Ruudiculous tag Killer - UTA

[sudokuEd]

We have a long weekend here in Aus so time for another Tag Killer - that is, one person starts and then 'tags' another to take over. If you can see one good move - post what you've found, then someone else takes over with the next good move.

This puzzle takes SumoCue 17 seconds to find a solution, compared to Uluru's 10. So, a definite UTA.

Don't know if this puzzle is solvable by logic - havn't tried. Just had a quick look to see that there are at least a couple of logical moves.

Oh yeah - nearly forgot - this is another Diagonals Killer, so 1-9 cannot repeat on the diagonals.

Based on experience with Uluru, here are a few suggested 'rules'
1. Wait 2 full days between consecutive posts. This will give more time for others to 'tag' in (and finish Assassin 18 first and watch the Australian Rules Football and National Rugby League Grand Finals!)
2. If no-one posts for 3 full days, I'll post SumoCues hints.

Would someone be able to set a pic? TIA.

3x3:d:k:6913:6913:5122:5122:5122:5134:5134:5134:5134:5138:6913:6913:6913:512217922320:5138:4373:4373:4373:5654:5654:56541305:5138:4373:4390:4390:6439:5941:5941:5941:5941:5915:4390:4390:6439:6439:64395931:5941:5915:5915:5915:5915:64393882:5931389423624355:4355:5931:5931134323705966:4355:4355:44325704:5704:5704:5704:5966:5966:5966:4432:4432:

[Ruud]

[Nasenbaer]

How should we do it? Just one step per post or 3 or until I have no clue how to continue? And the hints should be in tiny font, right?

Peter

[sudokuEd]

How should we do it? Just one step per post or 3 or until I have no clue how to continue?

Good question Peter- hard to answer until we get more experience at doing tag Killers. Why not try "until I have no clue how to continue". The main thing is that you tell us each step so we can follow.

If you're using SumoCue, why not post a copy of the "marks" of where you finish to make sure we are on the same playing field.

And the hints should be in tiny font, right?

I'm assuming you mean SumoCue's hints? Thought we could try leaving SumoCue's hints out of this one until we are all stumped.

Time to play!

[Nasenbaer]

I'm assuming you mean SumoCue's hints? Thought we could try leaving SumoCue's hints out of this one until we are all stumped.

Time to play!

I meant tiny text in this forum, so nobody gets a big spoiler. But your interpretation is also true.

For starters, I try to do the killers "on paper", so most likely I overlook an obvious clue. When I get really stuck I will switch to SumoCue.

I haven't done this before (I mean writng done my steps), so please excuse my mistakes in the syntax (I will read more about it, I promise). I hope I can make myself clear. Oh, and because I haven't done this before I will jump around a lot, just when something hits the eye.

Starting...

1. 22(3) in R3 = {589}/{679} -> 9 locked in R3, nowhere else
2. "90" on R12 -> R2C1 = 7
3. R34C1 = 13 = {49}/{58}
4. "45" on R3 -> R4C12 = 12 = {39}/{48}/{57}
5. Using the steps from above we get R3C1 = {458}, R4C1 = {589}, R4C2 = {347}
6. "45" on N4 -> R46C4 = 7
7. "45" on N5 -> R46C6 = 13
8. "45" on N7 -> R789C4 = 15
9. "45" on N8 -> R89C7 = 10
10. "45" on N9 -> R56C8 + R6C9 = 20
11. "45" on R9 -> R8C58 = 17 = {89} -> 8 and 9 locked in R8
12. "90" on R89 -> R8C679 = 14 = {167}/{257}/{356}

OK, that's my starter with the easy clues. I don't know if all of them are useful, but I always like to get more information in the beginning. Hope it helps.

Now I'm heading straight for the bed... (already 2 in the morning??? Oh my... )

Peter

EDIT: error in step 3 corrected, tiny text removed

[Andrew]

Thanks Ruud for posting the diagram for this puzzle.

Good to see that Peter has joined in this tag-killer. I hope others join in also.

Peter, don't worry about jumping about and putting in suggestions that might not immediately lead to anything. The more ideas that are thrown in, the quicker the puzzle will be solved.

