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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Wed Feb 27, 2013 11:00 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Puzzle rating table, with links to archive entries; each of these has a link to the puzzle thread.

Abbreviations used in Rating Table:

+-------------------------------+-----------+---------+----------+----------+
| Puzzle                        |  Made By  |  Rating | SS Score | SS Score |
|                               |           |  Andrew |  v3.3.1  |  v3.5.7  |
+-------------------------------+-----------+---------+----------+----------+
| Assassin 203                  |    Ed     |   1.50  |  *1.60   |   1.45   |
| Paper Solvable 5              |  HATMAN   |   1.25  |          |          |
| Weekly No.256 @ KSO           |   Other   |  H1.25  |  *1.45   |   1.30   |
| Assassin 204                  |    Ed     |   1.50  |  *2.00   |   1.70   |
| Assassin 205                  |    Ed     |   1.50  |  *1.55   |   1.40   |  
| Assassin 206                  |    Ed     |  E1.50  |  *1.60   |   1.55   |
| Assassin 207                  |    Ed     |  H1.50  |  *1.70   |   1.55   |
| Assassin 208                  |    Ed     |  E1.50  |  *1.85   |   1.65   |
| Assassin 209                  |    Ed     |  E1.25  |  *1.30   |   1.25   |
+-------------------------------+-----------+---------+----------+----------+

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.

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Wed Feb 27, 2013 11:03 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 203 by Ed (November 2010) here

Puzzle Diagrams with "udosuk style Killer Cages":

Note: this is an X-killer...1-9 cannot repeat on the diagonals.

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

In a PM about making this pic Børge: Very difficult to colour

Ed: Assassin 203 [edit to correct number! :oops:

]
Thanks to Børge for the pics.
and those annoying diagonal cages also make for a very hard puzzle. Takes me a really unusual move (but NOT complicated) which my optimised walk-through gets on step 12...but then many more steps to get it fully cracked. This cage structure ended up quite non-symetrical to get a nice balance between progress and stuckness.

Andrew: Thanks Ed for an interesting and fun Assassin!
Yes, it was certainly difficult to colour. I managed to do it with 4 colours but then added a 5th colour for one cage, which made the cage pattern a lot clearer to work with.
I've no idea whether I found Ed's unusual step. A few of my steps were interesting and unusual.
Rating Comment. I'll rate my walkthrough for A203 at 1.5.

Ed:

Andrew wrote:

I've no idea whether I found Ed's unusual step

Your step 21 (my step 12). Thanks to Andrew for posting a really nice walk-through. Love the rating! Here's my optimised walk-through which basically follows Andrew's way but without his step 9. Unusual for Andrew and I to follow the same path so perhaps it's the only one.

Walkthrough by Andrew:

Walkthrough by Ed:

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Fri Apr 26, 2013 2:51 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Paper Solvable 5 Zero X Killer by HATMAN (November 2010) here

Puzzle Diagram:

Diagrams with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

HATMAN: This has both types of zero: areas with no cages and cages with no sum.
I do not know how to enter zero cages into SudokuSolver so I am unsure of the score, but I have managed it on paper.

Andrew: Thanks HATMAN for another fun puzzle.

Cages without totals are an interesting concept! They proved useful in the later stages of my solving path.
I solved it by elimination solving although many of the steps are essentially paper solvable ones; for example step 2 since the follow-ups from Prelims (in step 1) can be easily visualised. Also I think that steps 7 and 11 are essentially paper solvable, and also human solvable, steps.
I was going to use one 45 but then spotted the clash in step 16 and found that the 45 wasn't needed.
Rating Comment. I'll rate my walkthrough for A203 at 1.25.

HATMAN: I think cages without totals were started a couple of years ago by Mike-Japan (another lost voice).
Note that your definition of paper-solvable is higher than mine, I'm looking for around 0.75 but definitely below 1.0. Of course we all see different things in a puzzle and I know by know that my "vision" is somewhat different to others.

Apologies for not responding to your PM, I was in Nigeria and workload (for once positive) prevented me checking in regularly.
For the corner lace with Windoku r1c2=r2c4, r2c1= r4c2 and r1c5r5c1 = r2c3r3c2 with these relationships in place both of the lace practice ones rattle out.

