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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Fri Jun 17, 2011 10:46 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

SOK (Special Occasion Killer) 2 by Nasenbaer (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Nasenbaer: Due to my computer meltdown I couldn't realize this Special Occasion Killer earlier. It should have been posted during the Olympic Games 2008. So now have a look at the Olympic flag and remember all the glorious moments.
Rating SSolver: 1.25.
Too hard??? Here's a hint: ***SPOILER*** Each ring was designed as a single cage, so no repetitions in the two cages it has now.
Have fun!

Børge: Hopefully there are no IOC members among the visitors here. The IOC is extremely protective of their symbols. Here a screen shot from en.wikipedia.org/wiki/Olympic_rings

This is the reason for my 8 ring sudoku. If you remove the 3 bottom rings and apply the correct colours, you have the 5 OL rings.

Afmob: Thanks for this fun killer! Nice cage pattern, too.
SudokuSolver's rating is so high because even though it spots step 2a, it didn't apply step 2c afterwards but decided to continue with some more difficult moves.
Rating: 1.0.

Andrew: Thanks Nasenbaer for a fun puzzle with an interesting cage pattern.
I'll also rate SOK 2 at 1.0.
I was intrigued by Nasenbaer's hidden hint. I set up a diagram with the appropriate 4-cell cages combined into rings and quickly realised that this appeared to make an extremely difficult puzzle because it took away most of the moves that Afmob and I used so I'm not planning to try to solve it. Just out of curiosity does anyone know what the SS score is with the five rings as 8-cell cages? Edit. I've now been told that combining those cages wouldn't give a unique solution so obviously it can't then have a score.

Walkthrough by Afmob:

Walkthrough by Andrew:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Fri Jun 17, 2011 10:52 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Old SSv3.2.1 scores:

Score = SudokuSolver v3.2.1 Score, rounded to nearest 0.05
E = Easy
H = Hard
In these tables, Rating is the lowest of the ratings given by Afmob,
Andrew and Mike, including estimates for puzzles by Afmob and Mike

+--------------------------+--------------------------+--------------------------+
| Puzzle    Rating   Score | Puzzle    Rating   Score | Puzzle    Rating   Score |
+--------------------------+--------------------------+--------------------------+
| A120       1.25     1.25 | HS3x       1.50     2.00 | A123      H1.25     2.50 |
| A120V2    H1.50          | A122       1.00     1.65 | A123V0.9   1.25     1.55 |
| A121       1.00     1.20 | A122V1.5   1.25     1.85 | A123V2     2.00     2.70 |
+--------------------------+--------------------------+--------------------------+

Puzzle rating table, with links to archive entries; each of these has a link to the puzzle thread.
Assassin 123 "Roulette" and Assassin 123 "Roulette" V0.9 are in the same archive entry.

Abbreviations used in Rating Table on this page:

+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Puzzle                 |  Made By  |  Est  | Afmob | Andrew|     Other Raters      | Score |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+
| Ass. 120 "Twin Towers" |    Ed     |  1.25 | E1.25 |  1.25 |                       |  1.35 |
| Assassin 120V2         |    Ed     |       | H1.50 |  1.75 |(Ed)1.75               |  3.70 |
| Assassin 121           | Nasenbaer |  1.00 |  1.00 | H1.00 |                       |  1.20 |
| Assassin 121V2         | Nasenbaer |  1.25 |  1.25 |  1.25 |                       |  1.30 |
| Human Solvable 3X      |  HATMAN   | H0.75 |  1.50 |  1.50 |(N)1.50(Ed)1.50        |!R3.65 |
| Assassin 122           |   Afmob   |  1.00 |   **  |  1.25 |(Ed)H1.0               |  1.85 |
| Assassin 122V1.5       |   Afmob   | H1.25 |   **  |  1.25 |                       |  1.90 |
| Ass. 123 "Roulette"    |  udosuk   |       | H1.25 |       |(Ed)E1.50              |!R3.25 |
| Assassin A123V0.9      |  udosuk   |       |       |  1.25 |                       |  1.55 |
| Assassin 123V2         |  udosuk   |       |  2.00 |  2.50 |                       |!R3.85 |
+------------------------+-----------+-------+-------+-------+-----------------------+-------+

Some of the selected quotes in the puzzle entries have been edited to remove "spoilers"; the full rating comments are included with the walkthroughs. In some cases the puzzle makers gave hints; these are included in tiny text in the selected quotes.

