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PostPosted: Sat Nov 20, 2010 11:44 am 
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These were once posted on the now vanished DJApe forum. I don't want to mention that name anymore. :rambo:
Hopefully the information will be preserved in this webspace for a longer time! :pray:


Bloomdoku

Similar to Windoku, but the windows are packed more tightly together:

Image

You guys can try to explore more about this format (vanilla, killer, etc). But I am more interested in combining the NC (Non Consecutive) rule on this.

Apparently the following puzzle has only 1 solution:

NC Bloomdoku #1
Image
NC Bloomdoku #1 solution:
Image


Here is a more human solvable puzzle:

NC Bloomdoku #2
Image
NC Bloomdoku #2 partial solving state:
Image

NC Bloomdoku #2 solution:
Image


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PostPosted: Sat Nov 20, 2010 11:54 am 
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Torn-Bloomdoku

A petal is torn from the bloom, to destroy the symmetry:

Image

Apperently, combining with the NC (Non Consecutive) rule, this variant has only a space of 2 solutions! :!:

So to make a valid puzzle, only 1 more constraint is required: R1C1<>1.
(Consider this: out of 729 initial pencilmarks, you only need to eliminate 1 to obtain a unique solution!)

NC Torn-Bloomdoku #1
Image
NC Torn-Bloomdoku #1 solution:
Image


A more human solvable puzzle:

NC Torn-Bloomdoku #2
Image
NC Torn-Bloomdoku #2 partial solving state:
Image

NC Torn-Bloomdoku #2 solution:
Image


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PostPosted: Sat Nov 20, 2010 12:08 pm 
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Ninjutsudoku

This variant is created for an overlapping variant called Ninja Sudoku, which I will post in the Gattai forum later.

Image

As you can see, apart from the 4 bloom petals, there are also 4 long axes surrounding them, as well as four "short diagonals" of length 4. You can consider those short diagonals as "zero cages" so that no cell values can repeat on those.

This time I don't need to use the NC rule or any other rule to have a valid puzzle with 8 initial givens:

Ninjutsudoku #1
Image
Ninjutsudoku #1 solution:
Image


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PostPosted: Sat Nov 20, 2010 2:15 pm 
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Interesting! I'll have to give those a try (at least the "human-solvable" ones).


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PostPosted: Wed Nov 24, 2010 9:43 am 
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Simon

I really enjoyed the NC but did not get anywhere useful with the other one - I feel I'm missing something (and so does JSudoku)

Maurice


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PostPosted: Wed Nov 24, 2010 12:40 pm 
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HATMAN wrote:
I really enjoyed the NC but did not get anywhere useful with the other one - I feel I'm missing something (and so does JSudoku)

Which is "the other one"?


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PostPosted: Sat Nov 27, 2010 8:00 pm 
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Simon

Sorry forgot about the torn ones, I meant Ninjutsudoku #1

I tried it when posted elsewhere and did not do well on it then - I think I am missing sometyhing on the zero cages,

Apologies for not posting the JSudoku codes - I do not know how to post extra groups - but now realise I can post ythem as twin killers.

I've got another way of filling out the Bloomdoku with X that seems interesting - I'll post a vanilla one shortly.

Maurice


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PostPosted: Sun Nov 28, 2010 2:00 pm 
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For Ninjutsudoku #1, paste the following text code to JSudoku:

text code 1:
3x3::k:9:10:11521:11521:11521:11521:11521:11521:11:11522:11522:11523:11523:11523:11521:11521:11521:12:11522:11522:11523:11523:11523:11524:11524:11524:11525:11522:11522:11523:11523:11523:11524:11524:11524:11525:11522:11526:11526:11526:13:11524:11524:11524:11525:11522:11526:11526:11526:11527:11527:11527:11525:11525:11522:11526:11526:11526:11527:11527:11527:11525:11525:14:11528:11528:11528:11527:11527:11527:11525:11525:15:11528:11528:11528:11528:11528:11528:16:17:


Then paste the following text code as "Twin Killer" in JSudoku:

text code 2:
3x3::k:5:6:1:7:8:9:10:11:12:13:14:15:1:16:17:18:19:20:21:22:23:24:1:25:26:27:2:28:29:30:3:31:1:32:2:33:34:35:3:36:37:38:2:39:40:41:3:42:4:43:2:44:45:46:3:47:48:49:4:50:51:52:53:54:55:56:57:58:4:59:60:61:62:63:64:65:66:67:4:68:69:


(Alternatively, can draw them using "New Extra Diagonal" in JSudoku.)

Then put in the 8 initial givens manually. It should be solvable in JSudoku, albeit with fishes.

But if one can find a certain "backdoor", the puzzle can be solved much, much more easily.


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PostPosted: Wed Dec 01, 2010 5:21 am 
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Here is a graphical walkthrough for Ninjutsudoku #1, to explain the "backdoor" I mentioned in the last post.

My graphical walkthrough (15 images):
To solve this puzzle, if one uses the traditional approach, chances are one has to apply quite a few advanced fishy techniques to solve it. I am going to introduce a completely different solving approach which I name as "label solving" to tackle this puzzle.


1. The first step is to ignore the actual given clues, but to fill in one area of the grid where we know must contain 9 different digits. In this case I choose the 9 uncoloured cells which are not covered by the 8 given "45-cages", and label these cells with 9 different letters:
Image


2. Directly from this layout, we can find 4 hidden singles and 4 hidden pairs for the 4 green regions:
Image


3. Also, because R3C3 sees R2C12345, it has to map to one of R2C6789, and since R1C12=R2C78, R3C3 must map to one of R2C69. Similar to the rest of R37C37:
Image


4. This is the most tricky part: from the 8 initial givens (which we have been ignoring till now), since they are all having different values, so as the labels covering those exact same cells. We can actually consider these 8 cells as a hidden disjoint "zero cage".

Obviously the label E cannot appear on those 8 cells, so the rest {A,B,C,D,F,G,H,K} must each appear once on them. 4 of them {A,B,H,K} must appear in D/2378, leaving the other 4 {C,D,F,G} to be in D\28+D/46:
Image


5. Applying CPE on this hidden cage, we have R2C4 seeing all F's and R8C6 seeing all D's:
Image


6. As a result we have 2 hidden pairs on R2 & R8 (R2C25={FG}, R8C58={CD}):
Image


7. R1C3, seeing R2C134 as well as R1C129 & R23C2, have only 1 possibility left. Ditto for R9C7:
Image


8. Next we have 2 hidden triples on N2 & N8 (R3C456={ABD}, R7C456={FHK}):
Image


9. Two simple row-cage intersections on two of the bloom petals:
Image


10. Another two row-cage intersections on the remaining two bloom petals:
Image


11. A series of hidden singles emerge after the previous step:
Image


12. With R3C9 seeing R134C8 there remains only 1 possibility left. Ditto for R7C1, resulting in a series of singles:
Image


13. More CPEs. R4C6 sees all F's of a petal while R6C4 sees all D's of another:
Image


14. Finally, two more simple row-cage intersections on two petals clean it up:
Image


15. This is the "labelled solution":
Image


To obtain the answer for the original puzzle, just convert all labels back to numbers corresponding to the initial givens. (F=1, B=2, K=3, G=4, C=5, A=6, H=7, D=8, E=9)

The thing I like about this approach is how we treat the initial givens as a "hidden cage" and a "hidden cage" as initial givens. Amazingly this simple twisting of concepts makes the solving so much easier. I am sure other difficult puzzles with 45-cages might be tackled more easily with this approach. Will be thankful if someone would give more examples.


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PostPosted: Thu Dec 02, 2010 2:51 pm 
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Simon

I'll try it again over the weekend before I look up your solution.

Maurice


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