Here are my first thoughts (originally posted in tiny text).

45 rule on R12 1 innie -> R1C2 = 7, R34C1 = {49/58}
22(3) cage in N23 must contain 9, no other 9 in R3
45 rule on R12 1 innie -> R1C2 = 7, R34C1 = {49/58}
22(3) cage in N23 must contain 9, no other 9 in R3
If the 9 is in R3C56 then there must be 9 in R1C789, R1C6 cannot contain 9
If the 9 is in R3C7 then the 9 in N2 must be in R1C456 or R2C45 and the 9 in N1 must be in R1C123 or R2C23 [edited - thanks for sudokuEd's comments on this in a private message - I must admit I'd only looked at one half of the alternative]
R3C89 = {14/23}
R7C12 = {69/78}
R8C12 = {14/23}
45 rule on R123 2 outies = 12 -> R4C2 = {3478}

Those were done before I looked at Peter's first moves which were then in tiny text. Having now done that I can add one more point

4 in R8 must be in R8C1234

As with sudokuEd's first tag killer, I'm not using SumoCue and at the moment I am working on the basis of only putting in candidates when required. Once we get to the stage when sudokuEd posts Sumocue hints and a grid of remaining candidates then I'll work from that like I did with his first one. Hopefully this time I'll be able to avoid asking questions about how candidates were eliminated using SumoCue hints.

Finally a suggestion to sudokuEd. I think it would be better for us to work in normal text rather than tiny text like Peter and I have done so far (before this message was edited). The aim is for this to be a tag puzzle where we each build on what has been done so far and others have suggested, obviously after convincing ourselves that those suggestions are correct.

I would suggest that if SumoCue hints are posted with a working diagram, the hints should be in normal text but after the diagram. That way people can scroll down just as far as they want to.

Andrew

[sudokuEd]

Well, looks like this puzzle is a real toughie. So don't think we need to worry about Tiny Text spoiling anything!

I've tried to summarize what I understand Peter and Andrew have contributed so far. Then added some of my own steps. I've numbered them to help us communicate. I have included the Marks from SumoCue - but c9 seems to be all wonky - on every second line under c1. Must be too many marks to handle it?

I suspect we're going to have to find a short contradiction chain to get much further. I'll give it 48 hours to let others digest whats here and find something more. If nothing comes by then, we'll see what SudoCue's hints have to add.

Combined- Peter and Andrew (with a few eliminations added by me :Edit)
1. 22(3) in R3 = {589}/{679} -> 9 locked in R3, nowhere else
2. "90" on R12 -> R2C1 = 7
3. R34C1 = 13 = {49}/{58} [Edit:typo]
4. "45" on R3 -> R4C12 = 12 = {39}/{48}/{57}
5. Using the steps from above we get R3C1 = {458}, R4C1 = {589}, R4C2 = {347}
6. If 9 not in R3C7 then there must be 9 in R1C789, R1C6 cannot contain 9
7. R3C89 = {14/23}
8. R7C12 = {69/[87]}
9. R8C12 = {14/23}
9a. r2c67 = 7 -> no 7, 8 or 9
9b. r2c89 = 9 -> no 9 or 2
9c. r7c34 = 9 -> no 9 [Edit: typo]
9d. r8c23 = 9 -> no 9 [Edit: steps 9a-9d added for clarity]
10. "45" on N4 -> R46C4 = 7 -> no 7,8 or 9 in r46c4
11. "45" on N5 -> R46C6 = 13 -> no 1,2 or 3 in r46c6
12. "45" on N7 -> R789C4 = 15
13. "45" on N8 -> R89C7 = 10 -> no 5
14. "45" on N9 -> 3 outies = 20 -> no 1 or 2 possible in R56C8 or R6C9 [edited: clarity]
15. "45" on R9 -> R8C58 = 17 = {89} -> 8 and 9 locked in R8 -> no 1 in r8c34 [edited]
16. "90" on R89 -> R8C679 = 14 = {167}/{257}/{356} (cannot be {347} because that would clash with the 5(2) cage in R8C12) [Edit]
17. 4 in R8 must be in R8C1234

