X, where no repeated digits are allowed on either diagonal.

It's still no walkover, but should be more fun to solve than the original A2X.

Enjoy!

[Caida]

In the meantime, maybe this is more like the puzzle you're looking for?:

This was much easier - nicer for my first attempt at a "Killer-X"

Thanks!!

Here's my walkthrough for A2XLite (kept in tiny text as it is still brand new). Any comments/suggestions/corrections are always appreciated!

I would consider rating A2XLite a 1.0 (but would like to hear what others have to say).

edited for typos and notes added Thanks Andrew!!
Also had some faulty logic at my step 11 - I made an elimination too early - have reworked my walkthrough to fix this.
A couple more edits completed

Assassin 2XLite walkthrough

Preliminaries:

a. 8(3)n12 and n14 and n9 = {125/134} (no 6..9)
a1. -> 1 locked in n9 -> no 1 elsewhere in n9
a2. -> r4c4 no 1 (CPE with 8(3)n12 and 8(3)n24)
Andrew pointed out that I missed the obvious CPEs of r1c56 and r56c1 oops!!
b. 20(3)n1 = {389/479/569/578} (no 1,2)
c. 19(3)n124 and n3 and n7 and n9 = {289/379/469/478/568} (no 1)
d. 10(3)n5 = {127/136/145/235} (no 8,9)
e. 21(3)n5 = {489/579/678} (no 1,2,3)
f. 6(3)n698 = {123} (no 4..9)
f1. -> killer pair {23} locked in n9 in r7c7 and 8(3)n9 -> no 2,3 elsewhere in n9

1. Innies n1: r1c3+r3c13 = 9(3) = {126/135/234} (no 7..9)
1a. -> 19(3)n124: r3c4 and r4c3 no 2,3 (requires 89 or 79)

2. Innies n9: r7c79+r9c7 = 18(3) = [2]{79}/[3]{69/78}
2a. -> r7c9 and r9c7 no 4,5

3. Innies r1234: r4c456 = 8(3) = {125/134} (no 6..9) -> 1 locked in r4c56 for r4 and n5
3a. cage overlap: r5c4 – r4c6 = 2
3b. -> r5c4 no 2

4. Innies r5: r5c456 = 19(3) ={379/469/478/568} (no 2)
Note: {289} blocked by r5c4

5. Innies r6789: r6c456 = 18(3)
5a. cage overlap: r5c6 – r6c4 = 3
5b. -> r5c6 no 4; r6c4 no 7,8,9

6. Innies c1234: r456c4 = 11(3) = {236/245} (no 7) -> 2 locked for c4 and n5
6a. -> r5c4 no 4 (step 3a)
Andrew noticed that I missed eliminating 5 from r4c6 also b/c of step 3a
6b. cage overlap: r6c4 – r4c5 = 1
6c. -> r6c4 no 3
6d. -> r5c6 no 6 (step 5a)
6e. r4c4 no 5 (from h8(3) step 3)
6f. h11(3)c4 = [236/362]
Note: [254] blocked from h11(3) by h8(3) and 10(3) and [452] blocked by step 5
You can't have 254 b/c this would put a 2 in the h8(3)r4 - but if 8(3) has a 2 then it must also have a 5 - but it can't have a 5 b/c it is in the h11(3)c4.
452 won’t work because this puts a 2 in r6c4 so then you need a 5 in r5c6 (step 5a) but the 5 is already placed in r5c4.
6g. 2,3,6 locked for n5 in c4
6h. -> r4c6 no 5 (step 3a)
6i. -> r5c6 no 7, 8 (step 5a)
6j. 21(3)n5 = [9]{48}/[5]{79}/[9]{57} -> 9 locked in 21(3) for n5

7. 14(3)n5 = [176/482]
7a. -> r5c5 no 4,5

8. Innies c6789: r456c6 = 18(3) = [198/459/495]
8a -> r6c6 no 4,7
8b. -> r6c5 no 5,8,9
8c. -> 7 locked in n5 in c5 -> no 7 elsewhere in c5
8d. -> 9 locked in n5 in c6 -> no 9 elsewhere in c6
8e. -> 8 locked in n5 in diagonal top left to bottom right - > no 8 elsewhere on that diagonal

9. 8(3)n14: r3c1 = 1
9a. -> killer quadruple {2345} locked for r4 8(3)n14 and h8(3)n5 -> no 2,3,4,5 elsewhere in r4

10. 8(3)n12 = [2]{15}/[3]{14}
10a. -> r1c3 no 4,5
10b. -> 1 locked in r12c4 for c4 and n2 -> no 1 elsewhere in c4 and n2

Changing walkthrough b/c of faulty early elimination to original step 11 (I had said that Innies c5: r456c5 = 16(3) = [574] Andrew pointed out that I missed [187] which is still valid. This was a BIG mistake on my part).

new11. hidden single: r9c9 = 1 (only 1 on \d)
new11a. hidden single: r2c4 = 1
new11b. innies n1 (step 1): r3c3 no 2,3,4

new12. 19(3)n124 = {469/568} (no 7) -> 6 locked in r34c3 -> no 6 elsewhere in c6
new12a. -> r3c4 no 9
new12b. -> 9 locked in n2 in c5 -> no 9 elsewhere in c5
new12c. -> 7 locked in n2 in c6 -> no 7 elsewhere in c6
new12d. 14(3)n2 = {239} -> locked for n2 and c5
new12e. -> {23} locked in n8 in r789c6
new12f. -> r89c6 <> {23} -> r7c6 = {23} (no 1) -> pair {23} locked in r7 in c67
new12g. -> r6c7 = 1 (only 1 in 6(3))
new12h. single: r1c8 = 1
new12i. -> r8c6 no 1 (not possible to have {12/13} in 15(3))
new12j. -> hidden single r4c6 = 1
new12k. -> r5c4 = 3 (step 3a)
new12l. -> r4c45 = [25]

Now the rest of my steps are valid
11. Innies c5: r456c5 = 16(3) = [574]
11a. -> r4c456 = [251]
11b. -> r5c456 = [379]
11c. -> r6c456 = [648]
11d. -> 278 locked for diagonal l->r
11e. -> 167 locked for diagonal r->l

12. 6(3)n689 = [123]
12a. -> 3 locked for diagonal l->r
12b. -> 8(3)n9 = {125} -> locked for n9

13. pair {34} locked in r4c12 for n4
13a. 14(3)n4 = {158} -> locked for n4 and r5
13b. hidden single: r4c3 = 6
13c. triple {279} locked in r6c123 for r6