Andrew: Thanks for those comments.
Assuming that you are referring to the same cage interactions as I did in my rating comment, I think that steps can be Paper Solvable and still rated higher than 1.0. The interactions in my steps 7 and 11 were definitely paper solvable ones. I assume that they were the key steps for this puzzle. If there was something easier which I missed, I'd be interested to know.

Thanks also for the comments about the Lace Windokus. I've also had helpful discussions about those with Ed and Simon by PM. Thanks guys.

simon_blow_snow: To me, "Paper Solvable" means you can solve it without using any pencilmarks. When I went through Andrew's walkthrough (briefly), I really could not see how a player can follow it without listing out the pencilmarks.
Below I will include a walkthrough, which I think one can follow it without listing pencilmarks. However one may need to jot down some (very few) small notes on the side to keep track of some tiny details.
I would urge the readers to try to follow this walkthrough by actually create a blank 9x9 grid on paper (you can draw it by hand if you don't want to use the printer), and try to fill in the 81 cells one by one while following this walkthrough. You can also have the image of this puzzle on the computer screen as a reference.
Please don't list any pencilmark, and if you find any particular gap in the walkthrough that needs more elaboration, please do post a comment, I will try to fill in the gap.
Note that when solving without pencilmarks it is not very often to use naked singles or subsets. In the puzzle I just used one naked single, which should be easy to spot on paper at that stage.
Also I used a lot of cage sums min-max analysis, which I believe HATMAN would consider appropriate as a Paper Solving techniques because the cage sums are all we have recorded on the grid when solving without pencilmarks.

Andrew: Well done Simon for posting a genuinely "Paper Solvable" walkthrough. I assume that steps where one combination is listed for a cage are written as notes outside the grid, what I call pencilmarks (see below), and only actual placements are written in the cells of the grid.
I liked the 3rd line of step 3. I wish I'd spotted that step; it would have simplified my solving path a bit.
Further Rating Comment. After going through Simon's walkthrough, I'll stick to my rating for this puzzle. While steps like minmax, must include and don't include are technically simpler, in my opinion the way that step 5a (for example) builds up a long chain of must include and don't include is at least a 1.25 step.
I'm inclined to think that this puzzle is easier to solve by elimination solving, but not a lot easier.

Simon wrote:

To me, "Paper Solvable" means you can solve it without using any pencilmarks. When I went through Andrew's walkthrough (briefly), I really could not see how a player can follow it without listing out the pencilmarks.

I take a broader view of "Paper Solvable". While it means that it can be solved without using pencilmarks (in your use of that term) I take it as meaning an easier puzzle which can be solved that way if one wishes. I use a sort of "paper solvable" approach on another sudoku site although not as rigorously as in Simon's walkthrough.
If HATMAN, or anyone else posting "Paper Solvable" puzzles, would prefer that they should only be solved that way then I'll limit myself to brief posts about them, without a walkthrough, unless I'm able to find a "paper solvable" solving path.

BTW How did the term pencilmarks become a word meaning some/all candidates written in the cells of a sudoku grid? Candidates seems to me a much more appropriate term. When I first saw the phrase pencilmarks I assumed it referred to notes written outside the grid; I was therefore very surprised when I later discovered that many people use it to mean candidates.
Also how did the term player get introduced in the context of sudokus? In my opinion solver is far more appropriate for sudukos, crossword puzzles, etc. Player implies playing, either individually or in a team, against opponent(s). I consider myself to be a solver so I trust that nobody will ever refer to me as a player.

simon_blow_snow: I think the term "pencilmark" originated from the Sudoku Players' Forum, used to be in http://www.sudoku.com and now in http://forum.enjoysudoku.com. Obviously the term "players" also came from there. Other similar forums such as the Sudoku Programmers Forum (in http://www.setbb.com) and another one (which no longer exists) used to have a certain group of common visitors, and they helped formulate a "standard terminology" in various places.