Ed
18.r8c58 = {89}-> 8 and 9 eliminated from r9c7 (same cage as r8c5) and r5c5 (linked through D\).
19. 17(3) cage in N9 must have 8 or 9 but cannot have both since 8 + 9 = 17 ->no 8 or9 in r9c89
20. In N9, 8/9 must be in r7c789. 15(2) cage in r7c12 must have 8/9 -> Killer pair on 8/9 in r7 -> no 8/9 elsewhere. -> no 1 in r7c34 [edited]
21. r89c7 = 10 -> r89c7 = {37/[64]} [edited out redundant info]
22. r789c4 = 15. Max. r78c4 = {67} = 13 -> min. r9c7 = 2
23. N7, 15(2) cage must have 8/9 but not both -> 8/9 must be in r9c123 -> 22{4} cage <>{4567} combination.
24."45" on N3 -> 1 outie + 11 = 2 innies -> min r23c7 = 12 -> no 1 or 2 in r2c7. r2c6 = {1234}. Max r23c7 = 15 -> Max r1c6 = 4. [edited for clarity]
25.7(2) cage in N23 cannot have [43] since that would require 9(2) cage in N3 = {18} but [3{18}] in r2c789 would leave no 3 or 1 for 5(2) cage in N3 -> no 3 in r2c7.->no 4 in r2c6 [edited: typo]
26. "45" on N3 -> 2 outies + 4 = 1 innie. r12c6min = {12} = 3 -> min r3c7 = 7

Code: Select all

.-----------------------.-----------------------------------.----------------------------------------

-------.
|(27)                   |(20)                               |(20)                                     

      |
| 12345689    12345689  | 12345689    123456789   123456789 | 1234        123456789   123456789   

123456789 |
:-----------.           '-----------------------.           

:-----------------------.-----------------------:
|(20)       |                                   |           |(7)                    |(9)              

      |
| 7         | 12345689    12345689    12345689  | 12345689  | 123         456       | 134568      

134568    |
|           

:-----------------------------------+-----------'-----------------------+-----------------------:
|           |(17)                               |(22)                               |(5)              

      |
| 458       | 1234568     1234568     12345678  | 56789       56789       789       | 1234        

1234      |
|           |           

.-----------------------+-----------.-----------------------'-----------------------:
|           |           |(17)                   |(25)       |(23)                                     

      |
| 589       | 347       | 123456789   123456    | 123456789 | 456789      123456789   123456789   

123456789 |
:-----------+-----------'           .-----------'           '-----------.-----------.-----------.     

      |
|(23)       |                       |                                   |(15)       |(23)       |     

      |
| 12345689  | 123456789   123456789 | 123456789   1234567     123456789 | 123456789 | 3456789   | 

123456789 |
|           '-----------------------'-----------.           .-----------'           |           

:-----------:
|                                               |           |                       |           |(15) 

      |
| 12345689    123456789   123456789   123456    | 123456789 | 456789      123456789 | 3456789   | 

3456789   |
:-----------------------.-----------------------+-----------'-----------.-----------'           |     

      |
|(15)                   |(9)                    |(17)                   |                       |     

      |
| 689         679       | 234567      234567    | 1234567     1234567   | 123456789   123456789 | 

123456789 |
:-----------------------+-----------------------+-----------.           '-----------.-----------:     

      |
|(5)                    |(9)                    |(23)       |                       |(17)       |     

      |
| 1234        1234      | 234567      234567    | 89        | 123567      367       | 89        | 

123567    |
:-----------------------'-----------------------:           '-----------------------:           

'-----------:
|(22)                                           |                                   |                 

      |
| 12345689    123456789   123456789   23456789  | 123456789   123456789   347       | 1234567     

1234567   |
'-----------------------------------------------'-----------------------------------'----------------

-------'

[Nasenbaer]

OK, here's another one:

27. 17(4) cage in N124 can't have both 5 and 6 because of step 1 (either a 5 or a 6 is needed for 22(3) in R3) -> possible combinations for 17(4) : {1358}/{1367}/{1457}/{2348}/{2357}
28. "45" on N1 -> 2 outties = 1 innie + 7 -> R23C4 min. 8, max 16 -> not both 8 and 9 possible in R23C4 (does this help?)