14. 15(3)n69 = {35}[7]
14a. -> r7c9 = 7
14b. -> r9c7 = 8 (step 2)

15. 15(3)n89 = {34}[8]
15a. -> {34} locked for n8 and c6 -> no 3,4 elsewhere in n8 and c6
Made some changes here – based on my new steps #11 and 12
new15b. -> triple {567} locked in r123c6 -> no 5,6,7 elsewhere in n2
new 15c. -> 8(3)n12 = [341]

16. this is now step new15b
16a. this is now step new12d
16b. single: r3c4 = 8
16c. 19(3)n124 = [586] -> 5 locked for diagonal l->r
16d. this is now step new11
16e. r9c5 = 6
16f. this is now step new12h
16g. this is now step new15c

17. 18(3)n23 = {567} no 2,9
17a. 18(3)n478 = [945]
17b. -> 4 locked for diagonal r->l
17c. 18(3)n234 = [729]
17d. -> 2 locked for diagonal r->l

Everything left is cage sums and singles

I'll have to give the original A2X another go in a bit.
But would really love if someone else did a walkthrough so I could take a peek

Cheers,

Caida

[Nasenbaer]

Beaten again. Oh well.

Yes, A2X-Lite is much easier. And here is my walkthrough. It's the way I solved it so no nice shortcuts and a lot of jumping around. Don't know about the rating, haven't looked into that.


A2X Lite

1. n12: 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3) -> no 1 in r1c56

2. n1: 20(3) = {389|479|569|578} -> no 1,2

3. n3: 19(3) = {289|279|469|478|568} -> no 1

4. n14: 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3) -> no 1 in r56c1

5. n124: 19(3) = {289|279|469|478|568} -> no 1

6. n5: 10(3) = {127|136|145|235} -> no 8,9

7. n5: 21(3) = {489|579|678} -> no 1,2,3

8. n689: 6(3) = {123} -> no 4,5,6,7,8,9 -> 1,2,3 locked for 6(3)

9. n9: 19(3) = {289|279|469|478|568} -> no 1

10. n7: 19(3) = {289|279|469|478|568} -> no 1

11. n9: 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3) and n9

12. n9: {23} locked in 8(3) and r7c7 for n9

13. n9: 19(3) = {469|478|568}
13a. -> {45} locked in 19(3) and 8(3) for n9

14. r7c79 + r9c7 = h18(3) = {279|369|378} -> no 1,2,3,4,5 in r7c9 and r9c7

15. n1: r1c3 + r3c13 = h9(3) = {126|135|234} -> no 7,8,9 in r3c3

16. n124: 19(3): cleanup -> no 2,3 in r3c4 and r4c3

17. 45 on r12: r3c258 = h19(3) = {289|279|469|478|568} -> no 1

18. 45 on r1234: r4c456 = 8(3) = 1{25|34} -> no 6,7,8,9 -> 1 locked for 8(3), r4 and n5

19. (step 4) -> r3c1 = 1

20. (step 1) -> 1 locked in r12c4 for c4 and n2

21. r9c9 = 1 (single for D\)

22. r2c4 = 1 (single for r2)

23. {12345} locked in r4c12456 for r4

24. n36: 18(3) = {279|369|378|468|567} -> r3c9 = {2345}

25. n5: 10(3): cleanup -> no 4 in r4c5

26. 45 on r6789: r6c456 = 18(3) = {279|369|378|468|567} ({459} blocked by h8(3))
26a. -> cleanup -> no 7,8,9 in r6c4 (r6c56 must be at least 12 from the 21(3) cage)

27. n5: 14(3): cleanup -> no 2,4 in r5c5

28. n1: h9(3): cleanup -> no 4 in r1c3, no 2,4 in r3c3

29. n12: 8(3): cleanup -> no 3 in r1c4

30. n124: 19(3) = {379|469|568}

31. 45 on c1234: r456c4 = h11(3) = 2{36|45} -> 2 locked for h11(3), c4 and n5

32. n12: 8(3): cleanup -> no 5 in r1c3

33. n1: h9(3): cleanup -> no 3 in r3c3

34. n124: 19(3) = 6{49|58} -> no 7 in r4c3, no 7,9 in r3c4

35. r4: 7 locked in r4c789 for r4 and n6

36. n1: 20(3): {569} blocked by r3c3 -> no 6 in 20(3)

37. n1: 16(3) = {268|349|358|457} ({259|367} blocked by h9(3))

38. n5: 10(3): {145} blocked by r1c4 -> 10(3) = 3{16|25} -> no 4 in r45c4 -> 3 locked for 10(3) and n5

39. n5: 14(3): cleanup -> no 5,6 in r5c5

40. n5: h8(3): cleanup -> no 5 in r4c4, no 3 in r4c5

41. n5: 10(3): cleanup -> no 5 in r5c4 -> 3 locked in r45c4 for c4 and n5

42. {23} locked in r4c4 and r7c7 for D\ -> no 2,3 in r1c1 and r2c2

43. 45 on c6789: r456c6 = h18(3) = {189|459|468|567}

44. n5: h8(3) and 10(3): no 5 in r4c6 (would mean r4c45 = [21], r5c4 = 7 -> not possible)
44a. 14(3): {257} not possible
44b. h18(3) at r4c6: {567} not possible -> no 7 in r56c6
44c. 21(3): no 5,6 at r6c5
44d. h18(3) at r4c6: {468} not possible (would force 6 in r5c4) -> no 4,6 in r56c6
44e. -> 9 locked in r56c6 for 21(3), c6 and n5
44f. no 8 in r6c5
44g. 14(3): {158} not possible, blocked by h18(3) at r4c6 -> no 4,5 in r6c4
44h. combination check: no 5 in r6c6, no 8 in r5c6, no 2 in r5c4 (h18(3) at r6c4 = [675] clashes with 14(3) = [176])

45. n5: h11(3) = {236} -> 2,3,6 locked for c4 and n5

46. n5: 7 locked in r56c5 for n5 and c5

47. n8: 7,9 locked in r789c4 for n8 and c4

48. n2: 9 locked in 14(3) -> 14(3) = {239} -> 2,3,9 locked for c5 and n2

49. n8: 15(3) = 6{18|45} -> 6 locked for c5 and n8

50. n23: 18(3) = {378|468|567} (no 1,2,9}

51. -> r1c8 = 1

52. n3: 14(3) = 1{49|58|67} -> no 2,3

53. 45 on r5: r5c456 = h19(3) = {379|568}

54. n4: 14(3) = {149|158|347} (other combinations blocked by h19(3) and r4c12)
54a. -> {45} locked in 14(3) and r4c12 for n4

