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Archive Part A - Assassins 1-50, variants & other killers

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Sun Jun 08, 2008 11:55 pm

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Old SSv3.2 scores:

Killer rating table      
Rounded Score from SSv3.2  
pg# on this thread
(E) = Easy  (H) = Hard
======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.25              0.80|SKX3              1.35|A.32              0.90|
|A.25v2            1.65|A.30              0.70|A.32v2            0.80|
|A.26       H1.25  1.40|Bullseye3 2.0(t&E)2.15|A.32v3            0.85|
|A.27              0.90|A New One         2.40|                      |
|A.28              0.75|A.31      H1.0    0.95|                      |
|A.29              0.90|Last06   H1.25    1.20|                      |
|====================================================================|
                              page #3

Old scores SSv3.3.0:

Killer rating table      
Rounded Score from SSv3.3.0
! = 0.10 change from previous version of score  
pg# on this thread
(E) = Easy  (H) = Hard
======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.25              0.80|SKX3             !0.90|Last06    H1.25  !1.10|
|A.25v2    H1.00  !2.40|A.30              0.75|A.32             !1.00|
|A.26      H1.25   1.40|Bullseye3   2.0  !3.80|A.32v2           !1.05|
|A.27             !1.05|A New One  H1.5  !3.00|A.32v3           !1.05|
|A.28              0.80|A New Onev2 H1.75 2.05|                      |
|A.29              0.95|A.31       H1.0   0.95|                      |
|====================================================================|
                              page #3

Killer rating table
SudokuSolver Target range v3.6.3

Rating.....Score
0.50   =   0.85
0.75   =   0.90-0.95
1.00   =   1.00-1.20
1.25   =   1.25-1.45
1.50   =   1.50-1.70   (E) = Easy  (H) = Hard

===========================================================================================
|A ##     by     Rate    Score|A ##     by     Rate    Score|A ##     by     Rate    Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.25    Ruud             0.90|SKX3    Ruud             1.10|Last06  Ruud   H1.25     1.25|
|A.25v2  Ed     H1.00     1.85|A.30    Ruud             0.85|A.32    Ruud             1.00|
|A.26    Ruud   H1.25     1.25|Bulls3  Ed      2.0      2.55|A.32v2  frank            1.00|
|A.27    Ruud             1.00|A NewOne nd    H1.5      2.30|A.32v3  Ed               0.95|
|A.28    Ruud             0.90|ANOv2    nd    H1.75     1.70|                             |
|A.29    Ruud             1.05|A.31    Ruud   H1.0      1.20|                             |
|=========================================================================================|
                                         page #3

Assassin 25 by Ruud (Nov 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 7 3 1 | 5 2 4 | 8 9 6 |
| 5 9 4 | 3 8 6 | 7 1 2 |
| 8 2 6 | 1 9 7 | 3 5 4 |
+-------+-------+-------+
| 4 1 5 | 7 6 8 | 9 2 3 |
| 9 8 2 | 4 5 3 | 1 6 7 |
| 6 7 3 | 9 1 2 | 4 8 5 |
+-------+-------+-------+
| 1 6 7 | 8 4 5 | 2 3 9 |
| 3 5 8 | 2 7 9 | 6 4 1 |
| 2 4 9 | 6 3 1 | 5 7 8 |
+-------+-------+-------+

Quote:

PsyMar: I found this one pretty easy -- solved it in under half an hour, without any hints
sudokuEd: Ruud must be going soft on us this week after last week's Tetris

First-ever Walkthrough by PsyMar:

Assassin 25 v2 by sudokuEd (Nov 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 7 3 1 | 5 2 4 | 8 9 6 |
| 5 9 4 | 3 8 6 | 7 1 2 |
| 8 2 6 | 1 9 7 | 3 5 4 |
+-------+-------+-------+
| 4 1 5 | 7 6 8 | 9 2 3 |
| 9 8 2 | 4 5 3 | 1 6 7 |
| 6 7 3 | 9 1 2 | 4 8 5 |
+-------+-------+-------+
| 1 6 7 | 8 4 5 | 2 3 9 |
| 3 5 8 | 2 7 9 | 6 4 1 |
| 2 4 9 | 6 3 1 | 5 7 8 |
+-------+-------+-------+

Quote:

sudokuEd, in lead-in: I found this one a lot harder. But still has a logical solve path
PsyMar: I'll see just how much harder this is...Edit: It's quite a bit harder. Took several hours
Andrew: I'll rate A25V2 at Hard 1.0, rather than 1.0

Walk-through by PsyMar:

Walk-through by Andrew in March '10:

Last edited by Ed on Sat Mar 27, 2010 11:02 pm, edited 8 times in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:02 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 26 by Ruud (Nov 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 6 5 | 4 9 3 | 7 8 1 |
| 1 8 3 | 7 6 2 | 9 4 5 |
| 4 9 7 | 8 1 5 | 2 6 3 |
+-------+-------+-------+
| 8 1 2 | 9 5 4 | 6 3 7 |
| 5 7 4 | 3 2 6 | 8 1 9 |
| 9 3 6 | 1 7 8 | 4 5 2 |
+-------+-------+-------+
| 7 5 1 | 6 8 9 | 3 2 4 |
| 3 2 8 | 5 4 7 | 1 9 6 |
| 6 4 9 | 2 3 1 | 5 7 8 |
+-------+-------+-------+

Quote:

Ruud, lead-in: it is one long stream of innie-outie differences
sudokuEd: More like an annoying drip - This solution is a joint effort between me and Peter. We had a terrible time with this puzzle - got tricked and totally stumped so many times
Andrew, in A27 & A34 threads: for really difficult puzzles such as Assassins.. 26...I haven't finished..
Andrew, in A71 thread: I'm surprised that the SS scores for A26 (0.94)..is that low [edit: see table above for current SSscore]
Andrew, in Jan '09: (had) another go... the breakthrough...was difficult to spot but apart from that A26 wasn't particularly difficult....I'll rate A26 at Hard 1.25 because of step 18.. but (also) IMHO we tend to rate outies (or innies) like 3+1 and 4+1 a bit too low

Joint walkthrough by Nasenbaer & sudokuEd:

Jan '09 Walkthrough by Andrew:

Last edited by Ed on Tue Nov 10, 2009 8:48 am, edited 4 times in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:12 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 27 by Ruud (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 6 8 | 9 1 5 | 7 4 3 |
| 9 7 3 | 4 2 8 | 1 5 6 |
| 4 5 1 | 7 6 3 | 9 2 8 |
+-------+-------+-------+
| 7 1 6 | 5 9 4 | 8 3 2 |
| 5 9 2 | 8 3 6 | 4 7 1 |
| 8 3 4 | 2 7 1 | 5 6 9 |
+-------+-------+-------+
| 3 4 5 | 6 8 9 | 2 1 7 |
| 1 2 9 | 3 5 7 | 6 8 4 |
| 6 8 7 | 1 4 2 | 3 9 5 |
+-------+-------+-------+

Quote:

Ruud, lead-in: This Assassin combines an aesthetically pleasing cage layout with an excellent package of possible solving techniques. It should be named by the first to post a walkthrough
nd: Nothing too fancy, though the overlap technique is needed to make things easier
PsyMar: I'll call this one "Hourglass Sudoku" due to the pattern of the cages.
Andrew: Hourglass is a good title from PsyMar. I'd been thinking of Flower Burst

Walkthrough by nd:

Verbose & newbie-friendly Walkthrough by PsyMar:

Verbose Walk-through for those who don't like elimination solving by Andrew:

Last edited by Ed on Sat Jun 14, 2008 8:55 am, edited 1 time in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:20 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 28 by Ruud (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 9 6 7 | 5 1 3 | 8 4 2 |
| 4 3 2 | 9 6 8 | 7 1 5 |
| 8 1 5 | 4 2 7 | 3 9 6 |
+-------+-------+-------+
| 7 5 8 | 6 9 4 | 2 3 1 |
| 3 9 6 | 2 7 1 | 5 8 4 |
| 2 4 1 | 8 3 5 | 9 6 7 |
+-------+-------+-------+
| 5 2 3 | 1 8 6 | 4 7 9 |
| 6 8 4 | 7 5 9 | 1 2 3 |
| 1 7 9 | 3 4 2 | 6 5 8 |
+-------+-------+-------+

Quote:

Your quote here

Walkthrough by Andrew:

Assassin 29 by Ruud (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 3 2 9 | 8 5 7 | 4 6 1 |
| 5 6 1 | 4 9 3 | 2 8 7 |
| 4 8 7 | 6 2 1 | 5 9 3 |
+-------+-------+-------+
| 9 1 4 | 5 7 8 | 3 2 6 |
| 2 7 5 | 3 1 6 | 9 4 8 |
| 8 3 6 | 9 4 2 | 1 7 5 |
+-------+-------+-------+
| 1 4 3 | 7 6 9 | 8 5 2 |
| 7 5 2 | 1 8 4 | 6 3 9 |
| 6 9 8 | 2 3 5 | 7 1 4 |
+-------+-------+-------+

Quote:

Ruud, lead-in: A chain is running through the center. Lots of quad moves in this Assassin
nd: While this one doesn't require exotic techniques, the endgame requires a fair bit of finesse. I didn't see any spots where chains were needed, though, which Ruud's comment seems to imply
Andrew: started making more use of remaining valid combinations, which I had started doing on some of the more difficult puzzles, although they are not as necessary here... I didn't need any "finesse in the endgame"
Andrew, on A30 thread: I was surprised to find could be solved without using them (innies/outies)

Walkthrough by nd:

While this one doesn't require exotic techniques, the endgame requires a fair bit of finesse. I didn't see any spots where chains were needed, though, which Ruud's comment seems to imply--what spot do you have in mind for this?

1. 15(5) in N8 = {12345}, and the remaining cells of N8 = {6789}. 24(3) in N3 = {789}. 45 rule on R1 => R2C3467 = 10 = {1234}. 45 rule on N147 => R37C4 = 13 => R3C4 = {4567}.

2. 45 rule on N3 => R3C79 = 8 = {26|35}. The 1 in N3 is locked in the 13(4) cage (it's required in all possible combos). 45 rule on N1 => R3C13 = 11 = {29|38|47} ({56} is blocked by the 8(2) cage we just found). 1 in N1 is locked in the 15(4) cage (because it cannot go in the 19(3) cage, obviously). Between the two of them, the 15(4) cage in N1 and 13(4) cage in N3 produce an x-wing on 1 in R12 => 1 is blocked from R12C456.

3. Min. value of each cell in R1C456 = 5, because if any cell in R1C456 were 4 or less the max sum of that cell + R2C46 = 9 and so the remaining two cells would add to 18 or greater, which is impossible.

4. 45 rule on C5 => R159C5 = 9 = {126|135|234} => R1C5 = {56}, R59C5 = {1(2|3)} (locking 1 in those cells in C5).

5. The only place for the 1 in N2 to go is now R3C6! 45 rule on N369 => R7C6 = 9.

6. R6C5 = {345} (difference between 18 and possible sums of remaining two cells = {678}). 45 rule on N5 => R4C5 = {678}. 9 is locked in C5/N2 in R23C5 => R23C5 = {(2|3)9}, R4C5 = {67}.