EDIT: One more:
29. because of step 16 the 4 in R8C7 can be eliminated -> 6 can be eliminated from R9C7 (see step 21)
Peter

[sudokuEd]

Now I'm heading straight for the bed... (already 2 in the morning??? Oh my...

Hope you had sweet UTA dreams. I've been a bit deflated but not from going to bed too late. Both the football teams I was barracking for lost in Grand Finals this weekend.

27. 17(4) cage in N124 can't have both 5 and 6 because of step 1 (either a 5 or a 6 is needed for 22(3) in R3) -> possible combinations for 17(4) : {1358}/{1367}/{1457}/{2348}/{2357}

Good point. But I can only make one tiny deduction from this. Hence, step 30. I normally hate this kind of nit-pickery, but maybe that's what this puzzle is going to need.

Step 30. following on from step 27 - 6 can be eliminated from r3c4.
Here's how. The only legal combination for r3c234 that involves a 7 is {167} with 3 in r4c2 (not {157} since 5 is already required in r3c1 when 4 in r4c2; not {257} as would leave no 2 or 4 for 5(2) cage in r3 [Edit:typo]).
{167} in r3c234 is also the only combination for the 17(4) cage that uses 6. Since the 7 can only go in r3c4, 6 must be in r3c23 in this combination
-> 6 eliminated from r3c4.

28. "45" on N1 -> 2 outties = 1 innie + 7 -> R23C4 min. 8, max 16 -> not both 8 and 9 possible in R23C4 (does this help?)

Not that I can see at the moment. 9 or 8 are still possible in r23c4 in other combinations.

But that "45" does mean that when 9 is in r1c3, r23c4 = 16 = [97]. But this does not contradict anything else from what I can see. So, we cannot eliminate 9 from r1c3 at this stage.

But hopefully this "45" will become useful later on - so is still very worthy of being step 28.

29. because of step 16 the 4 in R8C7 can be eliminated -> 6 can be eliminated from R9C7 (see step 21)

True. But I think of that elimination being implied in step 21. This might be about the "Killer syntax" so worth bringing up. So,

21. r89c7 = 10 -> r89c7 = {37/[64]}

The [square brackets] means "fixed in that cell" compared to {normal brackets} which mean "could go in either/any cell"
Does this make sense?
At least we're making some progress.

[sudokuEd]

here are a few suggested 'rules'
2. If no-one posts for 3 full days, I'll post SumoCues hints.:

That feels a bit long. So, I'm going to break that rule and jump in.

First, the bad news. SumoCue says "No More Hints". So, it looks like this is it.

Now the good news. I've changed some cages around and now it is solvable by logic. Hence UTA2.

So now its up to you guys if you want to continue. Obviously I won't be able to (unfortunately), but am happy to moderate and maybe help answer "does this help?". If you do continue, but get stuck, I'll post SumoCue hints after 2 full days (?).

Most of the steps that we developed for UTA stay exactly the same. I've edited the ones that have changed slightly, and added 9e and f to account for the new cages. I also left out step 30 (but kept the number) - too complicated and might not be valid. Plus, is not needed for UTA2. The new version of steps 1-30 follows. Don't think we need to worry about tiny text since this is 'tag'.

Many thanks to udosuk for making the beautiful pic for me.
Text File is also below. For any new-comers, this is a diagonals Killer (1-9 can't repeat on diagonals)

Enjoy!