55. n6: 2 locked in 12(3) for r5 and c6
55a. n6: 12(3) = 2{19|46} (other combinations blocked by h19(3)) -> no 9 at r5c7

56. r7: 2 locked in r7c67 for 6(3) and r7

57. r5: 14(3): {149} blocked by h19(3) and 12(3) -> no 9

58. 8 locked in r5c5 and r6c6 for n5 and D\

59. n6: 5 locked in r6c89 for n6, r6 and 15(3)
59a. 15(3) = 5{37|46} -> no 6 in r6c89

60. n9: h18(3): no 6,7 in r9c7

61. n89: 15(3) = {159|249|258|348} -> no 8 in r89c6

62. n6: 8 locked in r4c789 for n6 and r4

63. n124: 19(3): 6 locked in r34c3 for 19(3) and c3
63a. no 5 in r3c4

64. n3: 14(3): {167} blocked by r7c9 -> no 6,7

65. n3: 19(3): {289|478} blocked by 14(3) -> no 2
65a. {89} locked in 14(3) and 19(3) -> no 8,9 in r13c7

66. n7: 19(3): no 2 in r8c1 (blocked by r9c7)


67. 45 on n3: r1c7 + r3c79 = h12(3) = 2{37|46} -> 2 locked in r3c79 for h12(3), r3 and n3

68. n6: 3 locked in r6c789 for n6 and r6

69. n47: 17(3): {458|359} not possible -> no 5

70. 45 on c89: r258c7 = h15(3) = 5{19|28|46} -> no 3,7

71. from step 17: r3: h19(3) = 9{37|46} -> no 5,8 -> no 4 in r3c8

72. 45 on r89: r7c258 = h16(3) = {169|178|349|358|367|457}

73. 45 on c12: r258c3 = h16(3) = {178|349|358|457}

74. n78: 18(3) = {279|378|459} -> no 7,8,9 in r9c3

75. n8: 4 or 5 in r89c6 (15(3)) -> 15(3) = {168}

76. r456c5 = [574], r456c6 = [198], r456c4 = [236], r7c67 = [23], r6c7 = 1, r7c9 = 7

77. n6: 12(3) = {246}

78. r4c3 = 6, r3c34 = [58]

79. r1c34 = [34]

80. n1: 20(3) = {479}

81. r1c167 = [657], r23c6 = [67], r34c7 = [29], r4c89 = [78], r123c9 = [943], r123c5 = [239]



Edit: Thanks for your comments, Andrew. They are included in blue.
Cheers,
Nasenbaer

[Caida]

After several false starts I have finally managed to finish A2X.
Most of my earlier problems came from faulty math and eliminating combos prematurely.

I don't know that I would rate this as a 1.75 (I managed to finish it through perseverance) but I could see rating it as 1.5.

Interested to see other approaches.

Here's my walkthough - after several restarts I have put what I found were the key moves (my steps 6,7,8) as close to the beginning as I could.

Any comments/suggestions/corrections appreciated!
Edited for typos - thanks Andrew!!

Assassin 2X walkthrough

Prelims:

a. 10(3)n4 and n5 and n89 = {127/136/145/235} (no 8,9)
b. 21(3)n5 = {489/579/678} (no 1,2,3)
c. 24(3)n9 = {789} (no 1..6) -> 7,8,9 locked for n9

1. Innies r1234: r4c456 = 10(3) = {127/136/145/235} (no 8,9)
1a. overlapping cages: r5c4 – r4c6 = 4
1c. -> r5c4 no 1,2,3,4
1d. -> r4c6 no 6,7

2. Innies r6789: r6c456 = 14(3)
2a. overlapping cages: r5c6 – r6c4 = 7
2b.-> r5c6 = 8,9 (no 4,5,6,7)
2c. -> r6c4 = 1,2 (no 3,4,5,6,7)

3. Innies c1234: r456c4 = 10(3) = {127/136/145/235} (no 8,9)
3a. overlapping cages: r4c5 – r6c4 = 4
3b. -> r4c5 = {56} (no 1,2,3,4,7)
3c. -> r4c6 no 4,5 (step 1a)

4. Innies c6789: r456c6 = 20(3) = [3]{89} -> 3 locked for diagonal -> no 3 elsewhere in diagonal top right (tr) -> bottom left (bl)
4a. -> {89} locked for c6 and n5
4b. r5c4 = 7 (step 1a)
4c. -> r6c5 = 4 (cage 21(3))
4d. h10(3)c4 (step 3) = {1[7]2}
4e. -> {12} locked for c4 in n5
4f. -> {56} locked for c5 in n5

5. 10(3)n4 = {136/145/235} {1 | 2} {5 | 6}
5a. killer pair {56} in r5 in 10(3)n4 and r5c5 -> no 5,6 elsewhere in r5

6. Innies n478: r4c123+r789c6 = 36
6a. -> max r4c123 = 24 -> min r789c6 = 12
6b. -> max r89c6 = 9 + max r7c6 = 7
6c. -> max r789c6 = 16 -> min r4c123 = 20 (no 1,2)

7. since 10(3)n4 must contain either 1 or 2 (but not both) and r4c123 doesn’t have either than
7a. -> r6c123 must have the other 1 or 2 for n4
7b. -> killer pair {12} in r6c123 and r6c4 -> no 1,2 elsewhere in r6
7c. -> killer pairs of {12} are also in r5c123 + r6c123 and in r5c123 and r5c789

I don’t think this next bit is t&e – but don’t know how to write it without making it look t&eish

8. if r6c4 = 1 -> r5c6 = 8 and 10(3)n4 = {1..} -> 14(3)n6 must have a 2 and 9 but no 1 or 8 (239)
8b. if r6c4 = 2 -> r5c6 = 9 and 10(3)n4 = {1..} -> 14(3)n6 must have a 1 and 8 but no 9 (158) -> no 5 available
8c. -> 14(3)n6 = 239 -> locked for r5 and n6
8d. -> h10(3)r4 = [253]
Andrew pointed out that I forgot to note the hidden single in r4c4
8e. -> 10(3)n5 = [361]
8f. -> 21(3)n5 = [849]
8g. -> 10(3)n4 = {145} -> locked for n4
8h. -> 2,6,9 locked for diagonal from top left (tl) -> bottom right (br)
8i. -> 1,6,3 locked for diagonal from top right (tr) -> bottom left (bl)