7. 4 is locked in C5 in R6C5 => R78C5 = {68}, R37C4 = [67], R4C5 = 7, R1C5 = 5, R23C5 = {29}, R2C46 = {34}, R2C37 = {12}, R23C5 = [92], R3C8 = 9, R59C5 = {13}, R1C46 = [87], R2C12 = {56}, R3C2 = 8, R3C79 = R4C7 = {35}, R34C3 = [74], R3C1 = 4.

8. 45 rule on R5 => R5C456 = 10 = {136} or {235}, with 3 locked in those cells in N5/R5. 45 rule on R6789 => R6C46 = 11 = [92], R5C45 = {13}, R5C6 = 6, R4C46 = [58], R34C7 = [53], R3C9 = 3, R4C89 = {26}, R4C12 = {19}. 4 is locked in 21(3) cage in R5C789 => it is {489}, R5C123 = {257}.

9. R6C7 = {17}, R7C7 = {28}. 45 rule on N9 => R7C79 = 10 = {28} => R78C5 = [68]. 45 rule on N7 => R7C13 = {13}, R6C3 = {68}, R7C28 = {45}.

10. 3 is locked in N4/R6 in R6C12 => R7C1 = 1, R6C12 = [83], R67C3 = [63], R1C1 = 3, R9C3 = 8.

11. 45 rule on R9 => R8C3467 = 13 => they can only contain the numbers 1..7 => in C3 the only spot for the 9 is R1C3, R8C3 = {25}, R2C3 = 1, R1C2 = 2, R2C7 = 2, R67C7 = [18], R7C9 = 2, R4C89 = [26], 7 is locked in N9/C7 in R89C7 => the remaining cells of the 18(4) cage = 11 => the 9 cannot go in it => R8C9 = 9, R5C7 = 9, R78C8 = [53], R7C2 = 4, R6C89 = [75], R2C89 = [87], R5C89 = [48]. Only possible combo in the hidden 13(4) cage in R8C3467 = {1246} => R9C7 = 7, R8C6 = 4, and you carry on.....

Walkthrough by Andrew:

Last edited by Ed on Sat Jun 14, 2008 8:57 am, edited 1 time in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:22 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Special Killer X December 16 (aka SKX3) by Ruud (Dec 06)

Puzzle pic: 1-9 cannot repeat on the diagonals; & Solution:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 6 1 3 | 8 7 5 | 2 4 9 |
| 8 5 4 | 3 2 9 | 6 1 7 |
| 9 7 2 | 4 1 6 | 5 8 3 |
+-------+-------+-------+
| 1 3 8 | 9 6 2 | 4 7 5 |
| 4 6 7 | 5 8 1 | 3 9 2 |
| 2 9 5 | 7 3 4 | 1 6 8 |
+-------+-------+-------+
| 5 8 6 | 1 9 3 | 7 2 4 |
| 7 4 1 | 2 5 8 | 9 3 6 |
| 3 2 9 | 6 4 7 | 8 5 1 |
+-------+-------+-------+

Quote:

Ruud, lead-in: A combination of Killer and regular Sudoku techniques is required, unless you manage to find a shortcut that I have missed
Andrew in SKX4 thread: Assassin level

Walkthrough by Andrew:

Last edited by Ed on Sat Jun 14, 2008 8:58 am, edited 2 times in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:36 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 30 by Ruud (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 4 9 | 7 6 8 | 5 3 1 |
| 5 3 6 | 4 9 1 | 2 7 8 |
| 7 1 8 | 3 5 2 | 6 4 9 |
+-------+-------+-------+
| 3 2 1 | 5 8 9 | 7 6 4 |
| 4 8 5 | 6 3 7 | 1 9 2 |
| 9 6 7 | 2 1 4 | 8 5 3 |
+-------+-------+-------+
| 1 7 3 | 8 4 5 | 9 2 6 |
| 8 5 4 | 9 2 6 | 3 1 7 |
| 6 9 2 | 1 7 3 | 4 8 5 |
+-------+-------+-------+

Quote:

Andrew: This one started easily but then kept me thinking. Nice to see that innie/outie differences were back again
sudokuEd: came out a little too easy for my liking
Para: That center nonet is interesting. Putting together all hidden cages gives you a puzzle usually called microsums

Walkthrough by Andrew:

Bullseye 3 (aka A30 V2.1) by sudokuEd (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 8 4 9 | 7 6 2 | 5 3 1 |
| 5 3 6 | 4 9 1 | 8 7 2 |
| 7 1 2 | 3 5 8 | 6 4 9 |
+-------+-------+-------+
| 3 8 1 | 5 2 9 | 7 6 4 |
| 4 2 5 | 6 3 7 | 1 9 8 |
| 9 6 7 | 8 1 4 | 2 5 3 |
+-------+-------+-------+
| 1 7 3 | 2 4 5 | 9 8 6 |
| 2 5 4 | 9 8 6 | 3 1 7 |
| 6 9 8 | 1 7 3 | 4 2 5 |
+-------+-------+-------+

Quote:

sudokuEd, lead-in: a very very difficult V2...requires many contradiction moves between nonets
Para: Had to resort one trick and a "Richard-style 45-tests" but happy with the general result. Those big 45-tests are pretty cool to do, but a monster to analyze, so you have to carefully set your restrictions to get the proper results
Para: I feel it is 1.75 somewhere in the vicinity of A60RP-lite. Some tricky moves and careful analysis did the trick just like A60RP-Lite
sudokuEd: (tag solution) uses 1 hypothetical so should be rated a 2.0. However, Para's solution is much better (just leave out step 27 since it's not needed) ... He uses a 'trick' chain move to unlock it - so I would give a 2.0 rating for Para's WT as well
tag solution: by Caida, sudokuEd & Nasenbaer
2011 Walkthrough by Andrew: I probably wouldn't have posted it if it hadn't been listed as one of the Unsolvables.