HATMAN: Simon
I started these Paper Solvable for interesting puzzles that I can do on paper (including pencil-marks, but hopefully minimal). I am rather messy and for harder puzzles I have to do them on spreadsheet (developed on Udosuk's basis) or on JSudoku.
For stronger solvers doing them without pencilmarks (Andrew note the sale of pencils with rubbers has jumped manifold since the re-introduction of Sudoku to the English speaking world) seems eminently sensible.

Andrew
A few posts ago I talked of using dots and dashes as pencilmarks but did not make myself fully clear. The approach is to only partially mark-up and works well with non-consecutive or anti-chess. When you derive non-obvious placement possibilities: put dots. When you derive non-obvious placement eliminations: put dashes.

I'm just back in England for a few days awaiting my Nigerian visa. As you can imagine I am not enjoying the cold, however yesterday I had the pleasure of going to my grandson's second birthday. The difficulty was that I had to drive from London to Leeds and back which in snowstorms on English roads was not a pleasure. Tonight I go back to Africa; thankfully.
Maurice

Walkthrough by Andrew:

Walkthrough by simon_blow_snow:

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Fri Apr 26, 2013 2:54 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Weekly No.256 @ KSO posted by herschko (December 2010) here

Puzzle Diagrams with "udosuk style Killer Cages" by Børge:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

herschko: I highly recommend Weekly Killer No. 265 (11/29/2010) over at [url]killersudokuonline.com[/url]. Very challenging, with several large cages. I had to extend some techniques in ways I don't think I have done before.

simon_blow_snow: Actually, this one is not particular difficult compared to some former toughies. I think perhaps you missed a few critical moves from the very start.
In another forum which no longer exists I wrote a few walkthroughs for some KSO weeklies which were definitely much trickier than this. Real shame all those were lost forever. :rambo:

Joe Casey: I agree with both of you, more or less: it was quite a stinker; my way into it was similar to Simon's. Then I had partial solutions on opposite sides of the board, and only a few combinations were compatible.

Hidden Text:

Harder than the recent average, I thought, and I bungled it and had to restart, but on looking back after solving, it doesn't seem so hard (as often happens).

Andrew (in 2011): It was only yesterday, when I was setting up the outline for Archive Part H, that I realised that I hadn't looked at this puzzle at the time, possibly because there wasn't a diagram when this thread was started; it was only months later that I downloaded SudokuSolver, and then only to calculate SS scores for the archive.
Thanks Børge for posting the diagrams. Thanks also to whoever created the puzzle on the KSO website; I've never tried a puzzle from that site before.
As Simon said, it's not a particularly difficult puzzle if one finds a few critical moves from the very start. It took me until step 11 to spot one of them; if I'd spotted that one earlier it would have simplified things and shortened my solving path. I started with what seemed to me at the time to be other critical moves.
A nice observation by Joe Casey, making use of the fact that R3C79 must have a different total than R34C7; as a "clone" step it leads to a shorter solving path but puts up the technical difficulty.
Rating Comment. I'll rate my walkthrough at Hard 1.25.

Post by simon_blow_snow including spoilers:

Walkthrough by Andrew:

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Thu Oct 23, 2014 3:42 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 204 by Ed (December 2010) here

Puzzle Diagram:

Puzzle Diagrams with "udosuk style Killer Cages":

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: Merry Christmas! Found a really nice way to crack this one which might have to go into the techniques forum. Love the way hard killers keep surprising with the variety of ways to attack them.

Joe Casey: Nice one, Ed. Found a nice logical way into it. Don't know if it's the same as yours, but very satisfying anyway.
Have a Happy Christmas.

Andrew: Thanks Ed for a fun Assassin!
I don't know whether I found the same way as Ed did to crack this puzzle; my key breakthrough was in step 12 (with hindsight it was possible earlier than that) and I used another interesting move in step 19 to get a quick finish.
Rating Comment. I'll rate A204 at 1.5. I think step 12 probably deserves this rating, as does the combination blocker in step 19.
Happy Christmas to all forum members! :santa:

HATMAN: Joe
Very neat but let me check out that jump

Joe Casey: Thanks. I gather that my post was a bit too elliptical.
I still don't do walk-throughs. But sometimes I want to substantiate my claim to have solved the puzzle; or to let other solvers compare their route; or to offer a hint and encouragement to anyone who hasn't solved it. That, and my natural indolence, is why I'm a bit elliptical.