9. Outies r12: r3c258 = 22(3) = {589/679} (no 1..4) -> 9 locked for r3

10. Outies c12: r258c3 = 19(3) = [649/946/748/847/658/856] (no 1,2,3)
10a. -> r28c3 no 4,5

11. 17(3)n3 = {269/278/359/368/458/467} (no 1)
Note: combo {179} blocked by 24(3)n9
11a. Outies c89: r258c7 = 17(3) = [827/728/629/638/539]
11b. -> r2c7 no 2,3,4,9
11c. -> r5c7 no 9
11d. -> 17(3)n3: r2c8 no 5,7,8,9

12. Innies n1: r1c3+r3c13 = 10(3) = {127/136/145/235} (no 8,9)

13. Innies n9: r7c89+r9c7 = 8(3) = {125/134} (no 6) -> 1 locked for n9

14. 13(3)n69 = [571/751/562/652]
14a. -> 5 locked in n6 in r6c89 -> no 5 elsewhere in n6
14b. -> r6c89 no 8
14c. -> r7c9 no 3,4,5

15. {14} locked in n6 in r4c789
15a. -> r4c89 must contain at least 1 of {14} (could contain both)
15b. -> 13(3)n36 = [148/184/418/481/814/841/517/571/247/274/346/364]
15c. -> r3c9 no 6,7

16. {23} locked in n4 in r6c123
16a. -> r6c12 must contain at least 1 of {23} (could contain both)
15b. -> 13(3)n47 = [238/283/328/382/823/832/274/724/265/625/364/634]
15c. -> r7c1 no 1679

16. 17(3)n689 = [674/764/863/845/854] (no 1,2)
16a. -> 1 in diagonal tl-> br locked in n1 -> no 1 elsewhere in n1

17. h8(3)n9 (step 13) = [314/413/512/521]
17a. -> r9c7 no 5

18. 18(3)n14 = [567/576/468/486/369/396/378/387/279/297]
18a. -> r3c1 no 6,7
18b. 18(3)n1: min r2c3+r3c2 = 11 -> r2c2 no 8


19. Innies n7: r7c13+r9c3 = 12(3) = {129/138/147/237/246/345}
19a. -> r7c1 no 8
19b. -> r9c3 no 8, 9

20. 12(3)n236 = {147/246} (no 5,8)
Note combo [651] blocked by h22(3)r3; combo [156] blocked by h17(3)c7 and r6c7

21. Innies n3: r1c7+r3c79 = 15(3) = {258/348/357/456}
21a. -> r1c7 and r3c9 no 1,2,4,7,9
21b. -> single: r8c7 = 9
21c. -> pair {78} locked in n9 for c8
21d. -> h17(3)c7 = [539/629]
21e. -> r2c7 no 7,8
21f. -> 17(3)n3 = [629] -> 2 locked for diagonal
21g. -> r5c789 = [239]

22. h22(3)r3 = [679/589]
22a. -> r3c2 no 7,8

23. 9 locked for diagonal in n7 -> no 9 elsewhere in n7

24. 18(3)n1 = [495/396/486/576]
24a. -> r2c2 no 1,7
24b. triple {345} locked for diagonal in r2c2, r7c7, r9c9 -> no 3,4,5 elsewhere in diagonal (not in r1c1 or r3c3)

25. 15(3)n124 = [159/168/186]
25a. -> r3c3 = 1
25b. -> r3c4 no 3,4
25c. -> r4c3 no 7

26. Innies n7: r7c3 no 8, 9
26a. single: r9c1 = 9
26b. 17(3)n7: r8c1 and r9c2 = {17/26/35} (no 4,8)
26c. 8 in r9 locked in n8 -> no 8 elsewhere in n8

27. 12(3)n236 = {47}[1]
27a. -> {47} locked in r3
27b. -> h22(3)r3 = [589]
27c. -> 15(3)n124 = [168]
27d. -> 13(3)n36 = [3]{46} -> {46} locked for n6 and r4

singles and cages sums left


Solution:

867392514
349517628
251684793
798253146
514768239
632149857
425976381
186435972
973821465

Cheers,

Caida

[Afmob]

Seems my key moves are not much different from Caida's ones. I wonder if my step 8c can be considered a Killer XY-Wing?

A2X Walkthrough:

1. N5
a) Innies+Outies R6789: 7 = R5C6 - R6C4
-> R5C6 = (89), R6C4 = (12)
b) Innies R5 = 21(3) <> 1,2,3
c) Innies C6789 = 20(3) <> 1,2
d) 10(3) <> 7 because 1,2 only possible @ R6C4
e) Innies R5 = 21(3) must have 4,5 xor 6 and R5C5 = (456) -> R5C4 <> 4,5,6
f) Innies C1234 = 10(3) = {127} -> R5C4 = 7, (12) locked for C4+N5

2. N5+R5
a) 21(3) = {489} locked for N5
b) Innies C5 = 15(3) = {456} -> R6C5 = 4, (56) locked for C5+N5
c) Innies C6789 = 20(3) = {389} -> R4C6 = 3, (89) locked for C6
d) Killer pair (56) locked in 10(3) + R5C5 for R5

3. N9
a) Innies = 8(3) = 1{25/34} -> 1 locked
b) 6 locked in 13(3) = 6{25/34}

4. C123
a) Outies C12 = 19(3) <> 1
b) Outies C12 = 19(3): R28C3 <> 2,3 because R5C3 <= 6
c) Innies N1 = 10(3) <> 8,9
d) 15(3) @ R8C4: R9C3 <> 9 because R89C4 >= 7
e) 13(3): R7C1 <> 9 because {139} blocked by Killer pair (13) of 10(3)

5. R123
a) Outies R12 = 22(3) = 9{58/67} -> 9 locked for R3
b) 12(3) <> 8

6. C789
a) 17(3) @ N9: R6C7+R7C6 <> 1,2 because R7C7 <= 5
b) 17(3) @ N9: R6C7 <> 3,5 because R7C67 <> 8,9

7. N12+C6 !
a) ! R789C6 <= 16 because R89C6 <= 9 -> R123C6 >= 9 (step 1c)
b) ! Innies+Outies N12: 11 = R4C123 - R123C6
-> R4C123 >= 20 <> 1,2