Walkthrough by Para:

condensed walkthrough of tag solution by sudokuEd:

2011 Walkthrough by Andrew:

Last edited by Ed on Sat Jun 14, 2008 9:01 am, edited 1 time in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:41 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

A New One (aka nd#10) by nd (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 6 3 8 | 7 9 4 | 5 2 1 |
| 5 9 1 | 6 2 8 | 3 4 7 |
| 7 4 2 | 1 5 3 | 9 8 6 |
+-------+-------+-------+
| 3 2 5 | 9 4 6 | 7 1 8 |
| 4 1 9 | 8 7 2 | 6 5 3 |
| 8 7 6 | 5 3 1 | 4 9 2 |
+-------+-------+-------+
| 9 5 3 | 2 1 7 | 8 6 4 |
| 1 8 4 | 3 6 9 | 2 7 5 |
| 2 6 7 | 4 8 5 | 1 3 9 |
+-------+-------+-------+

Quote:

nd, in lead-in: It's plenty hard
Nasenbaer: It' all going veeeeerrrry slow, not much of a progress
sudokuEd: Finally worked out how to crack this nut. Used my favourite blunt instrument
Andrew: a tough challenge! Really neat key moves
tag solution: Nasenbaer, sudokuEd & Andrew
nd's blog: edit: unfortunately, is no longer available
Andrew (in 2012): After nd#9 (aka Night of the Living Sudoku), I moved on to nd#10 for the first time apart from a minor role in the "tag". This time I found it a lot easier, and also significantly easier than nd#9.
Rating: Hard 1.5.

tag solution:

This looks like a fantastically difficult one, thanks nd.

I've talked to sudokued and we agreed to do this nice killer in a joined effort. We invite all of you to participate. I'll start the whole thing with the obvious things and as explicite as I can.

Walkthrough nd10 "easy"

1. N1 : 12(2) = {39|48|57} -> no 1,2,6
2. N1 : 11(2) = {29|38|47|56} -> no 1
3. N12 : 21(3) = {489|579|678} -> no 1,2,3
4. N2 : 11(2) = {29|38|47|56} -> no 1
5. N2 : 9(3) = {126|135|234} -> no 7,8,9
6. N4 : 9(3) = {126|135|234} -> no 7,8,9
7. N47 : 29(4) = {5789} -> no 1,2,3,4,6
8. N78 : 12(4) = 12{36|45} -> no 7,8,9 -> 1,2 locked -> no 1,2 possible in r7c6

9. N45 : 33(7) = 126{3489|3579|4578}
10. 45 on N9 (3 innies) : r789c7 = 11(3) = {128|137|146|236|245} -> no 9
11. N14 : 19(5) : must have 1, locked in N1 -> no 1 in r4c3
12. 45 on N1 (1 innie, 1 outie) : r4c3 + 3 = r1c3
12a. r1c3 : min: 5, max: 9
12b. r4c3 : min: 2, max: 6
13. 45 on N2 (2 innies, 1 outie) : r1c3 + 4 = r12c6
13a. r1c3 : min: 5, max: 9
13b. r12c6 : min: 9, max: 13
14. 45 on r12 : r2c39 + 9 = r3c78
14a. r2c39 : min: 3, max: 8 -> no 8,9
14b. r3c78 : min: 12, max: 17 -> no 1,2
15. 45 on r123 (1 outie, 2 innies) : r4c3 + 8 = r23c9
15a. r4c3 : min: 2, max: 6
15b. r23c9 : min: 10, max: 14 -> max. r2c9 = 7 -> min r3c9 = 3 -> no 1,2 in r3c9 (edited, thanks Ed)
16. 45 on r1234 : r5c149 = 15(3)

Edit 1: next addition:

17. N69 : 34(6) : must have 9 -> locked in N6 for 34(6) (see also step 10)
18. N56 : 35(6) = 89{1467|2367|2457|3456} -> 9 locked in r4c456 for N5
19. 45 on r123 (3 outies) : r4c3 + r45c9 = 16 (doubles possible!)
19a. r4c3 : min: 2, max: 6
19b. r45c9 : min: 10, max: 14 -> no 1

Edit 2: one more:

20. 45 on r89 (4 innies) : r8c5678 = 24(4)
21. 45 on r789 (3 outies, 1 innie) : r7c7 + 8 = r6c126
21a. r7c7 : min: 5, max: 8 -> no 1,2,3,4
21b. r6c126 : min: 13, max: 16 -> no 5,6,7,8 in r6c6

Edit 3: I think I found some good moves:

22. n9 : (step 10) 11(3) has only one of {5678} -> locked in r7c7 -> r89c7 = {1234}
23. N589 : 19(4) : r6c6 and r8c7 both have {1234} -> r78c6 = {56789} -> no 1,2,3,4 -> combination {1567} for 19(4) not possible
24. r7 : 5,6,7,8,9 are in r7c1267 plus one of them has to be in r7c89 for 17(3) -> no 5,6 in r7c345 possible -> r8c5 = {56} -> no 1,2 in r7c89 (step 8) -> a 3 or a 4 is in r7c89
25. N9 : 17(3) in r78 has at most one of {56789} in r7c89 -> r8c8 = {56789}
26. r8c5 = {56} -> 11(2) in c5 can't have 5,6
27. r8c5 = {56} -> 14(3) in N89 : combination {356} not possible -> one of {789} is in r9c56
28. 45 on N7 (2 innies, 2 outies) : r79c3 + 5 = r6c12
28a. r6c12 : min: 12, max: 17
28b. r79c3 : min: 7, max: 12 -> no 1,2 in r9c3
29. 45 on c12 (3 innies, 1 outie) : r8c3 + 8 = r3c12 + r5c2 (doubles possible!)
29a. r8c3 : min: 1, max: 9
29b. r3c12 + r5c2 : min: 9, max: 17
30. 45 on c12 (1 innie, 4 outies) : r5c2 + 11 = r2348c3
30a. r5c2 : min: 1, max: 9
30b. r2348c3 : min: 12, max: 20

Edit 4: numbering corrected, thanks Andrew.