Last edited by Andrew on Thu Jan 26, 2012 4:38 am, edited 4 times in total.

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Thu Jul 07, 2011 3:07 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 120 Twin Towers by Ed (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed (after posting the V2 first): :bigoops:

Sorry guys. Goofed badly. Did a double-check after seeing Afmob needed forcing chains and found a really silly mistake. Back to plan A! I'll make the first one the V2.

Ed (on the V1): This time the Twins are not quite identical.
Estimated rating of 1.25. SS(V3.2.1)score = 1.27. JSudoku = "15 guesses".
[edit: forgot to say welcome to herschko!]
Enjoy this time!

Andrew: Thanks Ed. Great timing. I'd reached the stage with what is now the V2 ...
The SS score looks spot on. I'll rate A120 at 1.25.

Afmob: It seems that the most important move is ...
BTW, welcome herschko!
Rating: Easy 1.25.

Walkthrough by Andrew:

Walkthrough by Afmob:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Thu Jul 07, 2011 5:34 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 120 V2 by Ed (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: Change of plan.

I enjoyed this "V2" so much it's now "V1"! [edit: back to being the V2. A120 follows]. I have the old one ready to go, so if anyone is desperate for an easier one (though no pushover) I can post that also [Gone: see below]. But only if asked for.
The cage design was inspired by a solving strategy idea, which didn't work for this one. Inadvertently ended up with the Twin Towers! Still have vivid memories of that terrible day 7 years ago.
I'll give it an estimated rating of "old-style" 1.50 (ie Weekly Assassin level 1.5..and yes, still bothered by the "new" 1.5). You don't want to know the SSscore. It's so far wrong it's not worth publishing. :oops:

Instead, JSudoku, after "recursively solve" says, "17 guesses". I normally look for "16 guesses" to (often) get an SSscore of around 1.25. Hence, didn't throw the "17 guesses" one out. Boy, am I glad. Gremlins fixed.

herschko: This was a hard one for me.

Afmob: What a challenging Killer!
It took me quite some time to find the breakthrough move ...
Rating: (Hard) 1.5.

Andrew (in 2010): I'll rate my walkthrough for A120 V2 at 1.75 because I found this puzzle almost as hard as A108 V2 which I finished recently.

herschko's key step:

Walkthrough by Afmob:

Ed's Analysis of Afmob's Key Steps:

Walkthrough by Andrew in 2010:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Fri Jul 08, 2011 4:49 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 121 by Nasenbaer (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Nasenbaer: This week a little bit earlier than usual so you guys in Australia have something for breakfast)

I almost changed my plan for this weeks Assassin because of a new one that just popped up (rating: 1.5). It would be really great for a v2 but time is running short and I'm still working on a v1 so it will have to wait.

But don't be disappointed, this newborn killer is already reciting Arnold Schwarzenegger: "I'll be back!" :twisted:

But first you'll have to work on this one. Nothing fancy (except that it is a Killer X), just good old basic stuff. :whistle:

Rating SSolver(3.2.1): 1.20. My personal rating: 1.0
V2 is already waiting to be posted.
Have fun!

Andrew: Thanks Nasenbaer for a fun puzzle! I look forward to V2.
I'll rate A121 at Hard 1.0.

Afmob: Thanks Nasenbaer for this fun killer!
Rating: 1.0.
Nasenbaer: Wonderful! Two different walkthroughs in such a short time! Bravo! :applause:

And we can always rely on Afmob to produce a brilliant move (step 1j) that shortens the solving path. :cheesey:

Walkthrough by Andrew:

Walkthrough by Afmob:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Fri Jul 08, 2011 4:59 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 121 V2 by Nasenbaer (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Nasenbaer: This version has the same solution but a slightly altered cage pattern which removes the easy start from v1. It's only slightly harder than v1. Maybe I should have called it v1.5. Oh well.
Rating SSolver(3.2.1): 1.31. My personal rating: 1.25
(I would have liked to join the cages 15(2) @ r5c3 and 12(2) @ r6c4 because of the symmetry but that would produce a rating of 2.64 with extended T&E)

Have fun!

Afmob: Like Nasenbaer said A121 V2 is more a V1.5 than a V2 but fun nonetheless. Thanks Nasenbaer!
I checked SudokuSolver's and JSudoku's solving path and it seems quite narrow though my ...