HATMAN: I have similar views on walkthroughs, perhaps the phase skip-through instead?

Ed: Very interesting! Andrew got my way with his step 12 but his is better because it locks four candidates whereas I just saw the two highest ones. It looks like the Blocking Cages technique (see several posts starting at the bottom of this post). Great walkthrough Andrew and love the rating!
I still can't work out how Joe Casey and HATMAN get their way to work but know it is correct. [edit: got it now - thanks to Andrew and Joe for helpful PMs] Checked a number of puzzles with this same pattern (generated by JSudoku) and they all have the same feature with that sum of 45. Well done! :applause:

Joe Casey's solving outline:

Walkthrough by Andrew:

HATMAN's query:

Joe Casey's explanation, after HATMAN's query:

Ed's alternative way to look at Joe Casey's cracker:

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Sun Oct 26, 2014 3:06 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 205 by Ed (February 2011) here

Puzzle Diagram:

Puzzle Diagrams with "udosuk style Killer Cages":

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: Found a really neat way to make big inroads near the beginning. Unfortunately, the end is a bit tedious but hopefully I just missed something.

Frank: Tough one Ed. I liked the fact it was asymmetric.
My 2 key moves were:
Thanx for the puzzle

Andrew: Thanks Ed for a fun puzzle.
I found my first important step fairly quickly but it took me some time to find my other key moves; with hindsight ...

Ed:

Frank wrote:

Tough one Ed. I liked the fact it was asymmetric.

Thanks. Nice to know some of us are asymmetrics - it's not everyone's taste. The next couple I'm working on are also. Been aiming for simpler cage structures and using asymmetry to give that extra bit of a twist.
I used a variation on Andrew's "Killer pairs" move in his step 4 to make big inroads elsewhere (my step 5). Andrew's is a blocking move whereas mine is a locking move....perhaps Alternating Killer pairs (or AK blocks in Andrew's)???? If anyone can remember seeing it used before please let me know. It may be a good one for the techniques forum.
Thank you to Andrew for his walk-through, very easy to read. Appears that Frank used a similiar approach. Andrew's step 34 makes a huge difference to the ending of the puzzle compared to how I found it.

Andrew: Thanks for the kind comments, Ed, but your clever step 5 is a lot more powerful than my step 4. You were helped a lot by your step 2; I don't think I seriously looked at that "45". As a result you got one of your key results in your step 8; I didn't reach the same naked pair until my step 19a.
Thanks for commenting about my step 34. Yes, it was very useful.

Maybe you missed the fact that:

Ed wrote:

Nice to know some of us are asymmetrics - it's not everyone's taste.

I'm also happy with asymmetrics. I never assume that because I've found a "45" there must be a corresponding one on the opposite side of the grid.
I think if there's a feature of cage patterns that I'm not particularly keen about it's disjoint/remote cages. The one in A205 wasn't a problem, since it was completely enclosed in both R5 and N5; for this puzzle it didn't affect "45s" involving multiple columns. More generally disjoint/remote cages do tend to reduce the number of available "45s", often significantly.

Frank's key moves:

Walkthrough by Andrew:

Ed's start:

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Sun Oct 26, 2014 3:26 am

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 206 by Ed (February 2011) here

Puzzle Diagram:

Puzzle Diagrams with "udosuk style Killer Cages":

Andrew's Coloured Diagram:

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: This one is technically easier than the last couple. No tricks or really advanced moves needed. But....I found it harder and took longer to solve! Love killers like this. Takes me about 15 steps to crack it. All traditional Assassin moves, some of which took a long time to find. Savour.

Andrew: Here is the coloured image for A206 which I made while setting up my Excel worksheets.

Andrew: Thanks Ed! I enjoyed A206. As you said it's hard to find some steps. I'll guess from your introductory comment that my breakthrough step probably wasn't the way you intended it to be solved. However it led to a straightforward and fairly quick finish and, more important for me, it avoided messy combination analysis ...

Ed: Glad you enjoyed this puzzle Andrew. You interpreted my intro perfectly with the exception of your step 12. I avoid that type of combo analysis (which must sound pretty silly since this is killer sudoku!!) when there are so many combinations involved. I missed that nice chain you found...though we worked in the same areas. You'll kick yourself about a couple of "45"s you missed!! They took me a long time to find.