In r3 might be something going on with 19(4) an 9(3) and the numbers 1,2,3 but now I'm too tired to think because it's 1.30

So, this is how far I got (still not very much):

.-----------.-----------.-----------------------.-----------.-----------.-----------------------------------.
| 23456789  | 345789    | 56789       456789    | 234789    | 123456789 | 123456789   123456789   123456789 |
|           |           :-----------.           |           |           '-----------.           .-----------:
| 23456789  | 345789    | 1234567   | 456789    | 234789    | 123456789   123456789 | 123456789 | 1234567   |
:-----------'-----------'           :-----------'-----------'-----------.           |           |           |
| 123456789   123456789   123456789 | 123456      123456      123456    | 3456789   | 3456789   | 123456789 |
:-----------------------.           :-----------------------------------'-----------'-----------:           |
| 123456      123456    | 23456     | 123456789   123456789   123456789   12345678    12345678  | 2345678   |
|           .-----------'-----------:           .-----------------------.-----------------------:           |
| 123456    | 123456789   123456789 | 12345678  | 12345678    12345678  | 123456789   123456789 | 2345678   |
:-----------'-----------.           '-----------'           .-----------:                       '-----------:
| 5789        5789      | 123456789   12345678    12345678  | 1234      | 123456789   123456789   123456789 |
|                       :-----------------------------------:           |           .-----------------------:
| 5789        5789      | 1234        1234        1234      | 56789     | 5678      | 3456789     3456789   |
:-----------------------'-----------.-----------.           |           '-----------:           .-----------:
| 123456789   123456789   123456789 | 123456789 | 56        | 56789       1234      | 56789     | 123456789 |
|                       .-----------'           :-----------'-----------------------+-----------'           |
| 123456789   123456789 | 3456789     123456789 | 123456789   123456789   1234      | 123456789   123456789 |
'-----------------------'-----------------------'-----------------------------------'-----------------------'

yow - this one is a typical nd Killer. Havn't found the hidden key(s) yet. Thanks for your efforts too Peter. Unfortunately, I can't add too much at this point. But its been fun trying things while listening to James Hirschfeld's tromboning. Hopefully a good sleep will soften up the brain clog.

Just a few more steps to add.

Quote:
15. 45 on r123 (1 outie, 2 innies) : r4c3 + 8 = r23c9
15a. r4c3 : min: 2, max: 6
15b. r23c9 : min: 10, max: 14

add to 15b. max. r2c9 = 7 -> min r3c9 = 3

31. "45" r789 -> r6c6 + 21 = r7c127.
a. max r7c127 = 24 -> max r6c6 = 3 (no 4)
-> r7c127 = 22-24
= 22 = {89[5]/79[6]/59[8]}
= 23 = {89[6]}
= 24 = {89[7]}
->9 locked in r7c12 n7, r7 and also no 9 in r6c12

32. 9 in n4 locked in 33(7) = 12369{48/57}

Not much at all. Sad Tomorrow will have a look at r1234 outies combined with the 33(7):n456. Here is the marks only pic for this spot which can be pasted into Sudocue.

.-----------.-----------.-----------------------.-----------.-----------.-----------------------------------.
| 23456789  | 345789    | 56789       456789    | 234789    | 123456789 | 123456789   123456789   123456789 |
|           |           :-----------.           |           |           '-----------.           .-----------:
| 23456789  | 345789    | 1234567   | 456789    | 234789    | 123456789   123456789 | 123456789 | 1234567   |
:-----------'-----------'           :-----------'-----------'-----------.           |           |           |
| 123456789   123456789   123456789 | 123456      123456      123456    | 3456789   | 3456789   | 3456789   |
:-----------------------.           :-----------------------------------'-----------'-----------:           |
| 123456      123456    | 23456     | 123456789   123456789   123456789   12345678    12345678  | 2345678   |
|           .-----------'-----------:           .-----------------------.-----------------------:           |
| 123456    | 123456789   123456789 | 12345678  | 12345678    12345678  | 123456789   123456789 | 2345678   |
:-----------'-----------.           '-----------'           .-----------:                       '-----------:
| 578         578       | 123456789   12345678    12345678  | 123       | 123456789   123456789   123456789 |
|                       :-----------------------------------:           |           .-----------------------:
| 5789        5789      | 1234        1234        1234      | 5678      | 5678      | 345678      345678    |
:-----------------------'-----------.-----------.           |           '-----------:           .-----------:
| 12345678    12345678    12345678  | 123456789 | 56        | 56789       1234      | 56789     | 123456789 |
|                       .-----------'           :-----------'-----------------------+-----------'           |
| 12345678    12345678  | 345678      123456789 | 123456789   123456789   1234      | 123456789   123456789 |
'-----------------------'-----------------------'-----------------------------------'-----------------------'

Just one step for now; not as useful as I had first thought because of the doubles possibility but still provides a elimination. I'll look at this puzzle again later and try to find some more.

