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05.12.2005 at 03:36AM PDT, ID: 21421627
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Combinatorial theory anyone?

Tags: box, solutions
Hi Mathematicians -

" Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. "

Those are the rules for completing this kind of puzzle http://www.sudoku.com/ on a 9 x 9 grid.

The question is how many possible puzzles can be set?

Obviously it is a far greater number than the possible number of solutions.

- duz

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Question Stats
Zone: Other
Question Asked By: duz
Solution Provided By: softplus
Participating Experts: 3
Solution Grade: B
Views: 0
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05.12.2005 at 03:53AM PDT, ID: 13984792

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05.12.2005 at 03:56AM PDT, ID: 13984798

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05.12.2005 at 04:03AM PDT, ID: 13984820

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05.12.2005 at 07:22AM PDT, ID: 13986781

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05.12.2005 at 07:25AM PDT, ID: 13986827

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05.12.2005 at 08:19AM PDT, ID: 13987490

Rank: Guru

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05.12.2005 at 08:30AM PDT, ID: 13987624

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05.12.2005 at 08:31AM PDT, ID: 13987645

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05.12.2005 at 08:37AM PDT, ID: 13987716

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05.12.2005 at 08:52AM PDT, ID: 13987902

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05.12.2005 at 10:58AM PDT, ID: 13989225

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05.17.2005 at 04:05AM PDT, ID: 14017402

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06.30.2005 at 03:16AM PDT, ID: 14336712

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06.30.2005 at 03:39AM PDT, ID: 14336797

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05.12.2005 at 03:53AM PDT, ID: 13984792
Since the order is important: you have 9 slots, 9 items availble once, so it would be 9*8*7*6*5*4*3*2*1 (aka 9!) = 362'880
Now if this has to be in any functional order, it would be much less :))
 
05.12.2005 at 03:56AM PDT, ID: 13984798
ah, ok looking at the website (duh!), you're looking for something else :))
I'm not sure if you could calculate that or if you'd have to try them all out, i.e. test 9x 9! possibilities = 3'265'920 possibilities of which only a small fraction would count as a valid puzzle.
 
05.12.2005 at 04:03AM PDT, ID: 13984820
Take a look at this thread, there are several people with the same idea: http://www.sudoku.com/forums/viewtopic.php?t=44
Accepted Solution
 
05.12.2005 at 07:22AM PDT, ID: 13986781
softplus -

>several people with the same idea

So what is the answer to my question?

-duz
 
05.12.2005 at 07:25AM PDT, ID: 13986827
no idea :) - niether do they it seems :))). Should we use the (brute-)force?
 
05.12.2005 at 08:19AM PDT, ID: 13987490

Rank: Guru

There is only 1 basic 3x3 magic square and is  

8 1 6
3 5 7
4 9 2

All others are rotations and reflections of this giving a total of 8, eg

reflection

6 1 8
7 5 3
2 9 4

or rotation

4 3 8
9 5 1
2 7 6

In general the number of magic squares for an arbitrary order is unknown.
( see http://mathworld.wolfram.com/MagicSquare.html )
 
05.12.2005 at 08:30AM PDT, ID: 13987624

Rank: Guru

oh I should have gone to the site, your question is not magic squares,
 The number of possible puzzles is 9! for each 3 by 3 block and  (9!)^9 ways of arranging these (ie 9! choices for each 3x3 block with 9 3x3 blocks) ie

   Ans = (9*8*7*6*5*4*3*2*1)^ 9 = 1.091x10^50
 
05.12.2005 at 08:31AM PDT, ID: 13987645
GwynforWeb -

I think you have mistakenly posted an answer to a completely different question. This question has nothing to do with magic squares.

- duz

 
05.12.2005 at 08:37AM PDT, ID: 13987716
GwynforWeb -

>(9!)^9 ways of arranging these

But many of these arrangements will fail because of the "every row, every column" rule.

- duz
 
05.12.2005 at 08:52AM PDT, ID: 13987902

Rank: Guru

ah yes I missed the additional rule.
 
05.12.2005 at 10:58AM PDT, ID: 13989225

Rank: Wizard

This question was asked earlier, and it is still open.
You might find some leads there or at lease avoid some dead ends.

             http://www.experts-exchange.com/Miscellaneous/Math_Science/Q_21292549.html

 
05.17.2005 at 04:05AM PDT, ID: 14017402



d-glitch thanks I didn't see that. I see some possible answers but no explanation.  

This must be a non-trivial problem but I will leave this question open in case a genius turns up :)

- duz

 
06.30.2005 at 03:16AM PDT, ID: 14336712
This question has been classified as abandoned.  I will make a recommendation to the moderators on its resolution in approximately 4 days.  I would appreciate any comments by the experts that would help me in making a recommendation.

It is assumed that any participant not responding to this request is no longer interested in its final disposition.

If the asker does not know how to close the question, the options are here:
http://www.experts-exchange.com/help.jsp#hs5

Venabili
EE Cleanup Volunteer
 
06.30.2005 at 03:39AM PDT, ID: 14336797

Sorry I forgot I had posted this question. I have been following the thread in the link http://www.sudoku.com/forums/viewtopic.php?t=44 that softplus gave and the contributors there are now very close to a solution. Thank you softplus.

- duz
 
 
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