Andrew: Thanks Nasenbaer. Another enjoyable variant. As you said the cage changes took away the early entry ...
My impression after going through Afmob's walkthrough and mine is that it can't be too narrow ... I'll assume the comment meant that Afmob's solving path was very similar to that used by Sudoku Solver and JSudoku. Mine looks very different.
I'll also rate A121 V2 at 1.25.

Walkthrough by Afmob:

Walkthrough by Andrew:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Mon Jul 11, 2011 4:58 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Human Solvable 3X by HATMAN (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

HATMAN: Quite interesting JSudoku takes about 23 fishes (afmob points out that my version is not the latest, so) Sudoku Solver gives 2.01 with T&E which is very high, I'd put my solution below 1.0.

Nasenbaer: That was a very interesting puzzle, HATMAN. Thanks a lot! ;clapclap;

HATMAN: sketch of solution:
How did you find the difficulty? It was very hard to create. I had the basic idea but more than ten attempts before I could get one that I could solve without the computer finding it easy.
I'll create some less taxing ones for now. Hopefully someone will do it more neatly.

Afmob: Thanks for this interesting Killer!
Though all walkthroughs posted so far are quite short the moves themselves are advanced ... Rating: 1.5.

udosuk: This rating thing is a joke. :rambo:

From now on (after this post) I've decided I'm not talking about any numerical rating anymore.
The "experts" might rate my step 4 as 1.5 or 15.0 or whatever but for me the only "rating" is this: EASY
It is EASIER than most recent assassins which were rated 1.25. So a rating of 1.5 looks ridiculous to me, no matter what the "experts" claim. End of argument. :evil:

Lastly, here is another curious observation about the puzzle:

Andrew: For that reason I'll rate my solution as 1.5. However that doesn't mean that HS3 should be rated as 1.5.

Andrew: udosuk was the only one of us to spot that :applause:

although with hindsight it's not that difficult.
was the most difficult move, even though it may have been obvious to intuitive solvers.

HATMAN: Andrew. Thank you for your classification as solvers as “intuitive” as opposed to “detailed”. In many ways that is the core of the problem, when I occasionally solve an assassin it is because I have grasped some odd relationship (particularly multiple innies/outies – which is one of my few strengths) , hence intuitively solved it.

There was a lot more discussion about ratings, and some discussion about grammar/style. If you are interested, please read the full thread here

Walkthrough by Nasenbaer:

HATMAN's sketch of solution:

Walkthrough by Afmob:

Nasenbaer's comments on the earlier posts:

Andrew's general comment on the rating:

Walkthrough by udosuk:

HATMAN's general observations:

Walkthrough by Andrew:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Mon Jul 11, 2011 5:55 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 122 by Afmob (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Afmob: Apart from the remote cage that I had to put in for reasons of difficulty, this Killer came out just right. Like A116 this is also a concept Killer though there is no symbol used here but if you want you can look for hidden signs. :lol:

And don't listen to the software rating (JSudoku has problems with A122, too)! This one can be solved in a matter of seconds (though minutes is more realistic).
SS Score: 1.63. Estimated rating: 1.0.
A tougher version with perfect symmetry will be posted on Sunday.

udosuk: It seems these days the common goal is to attack the weakness of JSudoku... :ugeek:

Next week you'll get an assassin with a similar cage layout, but I'm sure it's just a pure coincidence! :alien:

Andrew: When I coloured the cages, the pattern looked like a flower.
I assume you mean that the breakthrough can be achieved in that time. Congratulations to everyone who does that! Unfortunately I didn't. It took me about 2 hours until I eventually spotted the breakthrough and then about another hour to complete my walkthrough. Still I'm not a quick solver.
I'm surprised at the SS rating. I'll rate A122 at 1.25 the way I solved it. If one gets the breakthrough move early then it's probably Hard 1.0.

Joe Casey: Thank you Afmob! A new first for me

Ed: Thanks for these very enjoyable puzzles Afmob. Feel very happy to have found the break-through tricks relatively easily for both these, though not as elegantly as Andrew for V1.5.
To celebrate, here's a full walkthrough for the V1 using Andrew's V1.5 beginning. 8-)

I see now that udosuk started the V1 this way too :applause:

. Sounds like Joe-Casey got the step 1 part. Great! Any chance of a walkthrough next time?

