Assassin 57

[Jean-Christophe]

deleted

[CathyW]

I have to agree with JC. I thought more combination analysis would be required from Ruud's comment on the puzzle page. Still fun to solve!

1. Innies c5: r5c5 = 1

2. 17(2) r34c5 -> {89} not elsewhere in c5.

3. 17(2) r6c34 -> {89} not elsewhere in r6.

4. NP {89} in r4c5/r6c4, not elsewhere in N5
-> 15(2) r4c67 = [69/78]
-> NP {89} r4c57, not elsewhere in r4
-> 10(2) r4c34 = {37/46}
-> Killer pair with r4c6 -> 6,7 not elsewhere in r4 -> r4c1289 = (12345)

5. 6(2) r6c67 = {24}/[51]

6. Innies r12: r2c28 = 14 = {59/68}

7. Innies r89: r8c19 = 14 = {59/68}

8. Innies r1234: r4c28 = 6 = {15/24} (no 3)
-> r4c159 = 14 = {158/248/149/239}

9. Innies r6789: r6c19 = 7 = {16/34} ({25} blocked by 6(2))
-> r6c258 = 15

10. Innies c34: r5c34 = 11 -> r5c67 = 11

11. If split 14(2) r8c19 = {59} -> 12(2) r8c67 = {48} -> CONFLICT as no options for 6(2) r8c34
-> r8c19 = {68}, not elsewhere in r8 -> r8c67 <> 4, r9c5 <> 3

12. 13(2) r2c34 = {49/67} ({58} blocked by split 14(2) r2c28)
-> 13(2) r2c34 and split 14(2) r2c28 form killer pair on 6 and 9, not elsewhere in r2
-> r1c5 <> 3, r2c67 <> 1

13. r2c159 = 11 = {128/137}
-> r12c5 <> 4,5
-> Analysis of 11(3) options -> r2c19 <> 2.

14. Split 7(2) r6c19 and 6(2) r6c67 form killer pair on 1 and 4, not elsewhere in r6
-> r7c5 <> 5
-> 4 locked to r789c5, not elsewhere in N8
-> r79c3 <> 6, r8c3 <> 2, r9c7 <> 3

15. Split 15(3) r6c258 = {267/357}

16. 1 locked to r13c4, not elsewhere in c4 -> r79c3 <> 9, r8c3 <> 5

17. 1 locked to r2c19 and 1 locked to r4c12/r6c1 in N4
If r2c1 = 1 -> r4c2 = 1 -> r4c9 <> 1
If r2c9 = 1 -> r4c9 <> 1
Either case r4c9 <> 1
-> Analysis of split 14(3) r4c159 (see step 8) -> r4c1 <> 5

18. Outies N9: r789c6 + r6c8 = 22
Must have 1 in r79c6
Options: {1579/1669} – only place for 9 is r8c6 -> r8c7 = 3
-> r79c6, r6c8 <> 2,3
Clean up
-> r7c7 <> 6, r7c67 <> 5, r79c3 <> 1, r9c7 <> 4,5, r1c7 <> 4, r2c6 <> 4, r3c6 <> 8, r3c7 <> 2


19. 8 locked to r79c4, not elsewhere in c4
-> r6c4 = 9, r6c3 = 8, r4c5 = 8, r3c5 = 9, r4c7 = 9, r4c6 = 6
Clean up -> 8(2) r7c67 = {17} not elsewhere in r7, r9c4 <> 2, r9c7 <> 1 and 10(2) r4c34 = {37} not elsewhere in r4; r7c3 <> 3, r7c4 <> 2,3, r7c5 <> 3

20. HS r1c6 = 8 -> r1c7 = 5
-> r2c6 <> 2, r1c34 <> 2, r2c2 <> 9

21. HS r9c4 = 3 -> r4c4 = 7, r4c3 = 3
-> r2c3 <> 6, r5c3 <> 4, r9c3 <> 3, r5c7 <> 4, r7c5 <> 2

Straightforward from here

[Ruud]

It isn't as hard as usual.

Time for a V1.5

This Assassin has plenty of upgrade opportunities.



