New method to solve Sudoku

Advanced methods and approaches for solving Sudoku puzzles

New method to solve Sudoku

Postby harshgoel2k » Thu Oct 28, 2010 2:51 pm

I have found one mathematical way to solve the Sudoku , it is systematic and step-by and guarantee( I feel so ) to solve any valid Sudoku, please help to review it.

http://www.scribd.com/doc/39235249/How-to-Solve-Sudoku-Mathematically
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Re: New method to solve Sudoku

Postby harshgoel2k » Sat Oct 30, 2010 2:43 am

I am getting some private message regarding this new method, but not able to reply, giving message I am too new to post /reply private message, some please suggest , how to get is enable. thanks
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Re: New method to solve Sudoku

Postby StrmCkr » Sat Oct 30, 2010 6:56 am

there is a "send reply button" in the upper left hand corner once u open the msg...

to me this is a complex way of making deductions based on possible pencil marks for each cell.

through the constructing of basic techniques
ie
hidden/naked singles
locked candidates
subsets/hidden naked
to list a few
Last edited by StrmCkr on Sat Oct 30, 2010 11:36 am, edited 1 time in total.
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Re: New method to solve Sudoku

Postby harshgoel2k » Sat Oct 30, 2010 8:29 am

Thanks, for simple and easy one, this is somewhat tedious, but I tried this model for difficult puzzles and found solution easily, Also I need you expert comment on number of possible valid Sudoku, using this method I arrived at different figure that what it is now most agreed number, Please comment.
Also I think this model is a alternative approach to understand Latin Squares and Sudoku.... Thanks
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Re: New method to solve Sudoku

Postby StrmCkr » Sat Oct 30, 2010 11:08 am

000700104003400000900100053021004000000000002400860501002000070080007000060000830 {easy}

depends on your definition of difficult.

here's some puzzles to try out that are medium - harder

020510000610003000300027500140005000000000037000930000052004100008000020000300905
005902600001000000000040000000006500800005020009000001500003070403501009700800004
100000008970600000008009030600503100020000040000001007003800065000200300090000000
040190000000503060000000007080005020020400300705001900002000051091600002003000000

and one that's well :twisted: Fata Morgana
........3..1..56...9..4..7......9.5.7.......8.5.4.2....8..2..9...35..1..6........

Also I need you expert comment on number of possible valid Sudoku, using this method I arrived at different figure that what it is now most agreed number, Please comment.


im not sure what u are asking here??

ive also noticed some errors in your own examples

Code: Select all
 *-----------*
 |183|7..|.9.|
 |2.4|..6|3..|
 |.75|9..|...|
 |---+---+---|
 |...|.61|85.|
 |.3.|...|.1.|
 |.41|57.|...|
 |---+---+---|
 |...|..7|12.| 
 |..2|8..|5.9|
 |.1.|..5|478|
 *-----------*


under the section of impossible cordials.

given the state of the grid
the only cardinals that should be depicted for digits 7 in box 7 is R8C1 {ie a hidden singles}
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Re: New method to solve Sudoku

Postby surbier » Sat Oct 30, 2010 6:28 pm

Hi harshgoel2k

StrmCkr is certainly right on your easy example.

However, you second example
Code: Select all
00530000080000002007001050040000530001007000600320008009004000030000009700


has a difficulty grade of (according to sudoku explainer) 10.6
and I find it impressive that you can solve it within your grid.

Although your description is detailed and is easy to follow, there are still some points
which don't yet fully understand.

e.g. on page 16, I don't understand the implication of

In B3N3 Y=9 is unique


on the following steps.

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Re: New method to solve Sudoku

Postby StrmCkr » Sat Oct 30, 2010 10:43 pm

Code: Select all
 *-----------*
 |..5|3..|...|
 |8..|...|.2.|
 |.7.|.1.|5..|
 |---+---+---|
 |4..|..5|3..|
 |.1.|.7.|..6|
 |..3|2..|.8.|
 |---+---+---|
 |.6.|5..|..9|
 |..4|...|.3.|
 |...|..9|7..|
 *-----------*


ps fox news is wrong as well this not the hardest puzzle known to date.

the hardest puzzles known to date are found in this thread and have been known to exist long before that news broad cast was made.

i really think the language used needs to be revised you seem to be using the word unique a lot: a suggestion. when its usually the last one remaining or an impossible xy values.

i'll do a walk through on your solution path when i get home from work later tonight to verify that its actually is valid logic.

on a quick once over I've also noticed similar errors in the board presentation for valid digits remaining from the starting grid state listed above.