I'll rate the V1 as a Hard 1.0 based mostly on the first 2 steps.

udosuk's critical step:

Walkthrough by Andrew:

Joe Casey's note:

Ed's walkthrough:

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Mon Jul 11, 2011 6:13 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 122 V1.5 by Afmob (September 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Afmob: This Killer has an easy start but it gets tougher as you progress. Have fun with it and don't think that (only) the cracking move from V1 will solve it for you!
SS Score: 1.84. Estimated rating: 1.25 - (Hard) 1.25.

Para: Funny fact about V2. Remove the diagonals and it scores lower in SudokuSolver.

Andrew: Thanks Afmob for a nice variant. As you say there is more work after the cracking move for V1 and its logical extension which gives the first placement.
I'll rate A122 V1.5 at 1.25. Maybe that's a bit high but I'll stick with it because ...
And on Para's comment That surprises me. It must be something about the order of doing moves. It looks to me as if it would make this puzzle much harder because ...

udosuk: I suspect if you put the priority of the ... techniques (provided they're there) higher it would score much lower with diagonals.
Meanwhile, here is my walkthrough for the "non-diagonal" version. I don't think it's that much harder than the one using diagonals (see Andrew's walkthrough above) but you need to think "instinctively/intuitively" and think outside of the way a computer thinks to appreciate my tricks.

Walkthrough by Andrew:

udosuk's walkthrough (without using diagonals):

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Andrew

Post subject: Archive Part D. Assassins 101-125, variants, other puzzles

Posted: Thu Jul 14, 2011 4:56 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Assassin 123 "Roulette" by udosuk (October 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

udosuk: SSR: 2.51 :!:

"True" SSR: 1.26.
Bear in mind all puzzles in this thread which I have posted or will post are valid ones. Use this information smartly this puzzle can be solved without any fish or chain (corresponding to the "true" SSR). :ugeek:

Good luck! V2 will be posted when (if) this thread (ever) gets to page 2, or one week later. :alien:

(Added later: A hearty note of thanks to Ed, who helped immensely on the SSR department. Good on you mate! :mrgreen:

Although personally I'm not into the "personal rating system", I don't oppose to anyone posting a (subjective) personal rating on this puzzle or his/her own walkthrough. :geek:

)

Afmob: Thanks for this week's Assassin!
It took me quite some time to find the first breakthrough move (step 2d) but after that I found the final cracking move (step 3d) in no time ...
By the way, V2 shouldn't be posted later than this mid-week since in one week the next Assassin awaits.
Rating: (Hard) 1.25.

udosuk: Nice work Afmob. ;clapclap;

I can understand every move you did in step 2, but I probably will never do it that way myself, just like you'll probably never do it my way. And that's perfectly fine because everyone has a unique style of his/her own, right?

Your step 3d is exactly how I picked as my "critical step". (Although I used a totally different way to get to that stage - you guys will see how later.) So congrats for spotting it! :thumbs:

I'll post v2 no earlier than Wednesday. Hopefully some others will have made more responses about v1 and v0.9 by then.

Para: This puzzle has a special property, which i can't really explain properly. Just something i noticed. Pretty sure udosuk had it in mind. (see below for full explanation)

Ed: Thanks udosuk for a really interesting puzzle! Sounds like Para has worked out why the "true" SSR is 1.25! Don't really understand it yet!
Here's another way to solve Assassin 123. I really like this way 8-)

.

Andrew: Having got stuck on A123 I went back to it about 3-4 weeks later and managed to solve it then. However I've only just gone through Afmob's and Ed's posted walkthroughs.
My solving path was much more like Afmob's than Ed's but I took much longer to find the breakthrough moves so there are some heavier moves before each of them.
Ed's breakthrough step 7 was neat!
... but I'm not going to give a rating for it since it's clearly harder than either of the earlier ones.

Walkthrough by Afmob:

Para's Comment on Special Property:

Walkthrough by Ed:

Discussion/Explanation of the Special Property and udosuk's comments on walkthroughs:

udosuk wrote:

Guys, gone through all your nice walkthroughs. Excellent work all around! :applause:

Andrew, thanks for your considerate decision to limit your combo crunching. :thumbs:

I mostly have problems with deep crunching of 4- or 5-cell groups so for this puzzle (mostly 3-cell groups) there shouldn't be any issues anyway. However you don't need to change your style for me, just go ahead with your most comfortable moves for all future puzzles!

Note your walkthrough also demonstrates most the property as observed by Para, with most moves applied coming in "pairs".