3x3::k:4864:4864:4610:46105381:5381:4615:4615:4864:5642:4610:46105381:5381:5392:4615:5642:5642386018155392:5392:5642:5148130931045154:5392:5148:5148:6950:6950:6950:6950:6950:5154:5154:5148:49102351818:818:4660:5154:4910:491026164155:4155:4660:4660:49105441:54415956:595646602624:5441:54415956:5956:3398

Ruud

[CathyW]

Plenty of combination analysis required on the V1.5 methinks!

So far:

1. Innies c5: r5c5 = 7

2. r12c5 and r34c5 both 6(2) = {15/24}, not elsewhere in c5
-> 14(2) c5 = {68}, 12(2) c5 = {39} -> 3, 9 not elsewhere in N8

3. 16(2) r7c67 = [79]

4. 10(2) r7c34 = {28/46} -> KP with r7c5, 6 and 8 not elsewhere in r7
-> r7c1289 = (12345)

5. 3(2) r6c67 = {12}, not elsewhere in r6

6. 9(2) r6c34 = {36/45}

7. 12(2) r4c67 = [93/57]/{48}

8. 5(2) r4c34 = {14/23}

9. 15(2) r3c34 = {69/78}

10. 7(2) r3c67 = {16/25/34}

11. Innies c34: r4c34 = 12 = {39/48}
-> r5c67 = 8 = {26/35}

12. Innies r12: r2c28 = 8 = {17/26/35}

13. Innies r1234: r4c28 = 10 = {19/28/37/46}

14. Innies r89: r8c19 = 11 = [92]/{38/47/56}

15. Innies r6789: r6c19 = 12 = {39/48/57}

16. Outies r123: r4c159 = 18
r4c5 is max 5 -> r4c19 is min 13 -> r4c19 <> 1,2,3

17. Outies r789: r6c258 = 21 = {489/678} – must have 8, not elsewhere in r6
-> r6c19 <> 4

18. Outies N1: r123c4 + r4c1 = 29 – must have 7, repetition possible but no 1 or 2

19. Outies N3: r123c6 + r4c9 = 22

20. Outies N7: r789c4 + r6c2 = 15 -> r6c2 <> 9 as no 3 in r789c4 -> r6c8 <> 4

21. Outies N9: r6c8 + r89c6 = 18

22. 23(4) r89c67 can’t have 9 -> options {2678/3578/4568}
-> r89c67 <> 1
-> options for r6c8 + r89c6 are {288/459/468/567}
-> 1 locked to r89c4 -> r89c3, r4c4 <> 1 -> r4c3 <> 4

23. r789c4 + r6c2 must have 1. Options: {1248/1257/1266/1446}
Can’t have both 1 and 2 within r89c4
Analysis: r7c4 <> 8 -> r7c3 <> 2; r89c4 <> 2

24. 21(4) r89c34 options {1389/1479/1569/1578} (no 2)
Analysis: r89c3 <> 4

25. UR: since r89c5 = {39}, r89c3 can’t also be {39} -> option {1389} for 21(4) eliminated -> r89c3 <> 3


Still a long way to go

Code: Select all

+-------------------------------+-----------------------+------------------------------+
|  23456789  23456789 123456789 | 3456789 1245 12345689 | 12345678 123456789 123456789 |
|  23456789   123567  123456789 | 3456789 1245 12345689 | 12345678   123567  123456789 |
| 123456789 123456789    6789   |   6789  1245  123456  |  123456  123456789 123456789 |
+-------------------------------+-----------------------+------------------------------+
|   56789    12346789    123    |   234   1245   4589   |   3478    12346789   456789  |
|  12345689  12345689    3489   |   3489    7    2356   |   2356    12345689  12345689 |
|    3579      4678      3456   |   3456   68     12    |    12       6789      3579   |
+-------------------------------+-----------------------+------------------------------+
|   12345     12345      468    |   246    68      7    |     9      12345     12345   |
|  3456789   1234567    56789   |  14568   39    24568  |  2345678  12345678  2345678  |
|  1234567   1234567    56789   |  14568   39    24568  |  2345678  12345678  12345678 |
+-------------------------------+-----------------------+------------------------------+

[Para]

Hi

Really you were almost there.
Here's the rest.