This is an alternative way to crack A206

Walkthrough by Andrew:

Ed's start:

Andrew wrote:

I'll guess from your introductory comment that my breakthrough step probably wasn't the way you intended it to be solved....However.... it avoided messy combination analysis

Glad you enjoyed this puzzle Andrew. You interpreted my intro perfectly with the exception of your step 12. I avoid that type of combo analysis (which must sound pretty silly since this is killer sudoku!!) when there are so many combinations involved. I missed that nice chain you found...though we worked in the same areas. You'll kick yourself about a couple of "45"s you missed!! They took me a long time to find.

This is an alternative way to crack A206. Starting after Andrew's step 6.
6 steps End of Andrew's step 6 here

.-------------------------------.-------------------------------.-------------------------------.
| 4789      4789      4789      | 234567    1234567   1234567   | 123456789 1234567   12345678  |
| 1256      4789      2356      | 4589      4589      1234567   | 2345678   1234567   12345678  |
| 1256      12356     1235      | 6789      6789      234567    | 3456789   1234567   2345678   |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 345789    12345     | 123456789 123456789 123456789 | 12345678  1234567   123456789 |
| 123456789 345789    12345     | 123456789 23456789  23456789  | 123567    123567    123456789 |
| 123456789 123456789 23456789  | 123456789 23456789  123456789 | 12345678  1234567   123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 123567    123567    6789      | 123456789 123567    123456789 | 1234567   1234567   1234567   |
| 3489      1234567   6789      | 4567      123567    123456789 | 1234567   89        1234567   |
| 3489      1234567   234567    | 12345678  12345678  123456789 | 1234567   89        1234567   |
'-------------------------------.-------------------------------.-------------------------------'

7. "45" on r12: 1 outie r3c1 + 3 = 2 innies r1c4 + r2c3
7a. -> no 3 in r1c4 (IOU)

8. 3 in r1 only in r1c56789 -> no 3 in r2c7 (CPE)
8a. no 8 in r3c7 (h11(2)r23c7)

9. "45" on n14: 1 outie r1c4 + 4 = 1 innie r6c3
9a. r1c4 = (245), r6c3 = (689)

Now the hardest one
10. "45" on r12: 3 innies r1c4 + r2c13 = 10
10a. the only way for r1c4 + r2c3 to sum to 9 (and -> have 1 in r2c1) is [45]: however, this is blocked by 13(2)n2 which must have 4/5
10b. -> no 1 in r2c1
10c. no 6 in r3c1

11. 1 in n1 only in r3: locked for r3
11a. no 8 in r3c9

12. 8 in r3 only in 15(2)n2 = {78} only: both locked for r3 and n2

Cracked.

Top

Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Sun Oct 26, 2014 9:38 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 207 by Ed (March 2011) here

Puzzle Diagram:

Puzzle Diagrams with "udosuk style Killer Cages":

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: Hard to believe it's now three years since Ruud posted his last Assassin. This one is worthy of his legacy except it is not symmetrical. Found a fun way through this one with two key moves. Not complicated but both are a twist on the simplest version of that type of move. Presumably that means there are other ways to solve this. Good luck!

Andrew: Thanks Ed for a challenging Assassin! I've no idea whether the steps I used are the ones you referred to but my first key move is certainly a twist on a known technique. I found it harder than your recent Assassins so maybe I missed something.
My walkthrough would have been shorter if I hadn't missed one important step when it first became available; however I didn't feel that it was an obvious step (some may disagree with that) so I haven't re-worked my steps but only made comments about it.
Many thanks to Ed for the comments and one correction, all given in blue in my walkthrough; I've also added a general comment at the end.
Ed told me that his solving method was very different. I'll be interested to see how you did it.

Ed:

At the end of his WT Andrew wrote:

[R..C.. and R..C.. were very important in my solving path, with some of the steps involving them being hard to spot.]

Got another step to add to those cells! Plus, a very different way to get to Andrew's first placement. Thanks very much Andrew for finding another way through this one. It shows how long and difficult a puzzle it is without my two key steps (8 & 15), especially the second. I managed to find those two fairly quickly so didn't realise how resistant this puzzle could be.