UTA2
1. 22(3) in R3 = {589}/{679} -> 9 locked in R3, nowhere else
2. "90" on R12 -> R2C1 = 7
3. R34C1 = 13 = {49}/{58}
4. "45" on R3 -> R4C12 = 12 = {39}/{48}/{57}
5. Using the steps from above we get R3C1 = {458}, R4C1 = {589}, R4C2 = {347}
6. If 9 not in R3C7 then there must be 9 in R1C789, R1C6 cannot contain 9
7. R3C89 = {14/23}
8. R7C12 = {69/[87]}
9. R8C12 = {14/23}
9a. r2c67 = 7 -> no 7, 8 or 9
9b. r2c89 = 9 -> no 9 or 2
9c. r7c34 = 9 -> no 9
9d. r8c34 = 9 -> no 9
9e. r9c12 = 10 -> no 5 and no 3 in r9c2
9f. r9c34 = 12 -> no 1,2 or 6 [9e and 9f added for UTA2]
10. "45" on N4 -> R456C4 = 14 [changed for UTA2]
11. "45" on N5 -> R456C6 = 17 [changed for UTA2]
12. "45" on N7 -> R789C4 = 15
13. "45" on N8 -> R89C7 = 10 -> no 5
14. "45" on N9 -> 3 outies = 20 -> no 1 or 2 possible in R56C8 or R6C9
15. "45" on R9 -> R8C58 = 17 = {89} -> 8 and 9 locked in R8 -> no 1 in r8c34
16. "90" on R89 -> R8C679 = 14 = {167}/{257}/{356} (cannot be {347} because that would clash with the 5(2) cage in R8C12)
17. 4 in R8 must be in R8C1234
18.r8c58 = {89}-> 8 and 9 eliminated from r9c7 (same cage as r8c5) and r5c5 (linked through D\).
19. 17(3) cage in N9 must have 8 or 9 but cannot have both since 8 + 9 = 17 ->no 8 or9 in r9c89
20. In N9, 8/9 must be in r7c789. 15(2) cage in r7c12 must have 8/9 -> Killer pair on 8/9 in r7 -> no 8/9 elsewhere. -> no 1 in r7c34
21. r89c7 = 10 -> r89c7 = {37/[64]}
22. deleted for UTA2
23. deleted for UTA2
24."45" on N3 -> 1 outie + 11 = 2 innies -> min r23c7 = 12 -> no 1 or 2 in r2c7. r2c6 = {1234}. Max r23c7 = 15 -> Max r1c6 = 4.
25.7(2) cage in N23 cannot have [43] since that would require 9(2) cage in N3 = {18} but [3{18}] in r2c789 would leave no 3 or 1 for 5(2) cage in N3 -> no 3 in r2c7.->no 4 in r2c6
26. "45" on N3 -> 2 outies + 4 = 1 innie. r12c6min = {12} = 3 -> min r3c7 = 7
27. 17(4) cage in N124 can't have both 5 and 6 because of step 1 (either a 5 or a 6 is needed for 22(3) in R3) -> possible combinations for 17(4) : {1358}/{1367}/{1457}/{2348}/{2357}
28. "45" on N1 -> 2 outties = 1 innie + 7 -> R23C4 min. 8, max 16 -> not both 8 and 9 possible in R23C4
29. [edit- redundant step:covered in 21.]
30. deleted for UTA2 [too complicated and not needed to solve UTA2]



3x3:d:k:6913:6913:5122:5122:5122:5134:5134:5134:5134:5138:6913:6913:6913:512217922320:5138:4373:4373:4373:5654:5654:56541305:5138:4373:4390:4390384431254635:4390:439036233882:59314635:4635307738825931389423624355:4355:5931:5931134323705966:4355:4355:4432263230785966:5966:5966:4432:4432:

[Nasenbaer]

Oh well, then we will try the new version... but I won't be able to look at it until Thursday, sorry.

Nasenbaer

[Andrew]

Hi All

I'm also hoping to be able to contribute to UTA2 but possibly not for a day or two. I've got other things that have to be done first. Hopefully some other forum members will also contribute steps toward solving this puzzle. As sudokuEd has already said, because of the way that he has modified it, he can't contribute any more steps but will continue to moderate.

Andrew

[sudokuEd]

Now the good news. I've changed N457 and now it is solvable by logic. Hence UTA2.

As it turns out - not solved by logic but a 'lucky' mistake

I've been going crazy trying to make progress - especially trying to work out innies/outies on c1. Keep getting tricked.