26. Outies N7: R6C2 + R789C4 = 15 = [7]{[2]15}/[4]{[2]18}/[8]{[2]14}
26a. {1266} blocked: See all 6's in C5, so can't have 2 6's.
26b. {1446} blocked: R6C2 = 4 -> R6C34 = {36}, R7C789 = {146}: see all 6's in C5, so no room left for 6 in C5.
26c. R7C4 = 2; R7C3 = 8; R67C5 = [86]
26d. Outies N7 = [7]{[2]15}/[4]{[2]{18}
26e. Clean up: R6C2 = {47}; R89C4 = {15/18}; R6C8: no 7(step 17); R4C3: no 3; R3C4: no 7;

27. 21(4) at R8C3 = {1569/1578}: R89C4 = {15/18} -->> R89C3 = {57/69}: {5/6...} and {5/9...}

28. 19(4) at R6C2: needs one of {47} in R6C2 = {1459/1567/3457}
28a. 19(4) = {1459}: R7C12 + R8C1 = {159} -->> blocked by R89C3
28b. 19(4) = {1567}: R7C12 + R8C1 = {156} -->> blocked by R89C3
28c. 19(4) at R6C2 = {3457}: {35} locked in R7C12 + R8C1 -->> locked for N7

This about does it.

29. R89C3 = {69}(last possible combination) -->> locked for C3 and N7
29a. R89C4 = {15} -->> locked for C4 and N8
29b. R3C3 = 7; R3C4 = 8
29c. R5C34 = 12 = [39]; R6C34 = [54](last possible combination)
29d. R4C34 = [23]; R4C67 = [57]; R34C5 = [51]; R6C67 = [21]
29e. R5C67 = [62]; R6C12 = [97]; R6C89 = [63]
29f. R9C1 = 7(hidden); R89C2 = {12} -->> locked for C2

30. 20(4) at R4C2 = {146}9(last combination) -->> R4C2 = 6; R5C12 = [14]
30a. R4C1 = 8; R4C8 = 4(step 13); R4C9 = 9
30b. R1C8 = 9; R2C6 = 9; R3C2 = 9; R1C2 = 8 (all hidden)

31. 22(4) at R2C2 = {23}89 -->> R2C2 = 3; R3C1 = 2
31a. R2C8 = 5(step 12); R5C89 = [85]
31b. R8C8 = 7; R8C9 = 2(both hidden)
31c. R7C2 = 5; R9C9 = 4; R78C9 = [18]; R7C8 = 3
31d. R78C1 = [43]; R89C2 = [21]
And more naked singles to the end.

greetings

Para

[CathyW]

Thanks Para. A case of so near and yet so far (and running out of time before I'm away for a few days)!

[sudokuEd]

Been trying very hard to make a solvable V2 for Assassin 57. Haven't succeded - but decided this version should be a really good one to learn from. It has some really fun cross-over moves/chains (yes - it is a Diagonals puzzle). Kept trying to find generalized X-wings: but could never be convinced. JSudoku says it doesn't need any guesses - but have no idea how it goes about it. Am totally stuck.

Unfortunately, I can't do any more work on it till next week (going away for a few days too) and want to have another good crack at TJK18 before going. Anyway, feel free to take a peek and get started .

Cheers
Ed
[edit: a simplified walk-through for this puzzle follows the tag solution]

Assassin 57V2X1-9 cannot repeat on the diagonals
3x3:d:k:3328179425643077:4359:43595642281935983856:4359:5642:56423348:4374:4102:41023856:5642:41243348:43741824:48984124:41243366:43742601:4898:4898:4124:4910363118425428:4898:4910:4910:5688:568826115428:5428:4910:5184:5688:568828844678:5428:5184:51842634769:769:4678:4678:

Code: Select all

.-----.-----.--.-----.-----.
|13   |7    |10|12   |17   |
|  .--+-----:  :-----+--.  |
|  |22|11   |  |14   |15|  |
:--'  :-----+--+-----:  '--:
|     |13   |17|16   |     |
|  .--:     |  :-----+--.  |
|  |16|     |  |7    |19|  |
:--'  :-----:  :-----:  '--:
|     |13   |  |10   |     |
|  .--+-----+--+-----+--.  |
|  |19|14   |9 |7    |21|  |
:--'  :-----:  :-----:  '--:
|     |22   |  |10   |     |
|  .--:     :--+-----+--.  |
|  |20|     |9 |11   |18|  |
:--'  :-----:  :-----:  '--:
|     |10   |  |3    |     |
'-----'-----'--'-----'-----'

[mhparker]

Thanks Ed!