Ed, really ingenious breakthrough move in your step 7! :applause:

This makes your walkthrough the most elegant one posted so far. The trick I used myself (as observed by Para), despite being simpler, has to make use of the uniqueness property so your approach should be the better one. Hopefully you can find a similar brilliant cracking move in v2 which I'll release some time on or after tomorrow. :mrgreen:

Para, I'll do a pictorial explanation about that property later. Everyone should be able to see it clearly. :alien:

azpaull wrote:

Wowwwww. I've been struggling with v0.9, and thought I'd drop by to see what the discussion was. I suspected exactly what you described, para (I even had also used the term "rotationally symmetric" yesterday); but, I hadn't been able to figure it out. I'm looking forward to your pictorial explanation, udo.

Thanks again, to all of you.

Andrew wrote:

Since I'm stuck again on A123 I had a peek at Para's hidden message.

I can see what he's saying but I don't know that I'm convinced by the whole argument or that R5C5 is fixed immediately. It seems to me very much like UR, which some people use but by doing so avoid solving the whole puzzle.

I hope there are reasonable ways of solving A123 without needing to use this shortcut.

There are statements that the "true SS score" for this puzzle is about 1.25. Are they on the assumption that R5C5 is fixed immediately and working from there? I don't know what the rating of Para's suggestion is but I'd be surprised if it isn't considerably higher than 1.25. Of course if, in future, it becomes an established and well known technique then it might then get a lower rating but that wouldn't be appropriate at the moment with it not being widely known or understood.

Maybe udosuk will be able to show us how "rotationally symmetric", which azpaull uses in his message, leads logically to what Para said without relying in any way on uniqueness. That would certainly help it to become an established and well known technique.

BTW I did spot one interesting feature in the cage diagram. The outer cages total 180 making R19C19 = R28C28 but this doesn't seem to lead to anything useful.

Para wrote:

Don't see it as a technique. It's just an observation, which completely depends on the cage totals. I mean it only happens if the person who made the puzzle designs it that way on purpose. This also means you have to have a certain looking solution. That is also why udosuk has a puzzle with the same solution and a different cage pattern instead of a different solution in the same cage pattern. (well this is my assumption of course).

udosuk wrote:

Okay, here is a brief graphical explanation:

Firstly, in the solution grid, label each cell value A11 to A99 as the following:

Now, subtract each of these values from 10, and rotate the whole grid 180 degrees:

We know the cage structure in the original grid also applies in this new grid, because if two cells belong in the same cage in the original grid, they must also belong to the same cage in the new grid.

Now what do you notice about the cage sums in the new grid?

Yes, we can work them all out algebraically. For example, the cage sum at r1c456 in the new grid = (10-A96)+(10-A95)+(10-A94) = 30-(A94+A95+A96) = 30-24 = 6.

(We know A94+A95+A96 = 24 from cage at r9c456 in the original grid.)

So, working all the new cage sums out, we obtain the following grid:

Just take a look at all the cage sums, they are the exact copy of the original puzzle! :idea:

Because the original puzzle is a valid puzzle, we can immediately determine all the 81 cell values of this new grid. For example:

10-A99 = A11
10-A98 = A12
...

In particular:
10-A55 = A55
=> 2 A55 = 10
=> A55 = 5

Also this is an established technique in Vanilla Sudoku. Check out this thread. :ugeek:

Ed wrote:

OK, hmm. Thanks for all the work to make up the pics udosuk. I don't really understand it (or the link) yet... from what I can work out, as Para says and udosuk has implied, more like an interesting feature rather than a technique as such.

Don't know if this is related or not, but "45" rule on r1 + r9 + c1 + c9 = r2c2 + r2c8 + r8c2 + r8c8 = 180. Combined with the 45(9) cage that runs along the diagonals, does this imply that 1-9 cannot repeat on the diagonals? Does this make it an implied Diagonals puzzle? I can't see that it does. Don't see how this would help get r5c5 placed for example. (Note: it is "diagonal" since V2X has the same solution).