Here are my next lot of steps with the end marks which hopefully agree with what I've said [edit to marks pic-several errors corrected/step 46a added]

If we don't get much further, I'll post SumoCue hints in 48 hours. Hopefully this time there are some.

31.10(2) cage in r9 cannot be {37} since that requires the 12(2) cage to be {48}, but this means no 3, 4 or 7 is left for r9c7 -> no 3 or 7 in r9c12 -> 10(2) cage = {19/28/46}
32. 5 in N7 locked in c3 -> no 5 elsewhere in c3
33. "45" on N7 -> 3 innies = 15 [hidden (h)15(3) cage] ->r789c3 must have 5 (from step 32)-> other 2 cells = 10.
-Cannot be {19} since no 1 in r789c3.
-Cannot be {28} as that requires 15(2) cage = {69} but this leaves no 2, 6, 8 or 9 for 10(2) cage in N7 [edit:clarity].
-> h15(3) cage in N7 = 5{37/46} -> no 2, 8 or 9.-> no 7 in r78c4, no 3 or 4 in r9c4
34. h15(3) cage in N7 = 5{37/46} = [6/7...], 15(2) cage in N7 = {69/{87]} = [6/7..] -> Killer pair on 6 and 7 ->not elsewhere in N7
35. 10(2) cage now {19/28}
36."45" on c1 -> 4 outies - 23 = 1 innie. Max. r6789c2 = {4789} = 28 -> max. r1c1 = 5
37. "45" on c1 -> 1 outie + 7 = 4 innies. Min. r1789c1 = {1236} = 12 -> Min. r6c2 = 5
38. "45" on c89 -> 2 innies - 9 = 1 outie. Max r1c89 = {89} = 17 -> Max r7c7 = 8 -> no 9 [edit:typo]
39. Step 38 also means that 9 is now locked in r5678c8. Here's how. 23(4) cage in N69 must have 8/9 (not both as that would leave nothing for r8c8). r8c8 = {89} -> 9 must be in r8c8 or the 23(4) cage in c8 -> no 9 elsewhere in c8. [edit:typos + clarity]
40. "45" on c1234 -> 2 outies = 11 -> no 1 in r12c5 and no 4 in r1c5
41. "45" on c1234 -> 2 innies = 9 -> no 9 in r1c34 and no 2 or 4 in r1c4.
42. 9 in N1 now locked in 27(5) cage -> no 9 in r2c4
43. "45 on c5 -> 4 innies = 20. Min. r38c5 = {58} = 13 -> max. r79c5 = 7 -> no 7, 8 or 9.
44. "45" on N6789 -> 1 outie - 2 = 1 innie -> max.r4c7 = 7, min. r6c6 = 3
45. "45" on N1234-> 1 outie - 2 = 1 innie -> max.r6c3 = 7, min. r4c4 = 3 and no 7 in r4c4 (since no 5 in r6c3)
46. "45" on c12 -> 2 outies (r2c34) - 5 = 3 innies (r345c2) -> since min r345c2 = {123} = 6 -> min. 2 outies = 11 -> no 1 or 2 in r2c3 and no 1 in r2c4
46a. -> max.R2C34 =17 -> max. R345C2 = 12 -> no 9 in R5C2 because min.R34C2 = 4 (added by Peter - Edit -added to pic)[edited:7from r4c4]

