Sudoku Math Puzzle

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factorialite
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Sudoku Math Puzzle

Postby factorialite » Mon Nov 12, 2007 7:12 pm UTC

Do we know the 9x9 Sudoku with the largest determinant? If so, what is said puzzle?

Do we know the 9x9 Sudoku with the largest 3x3 determinant, where the 3x3 numbers are the determinants of each 1-9 section?

I've just been curious.

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quintopia
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Re: Sudoku Math Puzzle

Postby quintopia » Mon Nov 12, 2007 9:49 pm UTC

I'm sure you can quickly brute force the largest determinant value using only 1-9 for 3x3. From this, you'll know that any of the bajillions of puzzles which have a 3x3 section with this determinant value are solutions to your second question.

And since this doesn't seem to be a puzzle (by which I mean the solution is known and it is posted as a challenge to other users), perhaps it would go better on Math?

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Cosmologicon
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Re: Sudoku Math Puzzle

Postby Cosmologicon » Mon Nov 12, 2007 10:46 pm UTC

It may be possible to brute-force the 9x9 as well, at least part way. There are 5,472,730,538 unique sudoku if you count the symmetries as identical. Some of these symmetries - like swapping a row or column - leave the magnitude of the determinant invariant, but some - like interchanging all of two digits - don't. If you could come up with a way to find the maximum determinant for all symmetric variations of a given sudoku in under, say, a second, that would bring it into the realm of possibility.

factorialite
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Re: Sudoku Math Puzzle

Postby factorialite » Mon Nov 12, 2007 10:58 pm UTC

Cosmologicon wrote:It may be possible to brute-force the 9x9 as well, at least part way. There are 5,472,730,538 unique sudoku if you count the symmetries as identical. Some of these symmetries - like swapping a row or column - leave the magnitude of the determinant invariant, but some - like interchanging all of two digits - don't. If you could come up with a way to find the maximum determinant for all symmetric variations of a given sudoku in under, say, a second, that would bring it into the realm of possibility.


It may belong on math; I don't really know. I certainly don't know the answer; I just have a hobby of taking the determinant of each 3x3 matrix, and then taking the determinant of that 3x3 matrix of that. It seems like there should be some clean cut, easy-peasy example...but there probably isn't.

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Mouffles
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Re: Sudoku Math Puzzle

Postby Mouffles » Tue Nov 13, 2007 5:21 am UTC

Spoiler:
148
726
593

Determinant = 412, this is the maximum for a 3x3 box.

(should this be spoilerised?) yes
In the spirit of taking things too far - the 5x5x5x5x5 Rubik's Cube.

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quintopia
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Re: Sudoku Math Puzzle

Postby quintopia » Tue Nov 13, 2007 1:14 pm UTC

In order to make the second question more interesting. . .what is the sudoku puzzle with the greatest sum of determinants of 3x3 boxes? Is it possible to get 3708?

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Maurog
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Re: Sudoku Math Puzzle

Postby Maurog » Tue Nov 13, 2007 3:34 pm UTC

Easy as Pi:
Spoiler:

Code: Select all

148  726  593
726  593  148
593  148  726

481  267  935
267  935  481
935  481  267

814  672  359
672  359  814
359  814  672
Slay the living! Raise the dead! Paint the sky in crimson red!

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quintopia
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Re: Sudoku Math Puzzle

Postby quintopia » Tue Nov 13, 2007 5:23 pm UTC

+that also has digits 1-9 exactly once on the two diagonals?

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Maurog
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Re: Sudoku Math Puzzle

Postby Maurog » Wed Nov 14, 2007 9:13 am UTC

Still kinda obvious...
Spoiler:

Code: Select all

148  726  593
726  593  148
593  148  726

935  481  267
481  267  935
267  935  481

672  359  814
359  814  672
814  362  359
Slay the living! Raise the dead! Paint the sky in crimson red!


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