8. R456 !
a) R6C123 must have 1 xor 2 @ N4 because 10(3) <> {127}
b) Killer pair (12) locked in R6C123+R6C4 for R6
c) ! Consider placement of 6 in R5 -> R6C123 <> 1
- i) 6 in 10(3) @ N4 = {136} -> R6C123 <> 1
- ii) 6 in 10(3) @ N5 = {136} -> R6C4 = 1 -> R6C123 <> 1
d) Hidden Single: R6C4 = 1 @ R6 -> R5C5 = 6
e) R4C4 = 2, R4C5 = 5
f) Innies R6789 = 14(3) = {149} -> R6C6 = 9 -> R5C6 = 8
g) 1 locked in 10(3) @ N4 = {145} locked for R5+N4
h) 14(3) @ N6 = {239} locked for N6
i) 5 locked in 13(3) @ R6 (N6) -> 13(3) = 5{17/26}, R7C9 <> 5

9. N1
a) 17(3) @ N9 <> 1
b) 1 locked in D\ for N1
c) Innies N1 = 10(3): R3C3 <> 4,7 because R1C3+R3C1 <> 1
d) 18(3) @ R3C1: R3C1 <> 6,7 because R4C12 >= 13

10. C123
a) Outies C12 = 19(3) must have 4 xor 5 because R5C3 = (45) -> R28C3 <> 4,5
b) 13(3): R7C1 <> 1,6,7 because R6C12 <> 4,5

11. N9+D\
a) 10(3): R9C7 <> 2 because R89C6 <> 3 and Killer pair (17) of 12(3) @ N8 blocks {127}
b) Innies = 8(3): R9C7 <> 5 because R7C79 >= 4
c) 13(3) @ R8C9: R8C9+R9C8 <> 5 because R9C9 <> 2,6
d) 5 locked in R7C7+R9C9 for D\
e) 15(3) @ D\ must have 1 xor 3 because R3C3 = (13) -> R3C4 <> 3

12. C89 !
a) ! Innies+Outies C9: 7 = R1469C8 - R5C9
-> R5C9 <> 2,3 because R6C8 >= 5
b) R5C9 = 9

13. N12 !
a) ! Innies+Outies N1: 23 = R4C123+R3C4 - R1C3
-> R4C123 >= 22 because 9 locked there @ N4
-> R1C3 <> 2
b) 15(3) @ R1C3 <> 9
c) 9 locked in 18(3) @ N2 = 9{18/27} -> 9 locked for C5
d) 3 locked in 15(3) @ R1C3 = 3{48/57} for C4; R1C3 <> 3
e) 15(3) @ R1C3: R1C3 <> 5 because R12C4 <> 7
f) Innies N1 = 10(3) = 1{27/45} because R1C3 = (47) -> R3C3 = 1, R3C1 = (25)

14. C789
a) Hidden Single: R3C9 = 3 @ R3
b) 13(3) @ R3C9 = {346} -> (46) locked for R4+N6
c) Innies N3 = 15(3) = 3{48/57}, R1C7 <> 4
d) Hidden Single: R2C7 = 6 @ C7, R8C7 = 9 @ C7
e) 24(3) = {789} -> (78) locked for C8
f) 17(3) @ N3 = {269} -> R2C8 = 2, R3C8 = 9
g) 13(3) @ R6C8 = {157} -> R7C9 = 1, R6C8 = 5, R6C9 = 7
h) Innies N9 = 8(3) = {134} -> (34) locked for C7+N9
i) Innies N3 = {357} locked for N3
j) 17(3) @ R6C7 = 8[54/63] -> R6C7 = 8
k) 10(3) <> 7 because R9C7 = (34)

15. N12
a) 15(3) @ R3C3 = 1[59/68]
b) 18(3) @ R3C1 = {279} -> R3C1 = 2, (79) locked for N4
c) 15(3) @ R3C3 = {168} -> R4C3 = 8, R3C4 = 6

16. R123
a) 14(3) = {257} -> R1C6 = 2
b) 18(3) @ N2 = {189} locked for C5+N5
c) 15(3) = {357} -> R1C3 = 7, (35) locked for C4+N2
d) 18(3) @ N1 = {459} -> R2C2 = 4, R2C3 = 9, R3C2 = 5

17. N7
a) 16(3) = 6[28/37]
b) Hidden Single: R9C1 = 9 @ D/, R6C1 = 6 @ C1
c) 15(3) = {348} -> R9C3 = 3
d) 16(3) @ R6C3 = {259} -> R6C3 = 2, R7C3 = 5, R7C4 = 9

18. Rest is singles (without considering the diagonals).

Rating: 1.5, had some difficult moves but not too many of them.

[Andrew]

I finished A2X-Lite (I prefer Light) yesterday evening and went through Caida's and Nasenbaer's walkthroughs today. Since neither of them had my breakthrough move, I'm posting my walkthrough now. Must admit I didn't initially spot step 21 but when I did I reworked it to put it in the right place.

I'd originally been thinking of rating it as an easier 1.25 but after I found step 21 I'll make it a high 1.0.

Here is my walkthrough for A2X-Lite.

Prelims

a) 8(3) cage at R1C3 = 1{25/34}, CPE no 1 in R1C56
b) 20(3) cage in N1 = {389/479/569/578}, no 1,2
c) 19(3) cage in N3 = {289/379/469/478/568}, no 1
d) 8(3) cage at R3C1 = 1{25/34}, CPE no 1 in R56C1
e) 19(3) cage at R3C3 = {289/379/469/478/568}, no 1
f) 10(3) cage in N5 = {127/136/145/235}, no 8,9
g) 21(3) cage in N5 = {489/579/678}, no 1,2,3
h) 6(3) cage at R6C7 = {123}
i) 19(3) cage in N9 = {289/379/469/478/568}, no 1
j) 19(3) cage in N7 = {289/379/469/478/568}, no 1
k) 8(3) cage in N9 = 1{25/34}, 1 locked for N9

1. Killer pair 2,3 in R7C7 and 8(3) cage, locked for N9

2. 19(3) cage in N9 = {469/478/568}
2a. Killer pair 4,5 in 8(3) cage and 19(3) cage, locked for N9
2b. Min R7C9 = 6 -> max R6C89 = 9, no 9
2c. Min R9C7 = 6 -> max R89C6 = 9, no 9

3. 45 rule on N1 3 innies R1C3 + R3C13 = 9 = {126/135/234}, no 7,8,9

4. 45 rule on R12 3 outies R3C258 = 19 = {289/379/469/478/568}, no 1

5. 45 rule on R5 3 innies R5C456 = 19 = {289/379/469/478/568}, no 1
5a. 2 of {289} must be in R5C4 -> no 2 in R5C5

6. 45 rule on R1234 3 innies R4C456 = 8 = 1{25/34}, 1 locked for R4 and N5
6a. R3C1 = 1 (only remaining position for 1 in 8(3) cage), R4C12 = {25/34}
6b. Naked quint {12345} in R4C12456, locked for R4
6c. R13C3 = 8 (step 3) = [26/35], no 4, no 2 in R3C3

7. 8(3) cage at R1C3 = 1{25/34}, 1 locked in R12C4, locked for C4 and N2
7a. 3 of {134} must be in R1C3 -> no 3 in R12C4

8. R9C9 = 1 (hidden single in D\), R8C9 + R9C8 = {25/34}
8a. 1 in N3 locked in R1C78, locked for R1
8b. R2C4 = 1 (hidden single in C4), R1C34 = {25}/[34]
[Hidden single in R2 would have been slightly quicker but that’s not what I spotted.]