I've used Andrew's steps up to the end of 7.

Andrew: Congratulations Ed for spotting your two steps fairly quickly. :applause:

Neither of them are obvious so I don't feel that I missed something that I ought to have seen. Your steps should lead to a shorter solving path than mine. Not a "clone" in sight for you!

Ed:

Andrew wrote:

Congratulations Ed for spotting your two steps fairly quickly...Neither of them are obvious so I don't feel that I missed something that I ought to have seen.

Thanks! I routinely look for direct-link candidates (if X -> Y) in a cage whenever I look at a list of combinations....perhaps in the way you routinely do cage-placement clean-up in your walk-throughs. In contrast, I don't look for those clean-ups except if I'm stuck. I also look for killer halves routinely in case an easy block/pair is available. I rarely look for killer thirds as a block but do look for a third for if it may lead to a killer triple.
Another way to see my step 15 is using CCC but you have to see the direct linked candidate first.

Walkthrough by Andrew:

Ed's alternative breakthrough:

At the end of his WT Andrew wrote:

[R..C.. and R..C.. were very important in my solving path, with some of the steps involving them being hard to spot.]

Got another step to add to those cells! Plus, a very different way to get to Andrew's first placement. Thanks very much Andrew for finding another way through this one. It shows how long and difficult a puzzle it is without my two key steps (8 & 15), especially the second. I managed to find those two fairly quickly so didn't realise how resistant this puzzle could be.

I've used Andrew's steps up to the end of 7.

A207 alternate breakthrough 8 more steps

End of Andrew's step 7 here. Select and "Paste Into" A207 in SudokuSolver

.-------------------------------.-------------------------------.-------------------------------.
| 24578     24578     24578     | 13456789  13456789  13456789  | 6789      134567    134567    |
| 13        13        457       | 245       2456789   2456789   | 6789      24567     589       |
| 456789    45689     45689     | 13        24578     24578     | 1234      1234      458       |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 123456789 12345689  | 23456789  23456789  123456789 | 1234567   123456789 123456789 |
| 23456789  23456789  12345689  | 12345689  123567    123567    | 1234567   123456789 123456789 |
| 3456789   3456789   12345689  | 23456789  23456789  123456789 | 1234567   123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 3456789   12345689  12345689  | 23456789  23456789  23456789  | 1234      123456789 123456789 |
| 6789      6789      12456789  | 2456789   123       2456789   | 45        123       12456789  |
| 123456789 123456789 123456789 | 1234567   1234567   1234567   | 89        456789    456789    |
'-------------------------------.-------------------------------.-------------------------------'

8. from step 3, 10(3)r2c3 = {127/145/235} = [3->2....] (ie 3 in 10(3)r2c3 -> must have 2 in r2c4)
8a. since 3 in r3 is only in 10(3)r2c3 or in h5(2)r3c78 -> 2 locked for common peers (Locking Cages)
8b. ie, no 2 in r3c56

9. 2 in r3 only in h5(2)r3c78 = {23} only: both locked for n3, 3 locked for r3
9a. h5(2)r37c7 = {23} only: both locked for c7
9b. r3c4 = 1

10. 1 must be in 38(8)r3c2 -> no 1 in r89c3 (CPE)

11. "45" on c89: 1 outie r6c7 + 5 = 2 innies r34c8
11a. -> min r34c8 = 6 -> no 1,2,3 in r4c8 (can't be [33])

12. 2 & 3 in n6 only in 45(9) -> no 2,3 in r7c89 + r8c9

13. hidden pair 2,3 in n9 -> r8c8 = (23)

14. 15(3)n9; {348} blocked by 13(2)n9 = [4/8..]; {456} blocked by r8c7
14a. 15(3)n9 = {249/258/267/357} = [3->5..](no eliminations yet)

15. from step 6, h9(3)r8c578 = {135/234}
15a. but [153] blocked by 15(3)n9 (step 14a) (Blocking Cages)
15b. -> h9(3) = {234} only
15c. r8c7 = 4, 2 locked for r8
15d. r8c9 = 1 (hidden single r8)
15e. r9c7 = 9

Much easier now....but still with some work to do. Sorry I don't have time to go any further.