Code: Select all

.-----------------------.-----------------------------------.-----------------------------------------------.
|(27)                   |(20)                               |(20)                                           |
| 12345       12345689  | 123468      135678      2356789   | 1234        123456789   12345678    123456789 |
:-----------.           '-----------------------.           :-----------------------.-----------------------:
|(20)       |                                   |           |(7)                    |(9)                    |
| 7         | 12345689    34689       234568    | 2345689   | 123         456       | 134568      134568    |
|           :-----------------------------------+-----------'-----------------------+-----------------------:
|           |(17)                               |(22)                               |(5)                    |
| 458       | 1234568     123468      12345678  | 56789       56789       789       | 1234        1234      |
|           |           .-----------------------+-----------.-----------------------+-----------------------:
|           |           |(17)                   |(14)       |(15)                   |(12)                   |
| 589       | 347       | 12346789     345689   | 123456789 | 123456789   1234567   | 12345678    123456789 |
:-----------+-----------'           .-----------:           |           .-----------+-----------.           |
|(18)       |                       |(12)       |           |           |(15)       |(23)       |           |
| 12345689  | 12345678    12346789  | 123456789 | 1234567   | 123456789 | 123456789 | 3456789   | 123456789 |
|           '-----------.-----------'           |           :-----------'           |           :-----------:
|                       |                       |           |                       |           |(15)       |
| 12345689    56789     | 123467      123456789 | 123456789 | 3456789     123456789 | 3456789   | 3456789   |
:-----------------------+-----------------------+-----------'-----------.-----------'           |           |
|(15)                   |(9)                    |(17)                   |                       |           |
| 689         679       | 34567       23456     | 123456      1234567   | 12345678    123456789 | 123456789 |
:-----------------------+-----------------------+-----------.           '-----------.-----------:           |
|(5)                    |(9)                    |(23)       |                       |(17)       |           |
| 1234        1234      | 34567       23456     | 89        | 123567      367       | 89        | 123567    |
:-----------------------+-----------------------:           '-----------------------:           '-----------:
|(10)                   |(12)                   |                                   |                       |
| 1289        1289      | 3457        5789      | 123456      123456789   347       | 1234567     1234567   |
'-----------------------'-----------------------'-----------------------------------'-----------------------'

[Nasenbaer]

Comments to your new Steps:
31: Good one, didn't see that.
33: Didn't see the {28} part either.
36: Didn't see that (Am I blind?)
37: Whow. You really like the innies and outies, don't you?
44: It should read min.R6C6 = 3
45: It should read max.R6C3 = 7 ...
46: -> max.R2C34 =17 -> max. R345C2 = 12 -> no 9 in R5C2 because min.R34C2 = 4

Here are my new steps (from the PM I sent you earlier):
My Step 45 (same result, different way): R456C4 = 14 (Step 10), 12(3) in N45 -> R4C4 = R6C3 + 2 -> no 8,9 in R6C3, no 1,2,7 in R4C4 (no 7 because of eliminated 5 in C3)
47. "45" on C4 (Steps 10 and 12) -> R123C4 = 16
48. Because of Steps 1 and 26 there has to be either a 5 or a 6 in R3C56 -> 5,6 can be eliminated from R12C5
49. There has to be a 5 or a 6 in R123C4 -> R123C4 = 16 = {268}/{358}/{367}/{457} -> no 1 in R123C4 -> no 8 in R1C3
50. 1 locked in R12C6 for C6, nowhere else
51. 1 locked in R56C4 for C4 and N5 -> no 1 in R6C3 -> no 3 in R4C4 (Step 45)
52. R456C4 = 14 (Step 10) = 1 + 13 (Step 52) -> no 2,3 in R56C4 -> no 6 in R56C4 because there is no 7 in R4C4
53. 1 in N8 is in R79C5 (just stating the obvious)

Maybe I see something else later on.

Peter

[sudokuEd]

Brilliant Peter. I think you've busted this puzzle wide open.
Here's how.
54. we know from step 32 that 5 is locked in r789c3 -> 4 or 7 must be in r789c4 (since r789c34 are linked through 2 9(2) cages or the 12(2) cage
55. ->r123c4 = 16 cannot be {457} (as in step 49) since that would not leave a 4 or 7 for r789c4 -> r123c4 = {268/358/367} = [3/8,5/6...] -> no 4
56. r789c4 = 15 and must contain a 4 or 7 = {249/267/357} =[2/3,2/5, 2/7....}({348/456} are blocked because a 3/8 or 5/6 are needed for r123c4). -> no 8 in r789c4
57. -> 8 in N8 locked in 23(4) cage ->... (somebody else want to take that up - my head hurts too much from all those innies/outies)
58. In r789c4, each combination needs a 7 or 9 which are only available in r9c4 -> r9c4 = {79} -> r9c3 = {35} [edit]