33. 45 on r12 (5 outies, 1 innies) r2c3 + 33 = r3c789 + r45c9, min r3c789 + r45c9 = 34 (doubles possible, for example 7,8 in r3c78 and in r45c9 so doesn't necessarily contain 9)
33a. Max r3c789 + r45c9 = 39 {78789} -> max r2c3 = 6, no 7
33b. Min r3c789 + r45c9 = 34, max r3c789 = 24, min r45c9 = 10
33c. Min r3c789 + r45c9 = 34, max r345c9 = 24, min r3c78 = 10

I think we will need every bit of information, so I do this:

34. step 31 effects step 28: r6c12 : max: 15 -> r79c3 : max: 10
35. (step 20) r8 : 24(4) : {3489} not possible
36. (step 15) r5 : 15(3) : {159|249} not possible
37. 45 on N2 (3 outies) : r1c3 + r23c7 = 20(3) (doubles possible) -> no 1 in r2c7

Edit 1: Veeerrrry slow going. So I'll show every thought I have, even those with no immediate progress.

38. 45 on c9 (1 outie, 3 innies) : r9c8 + 4 = r167c9
38a. r167c9 : min: 6, max: 13
38b. r9c8 : min: 2, max: 9 -> no 1
39. 45 on c9 (3 outies, 2 innies) : r16c9 + 13 = r789c8
39a. r16c9 : min: 3, max: 10
39b. r789c8 : min: 16, max: 23
The following step 40 is actually unnecessary because step 41 is more precise but I invested too much thought in it so it will stay Wink
40. 45 on N78 (2 innies, 3 outies) : r6c6 + r89c7 + 10 = r7c12 (doubles possible)
40a. r6c6 + r89c7 : min: 4, max: 7
40b. r7c12 : min: 14, max: 17
41. 45 on N78 (5 outies) : r6c126 + r89c7 = 19
41a. r6c12 = 12 {57}, 13 {58} or 15 {78}
41b. r6c6 + r89c7 = 4, 6 or 7 (doubles possible)
= 4 = [121]
= 6 = [141]|[1]{23}|[2]{13}|[3]{12}
= 7 = [1]{24}|[232]|[2]{14}|[313]
42. 45 on N78 (4 innies, 1 outie) : r9c7 + 29 = r8c6 + r7c126
42a. r9c7 : min: 1, max: 4
42b. r8c6 + r7c126 : min: 30, max: 33 -> max. r7c127 = 24 -> min. r8c6 = 6

Edit 2: Found a good one, how could I have overlooked it?!? First cell is filled! Breakthrough!?!

43. 45 on c89 (4 outies, 1 innie) : r4c8 + 22 = r1567c7
43a. r4c8 : min: 1, max: 8
43b. r1567c7 : min: 23, max: 30
44. N2 : 9(3) : {234} not possible, one of them is needed in 11(2) -> no 4 in 9(3) -> 1 locked in 9(3) for N2 and r3 -> single in N1 : r2c3 = 1

Peter

Beat me by one minute Peter. Unbelievable that we found the same move at the same time - after how many hours???!

45. 1 in n3 locked in 20(5) -> {23456} lost
45a. 1 in n7 locked in 21(5) -> {23457} lost
45b. 1 required in 33(7) n45 either in n5 or r5c2 -> no 1 in r5c4

One more before I hit the sack (it's already 2 am, the training for tonight isn't going too well Wink )

Addition to 45: must have exactly one of {789} (might be useful); also must also have two of {234} and one of {56} (thanks Andrew)

46. N8 : 1 locked in r7c45 for r7 and N8

Edit: Step 47 was missing, sent it to Ed to check it tonight before I went to bed, wasn't posted yet.

47. 45 on N4578 (4 outies, 1 innie) : r4c3 + 6 = r489c7 + r4c8 (doubles possible)
47a. r4c3 : min: 2, max: 6
47b: r489c7 + r4c8 : min: 8, max: 12 -> min. r489c7 = 6 -> max. r4c8 = 6 -> no 7,8 in r4c8

Finally worked out how to crack this nut. Used my favourite blunt instrument - contradictions between nonets. Anyone find a subtle way to progress?

Thanks again nd! And really enjoyed working with Peter, Andrew and James H.

Now, back to Assassin 31 - totally defeated at the first attempt Very Happy

48. 4 in r4c3 -> r3c123 = {239/257/356} but these are all blocked by 9(3) in r3 -> no 4 in r4c3 -> no 7 in r1c3
[edit-deleted invalid 48a]

49. "45" n1:r4c3 + 3 = r1c3
2 in r4c3 -> r1c3 = 5 -> r3c123 = {349} ({358/457} blocked by r1c3;{367} blocked by 9(3):r3)
3 in r4c3 -> r1c3 = 6 -> r3c123 = {249} ({267/456} blocked by r1c3; {258/456} blocked by 9(3):r3)
5 in r4c3 -> r1c3 = 8 -> r3c123 = {247} ({238} blocked by r1c3; {346} blocked by 9(3):r3)
6 in r4c3 -> r1c3 = 9 -> r3c123 = {345} ({237} blocked by 9(3):r3)

50 . In summary r3c123 = {349/249/247/345} (no 6,8) = 4{39/29/27/35}
50a. 4 locked for n1, r3

51.12(2)n1 = {39/57} = [3/5, 7/9...]
-> from step 50, {345} is blocked from r3c123 -> no 6 in r4c3 (step 49), no 9 in r1c3, no 5 in r3c123

52. r3c123 now 4{39/29/27} = [7/9..] -> Killer pair with 12(2) -> 7 and 9 locked for n1
52a. 11(2)n1 = {38/56}

53. 2 locked in n1 in 19(5) -> 2 locked for r3 and no 2 in r4c3, no 5 in r1c3

54. 9(3)r3 now {135} only: locked for n2, r3

55.11(2):n2 = {29/47} (no 8) = [4/9..]