JSudoku says it doesn't need any guesses

Which version of JSudoku are you using? The latest released version (0.6b1) only manages 2 placements before giving up. It would be interesting to see what the upcoming version of JSudoku makes of it (if and when it ever hits the streets, that is ).

[rcbroughton]

Just ran it through my solver and it complete without any guesses - but it takes quite a ot of steps. Sumocue gives up fairly quickly. Haven't tried JSudoku.

I'm going to work on it manually for a while to see where I get to.

Rgds
Richard

[sudokuEd]

Just ran it through my solver and it complete without any guesses

That's great news Richard.

What if we do it this way: If no one posts with any more steps for 24 hours, someone gets the next hint from one of the softs and runs with it manually again.

If this sounds OK, up to you guys to get started. Hopefully you're still stuck next week .

Mike, I must be a bit out of date with JSv0.5b3. Was just going on what it said when first loading the puzzle in. Now hitting Ctrl D causes a big angry red welt eventually (what it looked like out of the corner of one eye ).

BTW: the pretty puzzle pic is courtesy of Richards soft. Thanks Richard. Still haven't mastered the manual pic colouring - another project for next week.

Cheers
Ed

[Andrew]

I agree with the comments from J-C and Cathy. A bit easier than some recent ones and definitely less combination work than suggested by Ruud's introduction to this puzzle. However there were far less opportunities than usual to apply the 45 rule. I only used it on rows and columns; I didn't find any useful application for it on the nonets although Cathy did have a useful application for it on N9.

Here is my walkthrough, before people start working on Ed's V2X.

First the preliminary steps

1. R1C34 = {16/25/34}, no 7,8,9

2. R12C5 = {18/27/36/45}, no 9

3. R1C67 = {49/58/67}, no 1,2,3

4. R2C34 = {49/58/67}, no 1,2,3

5. R2C67 = {16/25/34}, no 7,8,9

6. R3C34 = {15/24}

7. R34C5 = {89}, locked for C5, clean-up: no 1 in R12C5

8. R3C67 = {29/38/47/56}, no 1

9. R4C34 = {19/28/37/46}, no 5

10. R4C67 = {69/78}

11. R6C34 = {89}, locked for R6

12. R67C5 = {27/36/45}, no 1

13. R6C67 = {15/24}

14. R7C34 = {19/28/37/46}, no 5

15. R7C67 = {17/26/35}, no 4,8,9

16. R8C34 = {15/24}

17. R89C5 = {27/36/45}, no 1

18. R8C67 = {39/48/57}, no 1,2,6

19. R9C34 = {19/28/37/46}, no 5

20. R9C67 = {16/25/34}, no 7,8,9

21. 26(4) cage at R6C8 = {2789/3689/4589/4679/5678}, no 1

And now for the early present

22. 45 rule on C5 1 innie R5C5 = 1 [Alternatively hidden single in C5, after doing the 2-cell cages], clean-up: no 9 in R4C3, no 5 in R6C7

23. Naked pair {89} in R4C5 and R6C4, locked for N5, clean-up: no 1,2 in R4C3, no 6,7 in R4C7

24. Naked pair {89} in R4C57, locked for R4, clean-up: no 2 in R4C4

25. 45 rule on R1 3 outies R2C159 = 11 = {128/137/146/236/245}, no 9

26. 45 rule on R12 2 innies R2C28 = 14 = {59/68}
[I should then have seen that this eliminates {58} from R2C34]