9. 45 rule on R1234 1 outie R5C4 = 1 innie R4C6 + 2, no 2 in R5C4

10. 45 rule on R6789 1 outie R5C6 = 1 innie R6C4 + 3, no 4 in R5C6, no 7,8,9 in R6C4

11. 10(3) cage in N5 = {127/136/145/235}
11a. 1 of {145} must be in R4C5 -> no 4 in R4C5

12. 45 rule on C1234 3 innies R456C4 = 11 = {236} (cannot be {245} which clashes with R1C4), locked for C4 and N5, clean-up: no 5 in R1C3 (step 8b), no 3 in R3C3 (step 6c), no 5 in R4C6 (step 9), no 7,8 in R5C6, no 3 in R6C4 (both step 10)

13. Naked pair {23} in R4C4 + R7C7, locked for D\

14. 21(3) cage in N5 = {489/579}, 9 locked for N5

15. 14(3) cage in N5 = {167/248} (cannot be {158} because 5,8 only in R5C5, cannot be {257} because R4C6 only contains 1,4), no 5
15a. 4 of {248} must be in R4C6 -> no 4 in R5C5

16. 45 rule on C5 3 innies R456C5 = 16 = {178/457}, no 9, 7 locked for C5 and N5
16a. 5 of {457} must be in R4C5 -> no 5 in R6C5

17. 9 in N5 locked in R56C6, locked for C6
17a. 45 rule on N5 3 remaining innies R456C6 = 18 = {189/459}
17b. 4 of {459} must be in R4C6 -> no 4 in R6C6

18. 21(3) cage in N5 (step 14) = {489/579}
18a. 4 of {489} must be in R6C5 -> no 8 in R6C5
[At this stage I missed 8 locked in R5C5 + R6C6 for D\, fortunately it didn’t matter.]

19. 19(3) cage at R3C3 = {469/568} (cannot be {478} because R3C3 only contains 5,6), no 7, 6 locked in R34C3, locked for C3
19a. 4 of {469} must be in R3C4 -> no 9 in R3C4
19b. 7 in R4 locked in R4C789, locked for N6
19c. 7,9 in C4 locked in R789C4, locked for N8

20. 9 in N2 locked in R123C5 = {239} (only remaining combination), locked for C5 and N2
20a. 6 in C5 locked in R789C5, locked for N8

21. 2,3 in N8 locked in R789C6, R89C6 cannot be {23} -> R7C6 = {23}
21a. Naked pair {23} in R7C67, locked for R7
21b. R6C7 = 1 (only remaining position for 1 in 6(3) cage)

22. R1C8 = 1 (hidden single in R1), R12C9 = 13 = {49/58/67}, no 2,3

23. R5C456 (step 5) = {379/568}
23a. R5C789 = {246} (only remaining combination, cannot be {345} which clashes with R5C456), locked for R5 and N6 -> R5C4 = 3, R4C4 = 2, R4C5 = 5, R5C6 = 9, R6C4 = 6, R6C6 = 8, R5C5 = 7, R6C5 = 4, R4C6 = 1, 1,6,7 locked for D/, 2,7,8 locked for D\ -> R7C7 = 3, R7C6 = 2, clean-up: no 6,7 in R2C9 (step 22), no 4 in R8C9 + R9C8 (step 8)
23b. Naked pair {25} in R8C9 + R9C8, locked for N9

24. R4C3 = 6 (hidden single in R4), R3C3 = 5, R3C4 = 8 (step 19)

25. Naked pair {35} in R6C89, locked for R6, R7C9 = 7
25a. 45 rule on N9 1 remaining innie R9C7 = 8, R9C5 = 6
25b. R9C7 = 8 -> R89C6 = 7 = {34}, locked for C6 and N8

26. R1C4 = 4 (hidden single in C4), R1C3 = 3 (step 8b), clean-up: no 9 in R2C9 (step 22)

27. 18(3) cage at R1C3 = {567} (only remaining combination), no 2,9 in R1C7
27a. 5 in C6 locked in R12C6 -> no 5 in R1C7

28. R2C7 = 5 (hidden single in C7), clean-up: no 8 in R12C9 (step 22)

and the rest is naked singles, including eliminations along the diagonals, and cage sums

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

Maybe some of the steps I used here may be helpful for A2X, when I've got time to look at it.

[mhparker]

I wonder if my step 8c can be considered a Killer XY-Wing?

Interesting point (and great move!), Afmob. As you may have seen, I've gone into more detail on this question here.

[Andrew]

I finished A2X on Christmas Eve but only managed to go through Caida's and Afmob's walkthroughs yesterday evening.

Seems my key moves are not much different from Caida's ones.

There seems to be a very narrow solving path around Caida's step 8, Afmob's step 8 and my step 21.

Yes, it's a toughie. Unlike several recent Assassin V1's, which consist of finding one (or at most, two) key move(s), apart from which the rest is plain sailing, this is more like a traditional V2, which (whilst having easier sections) generally involves more of a fight to dig away at the candidates. This puzzle does contain at least one key move, however, that will make your life easier if you find it.

I assume Mike was referring to the narrow solving path mentioned above. It certainly took a lot more work after that. I've a feeling that my later stages were longer than those of Caida and Afmob although I haven't tried to compare them to see where they were quicker.

I'll agree with both of them and rate A2X as 1.5.

Here is my walkthrough.