~ watch this space~
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Re: New method to solve Sudoku

Postby harshgoel2k » Sun Oct 31, 2010 1:31 am

Thanks all for your valuable feedback, few point here ( Part-1 )

- I agree there are typo errors in the document.
- It is new model of Sudoku (and Latin squares) and it is naïve stage, need you expertise to use it as alternative solution method.
- Since each number here is presented into 4 variables, I feel we have got better control over digits to understand pattern

- It is clear that lot more work need to be done.

- Need some feedback from programmers also, whether the logic is simplified? , One of friend told me CPU may get some rest using this model.

Here are some clarifications
@ StrmCkr » Sat Oct 30, 2010 2:56 pm
Yes it is complex way, but we can consider it as alternative way to pencil mark method. As alternative approach to solve Sudoku. Thanks

@ by StrmCkr » Sat Oct 30, 2010 7:08 pm

Regarding medium –harder puzzles and fata Morgana

I would try these puzzles and would let update you, such kind of stress test is required to find-out new method in this model. Thanks

Regarding my other request, here is details

Number of classic 9×9 Sudoku solution grids
Extract from Wiki with thanks. (http://en.wikipedia.org/wiki/Sudoku)
The first known calculation of the number of classic 9×9 Sudoku solution grids was posted on the USENET newsgroup rec.puzzles in September 2003[12] and is 6,670,903,752,021,072,936,960 (sequence A107739 in OEIS), or approximately 6.67 x 1021. This is roughly 1.2×10−6 times the number of 9×9 Latin squares. A detailed calculation of this figure was provided by Bertram Felgenhauer and Frazer Jarvis in 2005.[13]

As per my calculation based on mathematical model the number of classic 9X9 Sudoku solution grids is 1,908,360,529,573,850,000,000,000,000 or approximately ~ 1.908x10^27
Please refer link for detail document (http://www.scribd.com/doc/39235249/How- ... ematically)

Need your valuable feedback on method adopted.

@ ive also noticed some errors in your own examples

Will check and update you. , Thanks
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Re: New method to solve Sudoku

Postby harshgoel2k » Sun Oct 31, 2010 1:32 am

Part-2
@ surbier » Sun Oct 31, 2010 2:28 am
Regarding “In B3N3 Y=9 is unique “

Page no. 16 In B3N3 Y=9 is unique , Means since Y in the cell B3N9 is 9 so in Column Y=9 is not possible i.e. Y=9 is unique coordinate for that cell , it means we can eliminate Y=9 from that column. - Thanks

@ by StrmCkr » Sun Oct 31, 2010 6:43 am



Ref: hardest puzzles

I would try them and will update you one-by-one. Thanks


And yes, I need to revise the language as well.
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Re: New method to solve Sudoku

Postby StrmCkr » Sun Oct 31, 2010 7:18 am

1,908,360,529,573,850,000,000,000,000 or approximately ~ 1.908x10^27

your calculations are incorrect.

http://www.afjarvis.staff.shef.ac.uk/su ... group.html

there is several ways to approach the problem and the number has been confirmed by several other sources since.

Need some feedback from programmers also, whether the logic is simplified?

no, it is not simplified it remains the same if not much more complicated.

in programing most of us use
Rn,Cn, Bn, RC space that is used to derive the active digits for which all logic is based.

RC as active/not for all 81 cells

Rn,Cn,Bn represent if the Digit N is active/not for the corresponding location.

= 9*9*9 = 729

and to solve the grid all (9*3*9)+81 = 324 constraints must be satisfied.

in your method we only have partial information required to solve a grid you have box constraints only.

for starters you cannot eliminate specific cells combination based only on x+y cordinals

you can eliminate specific x or y values for n digit but you must also remember that x+y may be 1 of three combination.

so if u preemptively eliminate x you have removed all three combination's where some may actually be legal placements.

thus you need all three representations of spacial constraints Row, Col, Box.

{Pencil marks are a representation of the three areas combined R+C+B }

so far i've managed to replicate most of the work in ms excel and it is depicting the above problem easily.
i should have it completed later today and I'll post a link to it.

to show what the Boxes look like via x,y mark up {does it automatically for you}
Last edited by StrmCkr on Mon Nov 01, 2010 12:32 am, edited 4 times in total.
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Re: New method to solve Sudoku

Postby surbier » Sun Oct 31, 2010 7:56 am

Hi harshgoel2k

Part-2
@ surbier » Sun Oct 31, 2010 2:28 am
Regarding “In B3N3 Y=9 is unique “

Page no. 16 In B3N3 Y=9 is unique , Means since Y in the cell B3N9 is 9 so in Column Y=9 is not possible i.e. Y=9 is unique coordinate for that cell , it means we can eliminate Y=9 from that column. - Thanks

... and as there is no further 9 in columnn N3Y, no further 9 can be eliminated in N3Y

Thanks, I got this.