27. 45 rule on R1234 2 innies R4C28 = 6 = {15/24}

28. 45 rule on R123 3 outies R4C159 = 14, min R4C5 = 8 -> max R4C19 = 6, no 6,7
[Alternatively, after step 24, could have used killer pair 6/7 in R4C34 and R4C6, locked for R4]
28a. Valid combinations 8{15}/8{24}/9{23} (cannot be 9{14} which clashes with R4C28)
[The order of steps 27 and 28 has been exchanged for clarity]

29. 45 rule on R6789 2 innies R6C19 = 7 = {16/34} (cannot be {25} which clashes with R6C67), no 2,5,7

30. 45 rule on R89 2 innies R8C19 = 14 = {59/68}
30a. If R8C19 = {59} => R8C34 = {24} clash with all combinations for R8C67 so R8C19 cannot be {59}
30b. R8C19 = {68}, locked for R8, clean-up: no 4 in R8C67, no 3 in R9C5

31. 8 in N8 locked in R79C4, locked for C4 -> R6C34 = [89], R34C5 = [98], R4C67 = [69], clean-up: no 4 in R1C6, no 4,7 in R1C7, no 4,5 in R2C3, no 5 in R2C4, no 1 in R2C7, no 2 in R3C6, no 2,5 in R3C7, no 4 in R4C34, no 1 in R7C3, no 2 in R7C4, no 3 in R7C5, no 2 in R7C7, no 3 in R8C6, no 1 in R9C3, no 2 in R9C4, no 1 in R9C7
[I missed the fact that R8C6 = 9 (hidden single in C6) after R34C5 were fixed.]

32. Naked pair {37} in R4C34, locked for R4
[Alternatively 3 could be eliminated from R4C19 using step 28a with R4C5 = 8]

33. 7 in R6 locked in R6C258
33a. 45 rule on R789 3 outies R6C258 = 15 = 7{26/35}, no 1,4, clean-up: no 5 in R7C5
[Note that if 7 wasn’t already locked in this split 15(3) cage, then it would have to be 7{26/35} because {456} clashes with R6C67.]

34. 45 rule on C34 2 innies R5C34 = 11 = {47}/[65/92], no 2,3,5 in R5C3, no 3 in R5C4

35. 45 rule on C67 2 innies R5C67 = 11 = {47}/[56/83], no 2, in R5C6, no 2,3,5 in R5C7

36. 45 rule on R9 3 outies R8C258 = 13 = {139/157/247}
36a. If R8C258 = {139}, 3 must be in R8C5 -> no 3 in R8C28

37. R2C28 (step 26) = {59/68}
37a. If R2C28 = {59} => R2C34 = {67} => R2C67 = {34} => R2C159 = {128} => R2C5 = 2, R2C19 = {18}
37b. If R2C28 = {68} => R2C34 = [94] => R2C67 = {25} => R2C159 = {137} => R2C5 = {37}, R2C19 = {137}
Summary
R2C28 and R2C34 unchanged
R2C67 = {25/34}, no 1,6
R2C19 = {1378}, no 2,4,5,6
R2C5 = {237}, clean-up: R1C5 = {267}

38. 1 in C6 locked in R79C6, locked for N8, clean-up: no 9 in R7C3, no 5 in R8C3, no 9 in R9C3
38a. If R9C6 = 1 => R9C7 = 6, if R7C6 = 1 => R7C7 = 7 -> no 6 in R7C7, clean-up: no 2 in R7C6

39. 14(3) cage in N9 = {149/158/239/248/257/347/356} (cannot be {167} which clashes with R79C7)

40. 4 in C5 locked in R789C5, locked for N8, clean-up: no 6 in R7C3, no 2 in R8C3, no 6 in R9C3, no 3 in R9C7

41. 8 locked in R79C4 (step 31) -> 2 locked in R79C3, locked for C3 and N7, clean-up: no 5 in R1C4, no 4 in R3C4

42. 1 in C4 locked R13C4
42a. If R3C4 = 1 => R3C3 = 5, if R1C4 = 1 => R1C3 = 6 -> no 5 in R1C3, clean-up: no 2 in R1C4

43. R3C3 = 5 (hidden single in C3), R3C4 = 1, clean-up: no 6 in R1C3, no 9 in R2C8 (step 26), no 6 in R3C7

44. 5 in N2 locked in R12C6, locked for C6, clean-up: no 6 in R5C7 (step 35), no 1 in R6C7, no 3 in R7C7, no 7 in R8C7, no 2 in R9C7