56. r1c3 + 4 = r12c6 -> r12c6 = 10,12
r1c3 = 6 -> r12c4 = {78} -> r12c6 = 10 = [46] [edit: note, [64] not possible since 6 already in r1c3 in this hypothetical]
r1c3 = 8 -> r12c4 = {67} ({49} blocked by 11(2) step 55) -> r12c6 = 12 = [48] [edit: note, [84] not possible since 8 already in r1c3 in this hypothetical]
-> r1c6 = 4, r2c6 = {68}, r12c4 = {78/67} = 7{6/8} -> 7 locked for n2, c4,11(2) = {29}:locked for c5

57. rest of 24{4}:n23 now 20(3) = [659/839/857] -> r23c7 = [59/39/57], r2c7 = 35, r3c7 = {79}

58. Killer pair between r3c123 & r3c7 for {79}:locked for r3

59. r3c89 = {68} locked for r3, n3

and on till the end! Yippee.

Walkthrough by nd:

I'm typing this quickly as I have to get to bed (up tomorrow for a plane flight) so hopefully it's not got any errors--I'll doublecheck once I get where I'm going (Halifax) & have access to a computer.

1. 29(4) cage in N47 = {5789}. 45 rule on N789 => R7C127 = R6C6 + 21 => R6C6 = {123}, R7C127 = {5..9}, with 9 locked in those cells in R7. 45 rule on N9 => R789C7 = 11(3) => R7C7 = {5678}, R89C7 = {1234}, and the 9 is locked in R7C12 within N7, R7 and the 29(4) cage.

2. R78C6 must contain {5..9} (because of the {1..4} in R6C6 and R8C7). R7C89 must contain one cell of value 5 or greater (because otherwise the max of R7C89 = 3 + 4 which is impossible in a 17(3) cage). So in R7 we have a hidden quint on {56789} in R7C1267 + one of R7C89. Therefore R7C345 = {1234}. Since 12(4) must contain {56}, R8C5 = {56} and {12} are locked in R7C345 within R7.

3. 11(2) cage in N2 = {29|38|47} => 9(3) cage in N2 cannot be {234} => it is {1(26|35)}. R2C3 = 1 (only spot for it now in N1). 45 rule on R3 => R4C3 = {2..6}, R3C789 = 20..24.

4. In N4, 9 must be in the three cells of the 33(7) cage => the 33(7) cage = {12369(48|57)}, i.e. it must contain {123}. Note that the {123} in R6C6 forces one candidate from {123} to be in the three cells R5C23+R6C3 within N4. The 9(3) cage in N4 must also have two candidates from {123}, so in conjunction with the 3 cells of the 33(7) there is a hidden triplet on {123} in N4! => R4C3 = {456}.

5. This in turn means (by 45 rule on R3) that R3C789 = 22..24, i.e. {5..9}. Therefore the 4 in R3 is locked in R3C123 => R4C3 = {56}, R12C2 = {39|57}. 45 rule on N1 => R1C3 = {89}.

6. If R4C3 = 5 then R3C123 = {247} (only possible combo--{346} would conflict with the 9(3) cage in N2). If R4C3 = 6 then R3C123 = {345} (only possible combo). => R3C123 must contain either 5 or 7 => R12C2 = {39}, R1C3 = 8, R12C1 = {56}, R1C123 = {247}, R4C3 = 5, R3C456 = {135}, R3C789 = {689}, R6C12 = {78}, R7C12 = [95].

There's still more to do but it's straightforward mop-up from here on out so I'll leave the rest to you...... -- JC Godart's just posted a walkthrough on DJApe's site which is substantially the same, though he uses a slightly different version of the key hidden-subset move (he uses the split-off 24(4) cage in R8 to narrow things down to a hidden pair of {34} in R7)

Walkthrough by Andrew (in 2012):

A New One (aka nd#10) v2 by nd (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 6 3 8 | 7 9 4 | 5 2 1 |
| 5 9 1 | 6 2 8 | 3 4 7 |
| 7 4 2 | 1 5 3 | 9 8 6 |
+-------+-------+-------+
| 3 2 5 | 9 4 6 | 7 1 8 |
| 4 1 9 | 8 7 2 | 6 5 3 |
| 8 7 6 | 5 3 1 | 4 9 2 |
+-------+-------+-------+
| 9 5 3 | 2 1 7 | 8 6 4 |
| 1 8 4 | 3 6 9 | 2 7 5 |
| 2 6 7 | 4 8 5 | 1 3 9 |
+-------+-------+-------+

Quote:

nd: [just made a minor revision to make it a little more elegant--broke a cage in two]
Note the revision above. However, if people are looking for a REAAAL challenge, then you can "undo" the revision to make a V2--the only difference between the two puzzles is that the 12(2) and 21(3) cages in N12 are joined to make a 33(5).
The new one is solvable via pure logic; the 33(5) version requires some T&E, I believe.

Andrew (in 2012): I've only just spotted that this variant had been posted on Ruud's site. Definitely the hardest of nd's puzzles although #9 came close the way I solved it.
This variant took away a useful "45" without giving anything useful instead.
My solving path used several forcing chains but didn't go as far as T&E.
Rating: Hard 1.75.