Ed's alternative way to do his step 15:

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Sun Oct 26, 2014 9:53 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 208 by Ed (March 2011) here

Puzzle Diagram:

Puzzle Diagrams with "udosuk style Killer Cages":

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: One of the things I do to find interesting Assassins is try puzzles JSudoku solves (using "Deduce all moves") in a flash but SudokuSolver has a lot of trouble with. Unfortunately, I usually can't solve them so they have to get ditched. Fortunately, got to keep this one.
It takes me two key moves both similar in complexity to the last puzzle. Nothing heavy but still advanced moves. They are fairly common in walk-throughs here so am fairly hopeful that it will get a "fun" rating. It has big progress early so gets you hooked. However, it takes me about 30 steps to finally get it fully cracked so takes some patience.

Andrew: Thanks Ed for continuing to post Assassins!

Ed wrote:

...so am fairly hopeful that it will get a "fun" rating.

Not sure I'll go quite that far but the eliminations in the interestingly shaped 45(9) cage seemed fun; I don't think that's giving anything away.

Ed:

Andrew wrote:

Thanks Ed for continuing to post Assassins!

You're welcome! I'm really enjoying making them since I'm finding interesting puzzles without too much effort. Perhaps the non-symmetrical shapes with at least one big cage helps this. And I enjoy getting your feedback! I'm a couple ahead so should be able to continue fortnightly.
I missed Andrew's nifty blocks (18 and 21a) even though I looked hard in that area. Instead, my key move (16a) gets chunkier progress in the middle stages of this puzzle. Very satisfied.
I'll start with an alternate way to do Andrew's step 15a which is around the same difficulty level I guess.

Walkthrough by Andrew:

Ed's alternative breakthrough:

Andrew wrote:

Thanks Ed for continuing to post Assassins!

You're welcome! I'm really enjoying making them since I'm finding interesting puzzles without too much effort. Perhaps the non-symmetrical shapes with at least one big cage helps this. And I enjoy getting your feedback! I'm a couple ahead so should be able to continue fortnightly.

I missed Andrew's nifty blocks (18 and 21a) even though I looked hard in that area. Instead, my key move (16a) gets chunkier progress in the middle stages of this puzzle. Very satisfied.

I'll start with an alternate way to do Andrew's step 15a which is around the same difficulty level I guess.

Alternate breakthrough for A208 7 steps

Alternative way to get the elimination in Andrew's 15a.

Before Andrew's step 15a here; use "Paste Into" A208 in SudokuSolver

.-------------------------------.-------------------------------.-------------------------------.
| 234568    23456789  23456789  | 1234567   123456    123456    | 4567      6789      1235      |
| 1234      1234      34578     | 123456789 123456    123456789 | 45789     236789    12345     |
| 12368     13678     45789     | 123456789 123456789 123456789 | 2456789   236789    12345     |
:-------------------------------+-------------------------------+-------------------------------:
| 123579    123456789 123456789 | 123456789 123456789 123456789 | 2456789   1236789   24568     |
| 123579    123456789 123456789 | 123456789 123456789 123456789 | 2456789   1236789   234568    |
| 123579    24        123456789 | 234       123456789 123457    | 245678    1236789   234568    |
:-------------------------------+-------------------------------+-------------------------------:
| 179       79        179       | 345       35        45        | 268       268       268       |
| 468       468       468       | 12        79        12        | 3         5         79        |
| 235       235       235       | 6789      6789      6789      | 1         4         79        |
'-------------------------------.-------------------------------.-------------------------------'

15a. r123c1 must have two of 4,6,8 for c1 since the only other place is r8c1 -> {48} blocked from h12(2)r23c3 (no 4,8)
15b. no 4,8 in r2c7 (h12(2)r2c37)
15c. 9 in n1 only in r1 or r3c3 (no eliminations yet)

16. "45" on n12: 1 outie r2c7 = 1 innie r3c3
16a. -> from step 15c. no 9 in r1c8 (Clone CPE)
16b. no 4 in r1c7