45. R7C7 = 1 (hidden single in C7), R7C6 = 7, R8C67 = [93], R9C6 = 1 (hidden single in C6), R9C7 = 6 [I should then have put R8C19 = [68] here but maybe I forgot to eliminate the 6 from R8C9 at this stage; I do my eliminations manually. It gets done in step 48.], clean-up: no 4 in R2C6, no 8 in R3C6, no 4 in R3C7, no 4 in R5C7 (step 35), no 2 in R6C5, no 3 in R7C34, no 2 in R89C5, no 3,4 in R9C3
[Having missed that R8C6 was a hidden single in step 31, it seems a bit ironic that I have now fixed that cell by using the hidden single R7C7!]

Now for several naked pairs

46. Naked pair {24} in R6C67, locked for R6, clean-up: no 3 in R6C19 (step 29)

47. Naked pair {16} in R6C19, locked for R6
[Just noticed that I could have reduced to this pair after the clean-up in step 44.]

48. Naked pair {34} in R35C6, locked for C6 -> R6C67 = [24], R2C67 = [52], R1C67 = [85], R8C19 = [68], R6C19 = [16], clean-up: no 7 in R1C5, no 2 in R4C2, no 5 in R4C8 (both step 27)
[R1C6 had been a hidden single for a while. Must get better at spotting them!]

49. Naked pair {45} in R89C5, locked for C5 and N8 -> R8C34 = [42] , R89C5 = [54], R7C34 = [28], R67C5 = [36], R12C5 = [27], R8C8 = 7, R8C2 = 1, R6C8 = 5, R6C2 = 7, R9C34 = [73], R4C34 = [37], R1C34 = [16], R2C34 = [94], R5C34 = [65], R5C6 = 4, R5C7 = 7 (step 35), R3C67 = [38]

50. Naked pair {68} in R2C28, locked for R2 -> R2C1 = 3, R2C9 = 1, R1C12 = [74]

51. Naked pair {49} in R7C89, locked for R7 and N9 -> R7C12 = [53], R9C89 = [25]

52. Naked pair {29} in R5C12, locked for R5 and N4

and the rest is naked singles

Any corrections will be welcome by PM. I know from working through J-C's and Cathy's walkthroughs that I missed some things or might have seen them earlier.

[rcbroughton]

As I've not been around for a while, I'll kick off with Ed's V2 with a few easy moves to get us started:

0. Cage 7(2) n12 - no 789
0a. Cage 10(2) n2 - no 5
0b. Cage 12(2) n23 -no 126
0c. Cage 11(2) n12 - no 1
0d. Cage 14(2) n23 = {59}/{68}
0e. Cage 13(4) n1245 - no 89
0f. Cage 16(2) n23 = {79}
0g. Cage 7(2) n56 @r4c6 - no 789
0h. Cage 13(2) n45 - no 123
0i. Cage 10(2) n56 - no 5
0j. Cage 14(2) n45 - = {59}/{68}
0k. Cage 9(2) n58 - no 9
0l. Cage 7(2) n56 @r6c6 - no 789
0m. Cage 10(2) n89 - no 5
0n. Cage 20(3) n7 - no 12
0o. Cage 9(2) n8 - no 9
0p. Cage 11(2) n89 - no 1
0q. Cage 10(2) n78 - no 5
0r. Cage 3(2) n89 ={12}

1. {12} locked in 3(2)n89 for r9
1a. no 7,8 9(2)8 at r8c5
1b. 10(2) n78 - no 8,9

2. {79} locked in 16(2)n23 for r3

3. {79} at r3c7 blocks combination {179} in 17(3) n3 - no 1 in 17(3)

4. 1 now locked in cage 15(4) for n3
4a. no 1 from r4c9
4b. 15(4) can't be {2346}

5. 14(2) n23 block combination {56} in 11(2) n12

6. 45 Rule on n3 - outies r123c6 r4c9 total 29 - max in r123c6 is 24
6a. Removed candidates 234 from r4c9