My main reason for this post is to follow up to my earlier rating of Afmob's step 2 in his Assassin 123 Walkthrough. By PM, Afmob asked, quite rightly, what I found difficult in his step 2. In actual fact, it's not as difficult as I first thought. :cheers:

So, I'll withdraw that rating. Though steps 2 e & j still seem above the average Weekly Assassin and I never found them. Which is also why I called my solution (not udosuk's trick above!) an Easy 1.50. My key move is more like a one-off for this puzzle and could easily be missed. Of course, if most people found it, then it's average!! And my rating's wrong. But, it is finding this sort of trick that keeps me comin' back for more

(though won't be trying A123 V2: lots of T&E according to the SS log). Bring it on Frank... A nice Canadian Thanksgiving puzzle perhaps...?

udosuk wrote:

Ed wrote:

Hopefully others can see it better. I'm not sure if I can explain it more clearly. :bouncy:

Ed wrote:

Don't know if this is related or not, but "45" rule on r1 + r9 + c1 + c9 = r2c2 + r2c8 + r8c2 + r8c8 = 180. Combined with the 45(9) cage that runs along the diagonals, does this imply that 1-9 cannot repeat on the diagonals? Does this make it an implied Diagonals puzzle? I can't see that it does. Don't see how this would help get r5c5 placed for example. (Note: it is "diagonal" since V2X has the same solution).

With my symmetry property, r28c28 always sums to 20. And no it doesn't (directly) imply the diagonals must have no repeat. You only know r19c19 & r28c28 both consist of two pairs from {19|28|37|46|55}. Initially you can't even eliminate the possibilities of say, \19=\28. I think you're on the totally wrong track if you want to "see" the fact r5c5=5 from the X property.

Ed wrote:

My main reason for this post is to follow up to my earlier rating of Afmob's step 2 in his Assassin 123 Walkthrough. By PM, Afmob asked, quite rightly, what I found difficult in his step 2. In actual fact, it's not as difficult as I first thought. :cheers:

So, I'll withdraw that rating. Though steps 2 e & j still seem above the average Weekly Assassin and I never found them.

I already mentioned, all the moves in step 2 can be understood (fairly) easily, but it's a matter of whether you actually want to apply them. I think (at least for me) elegancy is an important factor. For example, the relationship 7 = R1469C3 - R5C2 (and the subsequent crunching deductions) feels not as elegant as your establishment one of r37c7 = r4c5 (I dubbed this move "cell cloning" although you've outdone me in using a "one of two cells cloning" :thumbs:

). Of course, it's all a matter of personal taste. I always think cracking moves involving fewer cells are more elegant than ones involving more cells. In this case the "cells involved" ratio is 5:3. However, if for some the process of sitting in front of the computer for a few minutes to crunch on a 5-cell group gives them the hots, I have nothing against that. :ugeek:

Ed wrote:

Which is also why I called my solution (not udosuk's trick above!) an Easy 1.50. My key move is more like a one-off for this puzzle and could easily be missed. Of course, if most people found it, then it's average!! And my rating's wrong. But, it is finding this sort of trick that keeps me comin' back for more

(though won't be trying A123 V2: lots of T&E according to the SS log).

I decided I'm not commenting on any personal rating anymore myself, but I think you need to make up your mind here. Which do you want to choose as your measurement, easiness/difficulty of the spotting of cracking moves, or simplicity/elegancy of the logic involved? :geek:

Andrew wrote:

Thanks udosuk for a very clear explanation about how Rotational Symmetry works for this puzzle. It clearly only works for the very few cases where the cage pattern is symmetrical about the centre cell and all the cage totals are complementary except, of course, the cage containing the centre cell. I take this to mean that the totals of a complementary pair of cages, for example 17(3) cage at R2C3 and 13(3) cage at R7C6, must total 10 times the number of cells in each of those cages. This brief description appears to be a way that it can be recognised by a software solver, if the programmer considers it worth including for the very occasional cases where it appears; however it could well be a situation that will appear more in the future. Edit. However after looking at Gurth's Symmetrical Placement on the linked thread, maybe it's not as simple as I thought above, unless there is something specific for Killers that makes what I've said above correct. udosuk, please tell me whether I was right or wrong. In any case I'll leave my above statement as it is, even if it is wrong.