Prelims

a) R5C123 = {127/136/145/235}, no 8,9
b) 10(3) cage in N5 = {127/136/145/235}, no 8,9
c) 21(3) cage in N5 = {489/579/678}, no 1,2,3
d) 10(3) cage at R8C6 = {127/136/145/235}, no 8,9
e) 24(3) cage in N9 = {789}, locked for N9

1. 45 rule on N1 3 innies R1C3 + R3C13 = 10 = {127/136/145/235}, no 8,9
1a. Max R3C1 = 7 -> min R4C12 = 11, no 1

2. 45 rule on N9 3 innies R7C79 + R9C7 = 8 = 1{25/34}, no 6, 1 locked for N9

3. 45 rule on R5 3 innies R5C456 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on R1234 3 innies R4C456 = 10 = {127/136/145/235}, no 8,9

5. 45 rule on C1234 3 innies R456C4 = 10 = {127/136/145/235}, no 8,9

6. 45 rule on C6789 3 innies R456C6 = 20 = {389/479/569/578}, no 1,2

7. 45 rule on C1234 1 outie R4C5 = 1 innie R6C4 + 4, R4C5 = {567}, R6C4 = {123}

8. 45 rule on C6789 1 outie R6C5 = 1 innie R4C6 + 1, no 9 in R6C5

9. 45 rule on R1234 1 outie R5C4 = 1 innie R4C6 + 4 -> R5C4 = 7, R4C6 = 3, locked for D/, R6C5 = 4 (step 8)

10. Naked pair {56} in R45C5, locked for C5 and N5
10a. Naked pair {12} in R46C4, locked for C4
10b. Naked pair {89} in R56C6, locked for C6

11. Killer pair 5,6 in R5C123 and R5C5, locked for R5

12. 45 rule on R12 3 outies R3C258 = 22 = 9{58/67}, 9 locked for R3

13. 45 rule on C12 3 outies R258C3 = 19 = {289/379/469/478/568}, no 1
13a. 2,3 of {289/379} must be in R5C3 -> no 2,3 in R28C3

14. 45 rule on C9 4 outies R1469C8 = 1 innie R5C9 + 7
14a. Min R1469C8 = 10 -> min R5C9 = 3

15. 17(3) cage at R6C7 = {179/269/278/359/368/458/467}
15a. 8,9 of {179/269/278/359/368/458} must be in R6C7-> no 1,2,3,5 in R6C7
15b. 1,2 of {179/269/278} must be in R7C7 -> no 1,2 in R7C6

16. 45 rule on C89 3 outies R258C7 = 17 = {179/269/278/359/368/458/467}
16a. 3,4 of {359/368/458/467} must be in R5C7 -> no 3,4 in R2C7

17. 17(3) cage in N3 = {179/269/278/458/467}
17a. 4 of {458} must be in R2C8 -> no 5 in R2C8

18. 45 rule on R89 3 outies R7C258 = 17 = {179/269/278/359/368} (cannot be {458/467} because 4,5,6 only in R7C2), no 4
18a. 3 of {359/368} must be in R7C5 -> no 3 in R7C2

19. 45 rule on N478 6 innies R4C123 + R789C6 = 36
19a. Max R89C6 = 9 (because of 10(3) cage at R8C6), max R7C6 = 7 -> max R789C6 = 16 -> min R4C123 = 20, no 1,2

20. R5C123 = {136/145/235} [1/2]
20a. Hidden killer pair 1,2 in R5C123 and R6C123 for N4 -> R6C123 must contain 1/2
20b. Killer pair 1,2 in R6C123 and R6C4, locked for R6

21. Chaining steps 20a and 20b, R5C123 and R6C4 must contain the same value of 1/2
21a. 45 rule on R6789, 1 outie R5C6 = 1 innie R6C4 + 7 -> R5C6 + R6C4 = [81/92]
21b. -> R5C123 + R5C6 must contain 1,8 or 2,9
21c. R5C789 = {239} (only remaining combination, cannot be {149/248} which clash with R5C123 + R5C6), locked for R5 and N6 -> R56C6 = [89], 9 locked for D\

22. R1469C8 = R5C9 + 7 (step 14)
22a. Min R1469C8 = 11 -> no 3 in R5C9 -> R5C9 = 9

23. R5C123 = {145} (only remaining combination), locked for R5 and N4 -> R5C5 = 6, locked for both diagonals, R4C5 = 5, R4C4 = 2 (step 4), locked for D\, R6C4 = 1, locked for D/
23a. R12C9 cannot be {13} -> no 9 in R1C8

24. 17(3) cage at R6C7 (step 15) = {368/458/467}, no 1
24a. 1 on D\ locked locked in R1C1 + R2C2 + R3C3, locked for N1

25. R7C79 + R9C7 (step 2) = 1{25/34}
25a. 5 of {125} must be in R7C7 -> no 5 in R7C9 + R9C7

26. 5 in R6 locked in R6C89 for 13(3) cage at R6C8 = 5{17/26}, no 3,4,8

27. Min R4C12 = 13 -> max R3C1 = 5

28. R1C3 + R3C13 (step 1) = {127/136/145/235}
28a. 1 of {127/145} must be in R3C3 -> no 4,7 in R3C3

29. 2,3 in R6 locked in R6C123 -> at least one of 2,3 must be in R6C12
29a. 13(3) cage at R6C1 = {238/247/256/346} (cannot be {139} because 1,9 only in R7C1), no 1,9
29b. 4 of {247} must be in R7C1 -> no 7 in R7C1
29c. 6 of {256/346} must be in R6C12 -> no 6 in R7C1

30. 1,4 in R4 locked in R4C789 -> at least one of 1,4 must be in R4C89
30a. 13(3) cage at R3C9 = {148/157/247/346}
30b. 2,3,5 of {157/247/346} must be in R3C9 -> no 6,7 in R3C9

31. 45 rule on N3 3 innies R1C7 + R3C79 = 15 = {159/168/249/258/267/348/357/456}
31a. 9 of {159} must be in R1C7
31b. 8 of {168} must be in R3C7
31c. -> no 1 in R1C7

32. R258C3 (step 13) = {469/478/568}
32a. R5C3 = {45} -> no 4,5 in R28C3

33. 18(3) cage in N1 = {189/369/378/459/468/567}
33a. 1,3,4 of {189/378/468} must be in R2C2 -> no 8 in R2C2
33b. 8 on D\ locked in R1C1 + R8C8 -> no 8 in R1C8 + R8C1

34. R258C7 (step 16) = {179/269/278/359/368}
34a. 9 of {269} must be in R8C7 -> 2 of {269/278} must be in R5C7 -> no 2 in R2C7
34b. 1 of {179} must be in R2C7
34c. 9 of {269/359} must be in R8C7
34d. -> no 9 in R2C7