There is a small typo on p16:
So on B8N3 Y=5 is not possible and Y=6 becomes unique

should be:

So on B8N3 Y=6 is not possible and Y=5 becomes unique.

On p17, I can follow: B4N6 and B4N7 are either xy=43 or 61, hence mark these two cells in the summary column.

But from B5N1 x={46}, y={46}, which can be either 44 or 66, I cannot conclude that B5N6 is also either 44 or 66.
From our gird I can conclude:

if B5N1=44 then B5N6=45 or 65 or 66
if B5N1=66 then B5N6=45 or 65 or 44

These aren't enough constraints to conclude B5N5=44 only and hence I cannot eliminate in B5N6 Y=5.

Could you please comment on this step ?

Furthermore the summary column claims x=5,y=4 is solved, which isn't.

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Re: New method to solve Sudoku

Postby StrmCkr » Sun Oct 31, 2010 11:42 pm

as mentioned before: http://strmckr.fileave.com/stormduko/test.xls

Ive preloaded the settings to automatically set up the active/deactivate xy values for each box +n

Ive also included the fox news grid to show exactly how the grid will look before we start applying and logic sequence.

on to the critique.

base methods:
box2 N5 = hidden single (there are other numbers that could go here in standard pencil mark ups which is why its called hidden}
box5 n3 = hidden single

{to see the updated grid simply manually add the digits in manual section}

a mistake: in box8n3 it can be either 7,5 Or 9,5
neither can be eliminated.

b4N67 = Hidden Pair: 6,7 in r4c3,r6c1 => r4c3<>2, r4c3<>8, r4c3,r6c1<>9, r6c1<>5

{given active combination of 4,1 & 6,3 these two digits are left in sets 4,3 & 6,1}

But from B5N1 x={46}, y={46}, which can be either 44 or 66, I cannot conclude that B5N6 is also either 44 or 66.
agreed. there is no other subset in this puzzle at this particular state.

then just after u say fresh for clarity end of page 16.

its trial and error there is no logic connection for guessing at b4n8 = 5,3
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Re: New method to solve Sudoku

Postby harshgoel2k » Tue Nov 02, 2010 8:58 am

Dear friends: I am in the mid of a new project (office work) and it is very demanding and takes whole of my time till mid night… I am sorry I could not work on most of the issue raised, But I would still say… this is just a naïve method and need tons of work further, it gives us flexibility to work more on numbers, and I hope we would find some new exploring way to find solution to Sudoku, then those solution can be transformed back to pencil mark method as both method have inter-changeable.

@ by StrmCkr » Sat Oct 30, 2010 7:08 pm

I tried the Fata Morgana , after just simple base activities ( as per my model ) , I reached to conclusion that this is hardest ( no need to apply ~ 30 techniques of pencil mark technique ) - will work on it, beleiveing some us find ways...

@ by StrmCkr » Mon Nov 01, 2010 7:42 am
The excel is excellent, please provide password to open it in read/write mode. 

@ by StrmCkr » Sun Oct 31, 2010 3:18 pm for number of possible sudoku

Will study the link and try to find out the gap.

Thank all for your help , I am new to Sudoku , and this model is very new to this world, but thinking differently could help us to redefine our skills….. God bless us….
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Re: New method to solve Sudoku

Postby harshgoel2k » Fri Feb 28, 2014 8:15 pm

Dear Friends, I have 3 more examples, two examples are rated as near imposible, please try out the method m provide feedback. thanks
_http://www.scribd.com/doc/39235249/How-to-Solve-Sudoku-Mathematically
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Entirely New mathematical model for Sudoku

Postby harshgoel2k » Sat Mar 01, 2014 2:26 pm

Dear Friends, I have formulated an entirely new mathematical model to solve Sudoku, after explaining the model , method and techniques I have solved 4 Sudoku in step-by-step manner, one is very simple but last two are in nearly impossible category. try out the method and provide feedback. thanks
http://www.scribd.com/doc/39235249/How-to-Solve-Sudoku-Mathematically
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