Unlike Ed, I've got no problem in accepting it as a technique. It's clearly logical. udosuk has told us that it's an established technique for Vanilla Sudoku. My first reaction to that was that it is an advanced technique but then I realised that most/all advanced techniques for Vanilla Sudoku start with a "what if" assumption whereas Rotational Symmetry is completely logical.

udosuk wrote:

Andrew wrote:

Thanks for confirming that I've explained it at least clear enough for some. :alien:

You're right that this technique only works for the few puzzles that display symmetry. However if the property is there it doesn't hurt to use it. For example, for a puzzle that isn't specified as an X puzzle, if you can somehow deduce that one or both of the diagonals must have no repeat, I don't see any problem to apply diagonal techniques (e.g. CPE) on your solving path. However, most randomly generated puzzles don't have non-repeating diagonals, just as most randomly generated puzzles don't have symmetry. If one decides to only use techniques that can apply to *all* puzzles, that's his/her personal choice but I'd think such a mindset is too narrow-sighted. :ugeek:

Andrew wrote:

I take this to mean that the totals of a complementary pair of cages, for example 17(3) cage at R2C3 and 13(3) cage at R7C6, must total 10 times the number of cells in each of those cages.

Spot on!

Andrew wrote:

This brief description appears to be a way that it can be recognised by a software solver, if the programmer considers it worth including for the very occasional cases where it appears; however it could well be a situation that will appear more in the future.

Yes, of course it's not difficult at all to be implemented into a program. It's up to the programmers (e.g. Richard, JC) if they want to implement it as it is rarely occured in randomly generated puzzles. As a matter of fact there are 5 main categories of symmetry (aka automorphism) in Sudoku puzzles (rotation is just one of them) and they each have quite different characteristics. There is a lot of info available in the sudoku.com forums but unless someone shows more interest I'll spare you all the (quite intimidating) details. :geek:

Andrew wrote:

Edit. However after looking at Gurth's Symmetrical Placement on the linked thread, maybe it's not as simple as I thought above, unless there is something specific for Killers that makes what I've said above correct. udosuk, please tell me whether I was right or wrong. In any case I'll leave my above statement as it is, even if it is wrong.

What you said above is perfectly correct. However, in vanilla puzzles you can freely permute the 9 digits so the "opposite cells must sum to 10" constraint is no longer necessary. For example, you can have {13|25|49|68|77} as the opposite pairs. In this case r5c5 must be the self-mapping digit, i.e. 7. But in killer puzzles I don't see any obvious pairing other than {19|28|37|46|55} (I call this the "orthodox" pairing) to easily transfer the symmetry to the cage sums.

Andrew wrote:

Unlike Ed, I've got no problem in accepting it as a technique. It's clearly logical. udosuk has told us that it's an established technique for Vanilla Sudoku. My first reaction to that was that it is an advanced technique but then I realised that most/all advanced techniques for Vanilla Sudoku start with a "what if" assumption whereas Rotational Symmetry is completely logical.

Thanks for accepting the technique! :salute:

Everyone has his/her own taste and limitation of what techniques/methods he/she would choose to use. Some people simply refuse to use any techniques related to the uniqueness/validity of the puzzle and consider it a disgrace to use the extra help from this information. Some people don't use elimination solving and only solve the puzzle from a completely blank grid. Some people even refuse to use pencilmarks and only do it using pen and paper. But there are too many puzzles out there to suit everyone's own scope of acceptable puzzles so if it happens to be out of your scope just feel free to ignore it. :ok:

Life is too short to waste time on every puzzle out there!

Andrew wrote:

Earlier in this thread I wrote:

Thinking further about that I'd like to qualify my acceptance slightly.

If the uniqueness is as a result of the complete rotational symmetry then I think I would find this technique acceptable although I'm not sure whether I'd use it. My A123 walkthrough in the previous message didn't use it. However if the uniqueness is only because a software solver has checked and said that a puzzle has a unique solution, then I would consider it to be like a UR and definitely wouldn't use it.

Can udosuk, or anyone else, please tell us whether the uniqueness of A123 and the other puzzles in this thread is as a direct result of their rotational symmetry?

Para wrote:

Nah. You can create puzzles which are not unique, which have a rotational cage pattern.

Walkthrough by Andrew:

Assassin 123 "Roulette" V0.9 by udosuk (October 2008) here

Puzzle Diagram:

Images with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

udosuk: However, here is a v0.9 which can be solved without fishes/chains even if one doesn't use the info above. :idea:

(Warning: potentional spoiler for the default version)
SSR: 1.56. "True" SSR: 1.14.

Andrew: I got stuck on A123 so decided to have a go at the v0.9.
Even this wasn't an easy puzzle although breaking up the six-cell cages in the four corner nonets was a great help.
I'll rate A123 v0.9 at 1.25.

Walkthrough by Andrew:

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