35. 17(3) cage in N3 (step 17) = {179/269/278/458/467}
35a. 2,4 of {278/458} must be in R2C8 -> no 8 in R2C8

36. 14(3) cage at R1C6 = {149/158/167/248/257/347/356} (cannot be {239} because 3,9 only in R1C7)
36a. 3,8,9 of {149/248/347} must be in R1C7 -> no 4 in R1C7

37. 45 rule on N7 3 innies R7C13 + R9C3 = 12 = {129/138/147/237/246/345} (cannot be {156} because 1,6 only in R9C3)
37a. 1 of {129/138} must be in R9C3 -> no 8,9 in R9C3
37b. 3 of {138} must be in R7C1 -> no 8 in R7C1

38. 2,3 in R6 locked in R6C123
38a. R6C12 cannot be {23} because max R7C1 = 5 -> R6C3 = {23}

39. 16(3) cage at R6C3 = {259/268/349/358/367} (cannot be {457} because R6C3 only contains 2,3)
39a. R6C3 = {23} -> no 2,3 in R7C34

40. 2,3 in R6 locked in R6C123 = {236/237/238}
40a. 45 rule on N7 6 outies R6C123 + R789C4 = 32
40b. R6C123 = 11,12,13 -> R789C4 = 19,20,21 = {389/469/489/568/569}
40c. Max R89C4 = 14 (because of 15(3) cage at R8C4) -> min R7C4 = 5

41. 12(3) cage at R3C6 = {147/156/246}, no 8
41a. 5 of {156} must be in R3C7 -> no 5 in R3C6

42. 9 in C8 locked in R237C8
42a. 45 rule on C89 4 innies R2378C8 = 1 outie R5C7 + 24 -> R2378C8 = 26,27
42b. R2378C8 = {2789/4589/4679/4689} (cannot be {5679} because 5,6 only in R3C8)
42c. 2,4 must be in R2C8 -> no 7,9 in R2C8

43. 17(3) cage in N3 (step 17) = {269/278/458/467} (cannot be {179} because R2C8 only contains 2,4), no 1

44. 9 on D/ locked in R7C3 + R8C2 + R9C1, locked for N7

45. 16(3) cage in N7 = {169/268/457} (cannot be {178} because R8C23 = {78} clashes with R8C8, cannot be {259} because R8C3 only contains 6,7,8)
45a. {457} must be [547]
45b. -> no 7 in R7C2, no 5,7 in R8C2

46. R7C258 (step 18) = {179/269/278/359/368}
46a. 1 of {179} must be in R7C2 -> no 1 in R7C5

47. R1C7 + R3C79 (step 29) = {159/348/357} (cannot be {168} because no 1,6,8 in R3C7, cannot be {249} which clashes with R2C8, cannot be {258/267/456} because there’s no place for 9 in N3), no 2,6
47a. 4 of {348} must be in R3C7 -> no 4 in R3C9

48. 12(3) cage at R3C6 (step 39) = {147/156/246}
48a. 6 of {156} must be in R4C7 (cannot be [651] which clashes with R3C258)
48b. 2 of {246} must be in R3C6
48c. -> no 6 in R3C6

49. R4C123 + R789C6 = 36 (step 19)
49a. R4C123 = 22,23,24 -> R789C6 = 12,13,14
49b. R789C6 = {147/156/246/157/247/256/167/257} [1/2]
49c. R789C5 = {129/138/237}
49d. Killer triple 1,2,3 in R789C56, locked for N8
49e. Min R89C4 = 9 -> max R9C3 = 6

50. 3 in N8 locked in R789C5, locked for C5
50a. R789C5 = {138/237}, no 9
50b. 9 in N8 locked in R789C4, locked for C4

51. R789C6 = 12,13,14 (step 47a) -> R789C4 = 19/20/21
51a. R789C4 = {469/569/489} [4/5]
51b. Hidden killer pair 4,5 in N8 -> R789C6 must contain 4/5 -> R789C6 not {167}

52. 45 rule on R89 4 innies R8C2378 = 1 outie R7C5 + 23
52a. Max R8C2378 = 30 -> no 8 in R7C5

53. R89C6 must contain 1/2 (step 49b)
53a. 10(3) cage at R8C6 = {127/136/145/235}
53b. 4 of {145} must be in R9C7 -> no 4 in R89C6

54. R7C258 (step 18) = {179/269/278/359/368} [8/9]
54a. Hidden killer pair 8,9 in R7 -> R7C34 must contain 8/9
54b. 16(3) cage at R6C3 (step 39) = {259/268/349/358} (cannot be {367}), no 7

55. R7C13 + R9C3 (step 37) = {129/138/246/345}
55a. 1,6 of {129/246} must be in R9C3 -> no 2 in R9C3
55b. R7C13 + R9C3 cannot be {246} because [246] clashes with R258C3 = {568}
55c. -> R7C13 + R9C3 = {129/138/345}, no 6
55d. 3 of {345} must be in R9C3 (cannot be in R7C1 because R79C3 = {45} clashes with R5C3) -> no 4,5 in R9C3
55e. {345} must be [453] (if [543] cannot make combination for 16(3) cage at R6C3) -> no 5 in R7C1, no 4 in R7C3
55f. R9C67 cannot be {13} -> no 6 in R8C6

56. R789C4 = {469/569/489}
56a. R9C3 = {13} -> R89C4 = {159/348} (cannot be {168} which clashes with R789C4), no 6
56b. R789C4 = {569/489} (cannot be {469} which clashes with R89C4) -> R7C4 = {69}

57. 16(3) cage at R6C3 (step 54b) = {259/268} (cannot be {358} because R7C4 only contains 6,9) -> R6C3 = 2, R7C34 = [59/86], no 9 in R7C3

58. 3 in N4 locked in R6C12, locked for 13(3) cage -> no 3 in R7C1

59. R7C13 + R9C3 = [453] (only remaining permutation), 5 locked for D/, R7C4 = 9 (step 57), R3C3 = 1, R5C3 = 4, R7C7 = 3, locked for D\, R5C78 = [23]

60. R7C79 + R9C7 (step 2) = [314] (only remaining permutation), R9C9 = 5, locked for D\

61. R2C2 = 4 (hidden single on D\), R2C8 = 2, locked for D/, R9C8 = 6, R8C9 = 2

62. Naked pair {78} in R78C8, locked for C8 and N9 -> R6C8 = 5, R8C7 = 9, R8C2 = 8, locked for D/, R8C8 = 7, locked for D\

and the rest is naked singles and cage sums, possibly only one cage sum if the right one is selected.