Forum "Revisit" thread on this puzzle here

Walkthrough by Andrew (in 2012):

Last edited by Ed on Sat Jun 14, 2008 9:06 am, edited 4 times in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:50 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 31 by Ruud (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 7 5 6 | 9 3 2 | 8 4 1 |
| 9 1 4 | 5 6 8 | 3 2 7 |
| 3 2 8 | 1 4 7 | 5 9 6 |
+-------+-------+-------+
| 4 7 5 | 3 9 1 | 2 6 8 |
| 8 9 3 | 4 2 6 | 1 7 5 |
| 2 6 1 | 7 8 5 | 9 3 4 |
+-------+-------+-------+
| 5 4 2 | 6 1 3 | 7 8 9 |
| 6 8 7 | 2 5 9 | 4 1 3 |
| 1 3 9 | 8 7 4 | 6 5 2 |
+-------+-------+-------+

Quote:

Nasenbaer: This one gave me some headache
sudokuEd: I found this a really tricky Assassin - took 3 attempts to get it properly
Andrew, in A34 & A71 threads: I haven't finished Assassin 31...I'm surprised that the SS score for .. A31 (is) that low (1.00) [edit: see table above for current version of SSscore]
Andrew, Jan '09: This time I found A31 a lot easier...I'll rate A31 as Hard 1.0 .... The current SS score of 0.95 still looks a bit low to me

The way he figured it out Walkthrough by Nasenbaer:

Condensed Nasenbaer's walkthrough by sudokuEd:

Jan '09 Walkthrough by Andrew:

Last edited by Ed on Sat Feb 07, 2009 2:58 am, edited 3 times in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:52 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Last Killer 06 by Ruud (Dec 06)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 4 8 | 6 3 1 | 7 9 5 |
| 3 9 1 | 7 2 5 | 6 8 4 |
| 7 6 5 | 9 4 8 | 3 2 1 |
+-------+-------+-------+
| 4 8 3 | 5 6 9 | 1 7 2 |
| 1 5 2 | 4 8 7 | 9 6 3 |
| 6 7 9 | 2 1 3 | 4 5 8 |
+-------+-------+-------+
| 8 2 4 | 1 7 6 | 5 3 9 |
| 5 3 7 | 8 9 4 | 2 1 6 |
| 9 1 6 | 3 5 2 | 8 4 7 |
+-------+-------+-------+

Quote:

sudokuEd: what a bomb!..this is as far as I can get this one
Nasenbaer: now I'm stuck. Has anybody a new idea?
Para: this is a really crude step, not pretty but effective
Para: On A32 thread: not getting any progress in the "Last Killer 2006"
tag solution: by sudokuEd, Nasenbaer, rcbroughton & Para
Many thanks Andrew for corrections/clarifications
Andrew in 2011: This puzzle probably had a fairly narrow solving path; my breakthrough was in the same area is in the "tag" solution. I'll rate my walkthrough.... at Hard 1.25; I only had a couple of heavier steps

Condensed Walkthrough by sudokuEd:

2011 walkthrough by Andrew:

Last edited by Ed on Sat Jun 14, 2008 9:09 am, edited 1 time in total.

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Post subject: Re: Assassin Archive & Ratings Update

Posted: Mon Jun 09, 2008 12:59 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 32 by Ruud (Jan 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 1 8 | 9 3 5 | 4 6 7 |
| 6 3 4 | 7 2 1 | 5 9 8 |
| 9 5 7 | 8 4 6 | 2 3 1 |
+-------+-------+-------+
| 4 8 3 | 6 9 7 | 1 2 5 |
| 1 7 6 | 2 5 3 | 9 8 4 |
| 5 2 9 | 4 1 8 | 6 7 3 |
+-------+-------+-------+
| 7 4 1 | 3 6 2 | 8 5 9 |
| 8 6 5 | 1 7 9 | 3 4 2 |
| 3 9 2 | 5 8 4 | 7 1 6 |
+-------+-------+-------+

Quote:

Nasenbaer: After a hard days work on Ruud's "Last Killer 2006" with sudokued, rcbroughton and Para (I had a lot of fun there) Assassin 32 was almost relaxing
Para: Did 32 to relax after not getting any progress in the "Last Killer 2006"
Andrew: (found) a couple of interesting moves which I wouldn't have found if I had followed a more direct solving path..(the) variants on Assassin 32 (were) Both definitely harder than Ruud's original

Walk-through by Nasenbaer:

Walkthrough by Andrew using clean-up steps (like Nasenbaer's):

Assassin 32 V2 by frank (Jan 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 1 8 | 9 3 5 | 4 6 7 |
| 6 3 4 | 7 2 1 | 5 9 8 |
| 9 5 7 | 8 4 6 | 2 3 1 |
+-------+-------+-------+
| 4 8 3 | 6 9 7 | 1 2 5 |
| 1 7 6 | 2 5 3 | 9 8 4 |
| 5 2 9 | 4 1 8 | 6 7 3 |
+-------+-------+-------+
| 7 4 1 | 3 6 2 | 8 5 9 |
| 8 6 5 | 1 7 9 | 3 4 2 |
| 3 9 2 | 5 8 4 | 7 1 6 |
+-------+-------+-------+

Quote:

frank, lead-in: I found it a very slow start, and then once I got the first few numbers the rest were easy
sudokuEd: does finish surprisingly quick, but did take a while to get to there
Andrew: definitely harder than Ruud's original puzzle...I found it the harder of the two variants

Walk-through by Andrew:

Assassin 32 v3 by sudokuEd (Jan 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 7 5 1 | 8 4 3 | 9 2 6 |
| 6 9 3 | 2 5 7 | 8 4 1 |
| 4 8 2 | 1 9 6 | 5 3 7 |
+-------+-------+-------+
| 8 1 6 | 7 3 5 | 2 9 4 |
| 3 2 4 | 9 8 1 | 6 7 5 |
| 9 7 5 | 6 2 4 | 3 1 8 |
+-------+-------+-------+
| 5 4 7 | 3 6 9 | 1 8 2 |
| 1 3 8 | 5 7 2 | 4 6 9 |
| 2 6 9 | 4 1 8 | 7 5 3 |
+-------+-------+-------+

Quote:

sudokuEd, lead-in: Faster start than Frank's, but then makes you work a bit harder in the middle
frank: got off to a fast start.... but then had to work hard as you predicted. Eventully I found a key to unlock the brute, and then sailed through the rest
Andrew: definitely harder than Ruud's original puzzle

Walkthrough by Andrew:

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