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PostPosted: Wed Dec 01, 2010 3:24 pm 
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Just discovered this thread.

Using my "backdoor" approach for Ninjutsudoku #1, even tarek's most difficult "hands" sudoku can be solved without considering the diagonal or the old lace at all:

Image

Spoilers for easy solving this puzzle:
First, label the top row as ABCDEFGHK of a blank "hands" sudoku grid. Then using singles/pairs/intersections, can solve it easily. Lastly subsititute the numbers back for the labels.


With this approach ANY "hands" sudoku can be solved within minutes. I wonder if this is the case for many other "regional constraints only" puzzles?


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PostPosted: Wed Dec 01, 2010 11:21 pm 
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That is very clever simon_blow_snow,

Essentially what you're saying is that there is only one solution grid for the hands variant which can be solved using the 9 clues of the 1st row.

I'm sure that you'll find many variants that can be solved using the same idea.

tarek


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PostPosted: Thu Dec 02, 2010 12:56 pm 
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tarek

I think for the hands variant, you can try positioning 9 givens in various known non-repeatable regions and compare their solvability. So far I found 3 regions allowing the easiest solving path: R1, N5, and the "hand" from R1C5. They each need only singles & intersections to solve.

I want to see if there is a region which makes it singles-only, or solvable without pencilmarks, but so far can't find any. Even the three easy ones above need pencilmarks because of the heavy intersections involved.

Are there more advanced techniques (e.g. LoL, cell cloning) which can be applied easily (like singles and hidden pairs etc) in no-pencilmark solving?


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PostPosted: Thu Dec 02, 2010 10:40 pm 
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simon_blow_snow wrote:
I think for the hands variant, you can try positioning 9 givens in various known non-repeatable regions and compare their solvability. So far I found 3 regions allowing the easiest solving path: R1, N5, and the "hand" from R1C5. They each need only singles & intersections to solve.

I see, You're using the power of 9 clues in a heavily constrained puzzle.

With heavily constrained puzzles where an 8 clue puzzle is easily achievable (like the AK AN variant), your method is one clever way of making some difficult puzzles easier. With so many regions to choose from it can be tedious though. I'm not sure that it is a guranteed success either.

I'm no expert on advanced solving without pencilmarks ... You can read the following thread for ideas though http://forum.enjoysudoku.com/solving-without-pencilmarks-t3640.html


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PostPosted: Fri Dec 03, 2010 12:20 am 
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Thanks tarek. Great link, even though it's like 4.5 yrs ago I still find the info very useful. :-)


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