7. 45 Rule on n7 - outies r789c4 r6c2 total 26 - max in r789c4 is 24
7a. Removed candidate 1 from r6c2

8. 45 Rule on r789 - outies r6c258 total 17
8a. Cage 14(2) n45 eliminates {269} and {458}
8b. Combined cages 14(2) n45 & 7(2) n56 eliminate {359}, {368} and {467}
8c. Removed candidates 3456 from r6c258
8d. Remaining combinations for r6c258 = {179/278} = 7{19/28}, 7 locked for r6
thanks toAndrew for pointing out the the clarification and extra step

9. Combination {36}/{45} no longer valid in 9(2) n58

10. 9(2)n58 blocks {28} from cage 10(2) n2

11. 9(2)n58 blocks {179}/{278} from cage 17(3) n25 - no 1 in 17(3)

12. Combination {467} in cage 17(3) n25 blocked by 10(2) in same col - no 7 in 17(3)
12a. Remaining combinations for 17(3) n25 = {269/359/368/458} [5/6, 8/9]

13. 45 Rule on rows 12 - innies r2c28 total 6 = {15}/{24}

14. 45 Rule on rows 6789 - innies r6c19 total 7 - no 7,8,9 in r6c19

15. 45 Rule on row 1 - outies r2c159 total 14
15a. combination of 11(2) n12 & 14(2) n23 block {149} {257}
15b. 14(2) n23 blocks {356} {158}
15c. 11(2) n12 blocks {248}
15d. no 5,8 in r2c19
15e. Remaining combinations for split cage r2c159 = {167/239/347}

Rgds
Richard

[Andrew]

Good to have you back Richard. We will almost certainly need your combination crunching expertise for this V2.

It's quite a while since I've participated in a tag solution. I'll start with a few comments on Richard's moves and try to find some of my own later this evening.

This message originally contained clarifications for step 8 since I find it difficult to picture clashes with combined cages and maybe some others do too. I also added remaining combinations at the end of steps 8, 12 and 15 to make it easier to keep track of the remaining combinations after the multiple eliminations.

Richard has now incorporated these changes in the previous message so I've now deleted them from here to make this thread easier to read.

[Andrew]

Only managed one small step this evening.

16. 15(4) n36 must contain 1 (step 4)
16a. Remaining combinations 1{239/248/257/347/356}
16b. For {1248} 8 must be in r4c9 -> no 8 in r3c89

[rcbroughton]

Add a few more onto Andrew's position.a few observations from Andrew
17. Limited placement of candidates in cage 22(4) n14
17a.{2479}/{1579} - no valid placement
17b. no combo with 1,2,4,5 in r4c1

18. 45 in n1 - innies = 32=
{125789/134789/135689/145679/234689/235679/245678}
18a r2c2+r3c12 can only be (to fit in with r4c1 totalling = 22(4))
{148} - r123c3 = {379} no placement
{256} - r123c3 = {478}/{379} no placement
{356} - r123c3 = {189}no placement {279} no placement
{456} - r123c3 = {179}/ {278} no placement
{168} - r123c3 1 @ r2c2 = {359} - 9 @ r2c3
{238} - r123c3 2 @ r2c2 = {469} - 9 @ r2c3
{258} - r123c3 2or5@r2c2 = {179} no placement {467} 7 @ r2c3
{346} - r123c3 4 @r2c2 = {289} no placement
{348} - r123c3 4@r2c2 = {179}no placement {269} 9 @r2c3
{358} - r123c3 5@r2c2 = {169} 9@ r2c3
{568} - r123c3 5@r2c2 = {139} 9 @ r2c3 {247} 7@ r2c3
18b. r2c3 = 7,9 - no 2,3,4,8
18c. r3c12 = 2,3,5,6,8 - no 1,4
18d. cleanup cage 11(2)n12 - no 3,7,8, 9 r2c4

19. innies on r12 r2c28=6 - {24} now blocked by 11(2) n12
19a. r2c28={15} - locked for r2
19b removes 1,5 from r8c8, r8c2 r5c5 on Diagonals

20. 14(2) n23 = {68} locked for r2

21. Cleanup 10(2)n2 = [19]/{37}/[64]

Rgds
Richard