17. 9 in r1 only in n1: locked for n1
17a. no 3 in r2c3, no 9 in r2c7

18. Killer pair 5,7 in n3 in 15(2) + r2c7: both locked for n3

19. 8(3)n3 = {134} only: 3,4 locked for n3 & c9

20. 14(3)n6 = {158/257/356} ({167} blocked by 1,7 only in r6c8;{239} blocked by 3,9 only in r6c8)
20a. must have 5; 5 locked for n6 & c9
20b. must have 1/3/7 -> r6c8 = (137)
20c. no 4 in r6c6

21. 22(4)r2c8: {1678} blocked by 1,7 only in r4c8
21a. = {2389} only

Back to Andrew's step 27.

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Andrew

Post subject: Archive Part H. Assassins 201-225, variants, other puzzles

Posted: Sun Oct 26, 2014 10:07 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada

Assassin 209 by Ed (March 2011) here

Puzzle Diagram:

Puzzle Diagrams with "udosuk style Killer Cages":

Code: Select, Copy & Paste into solver:

Solution:

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

Quote:

Ed: Technically easier than recent Assassins but took some good searching to find the way through. As usual, lots of nooks and crannies to explore.

For anyone who uses JSudoku, below is a screen shot of it working on finding cage totals for a previous version of this cage pattern. Incredible numbers!:

Andrew: Thanks Ed for a fun Assassin!

Ed wrote:

Technically easier than recent Assassins but took some good searching to find the way through. As usual, lots of nooks and crannies to explore.

That's a very good description of this puzzle. I didn't use any difficult steps but some of them took me a while to find.
Some time ago I typed up a table of combinations; they were very useful for the larger cages in this puzzle, including saving me the bother of typing the combinations again.

HATMAN: Very pleasant Ed

great combo eliminations and I liked the way:

Ed: Glad you enjoyed this one guys. I used a different breakthrough to Andrew's nice block. Missed that.

Walkthrough by Andrew:

Ed's alternative breakthrough:

Glad you enjoyed this one guys. I used a different breakthrough to Andrew's nice block. Missed that.

Alternate cracker for A209 6 steps

.-------------------------------.-------------------------------.-------------------------------.
| 123456789 123456789 123456789 | 2468      123457    123457    | 123457    689       689       |
| 123456789 123456789 123456789 | 2468      456789    456789    | 123457    134       236789    |
| 123678    123456789 123456789 | 1234568   123456789 123456789 | 13457     13457     1236789   |
:-------------------------------+-------------------------------+-------------------------------:
| 123678    123456789 123456789 | 1234568   123456789 12456789  | 123456789 123456789 1236789   |
| 123456789 123456789 123456789 | 1234568   123456789 123456789 | 123456789 123456789 1236789   |
| 12456789  12456789  389       | 38        12456789  456789    | 456789    12456789  45        |
:-------------------------------+-------------------------------+-------------------------------:
| 89        389       389       | 1245      1245      1245      | 67        67        45        |
| 45        457       457       | 9         68        68        | 12        123       123       |
| 126       126       126       | 7         345       345       | 4589      4589      89        |
'-------------------------------.-------------------------------.-------------------------------'

Andrew's end of step 13 above. Select marks and "Paste Into" A209 in SudokuSolver

14. 1&3 in n2 only in r1c56 + r3c456 -> no 1,3 in r3c78 (CPE)

15. "45" on r12: 2 outies r3c78 - 2 = 1 innie r2c9
15a. ->max r3c78 = 11 -> r3c78 = {45/47} = 9/11
15b. 4 locked for r3 and n3 and 22(6)r1c5
15c. r3c78 = 9/11 -> r2c9 = (79)

16. 16(3)r2c9 must have 7/9 for r2c9 = {169/178/367}(no 2)
16a. has only one of 7/9 -> no 7,9 in r34c9

17. 2 in n3 only in r12c7: 2 locked for c7 and for 22(6)r1c5
17a. r8c7 = 1

18. r8c89 = {23} -> r9c9 = 8 (cage sum)

19. 16(3)r2c9 = {169/367}; must use 6
19a. 6 locked for c9
19b. r1c9 = 9

Back to middle of Andrew's step 19 for the rest.

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