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 19 section?
I've just been curious.
Sudoku Math Puzzle
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Re: Sudoku Math Puzzle
I'm sure you can quickly brute force the largest determinant value using only 19 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?
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?
 Cosmologicon
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Re: Sudoku Math Puzzle
It may be possible to bruteforce 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.

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Re: Sudoku Math Puzzle
Cosmologicon wrote:It may be possible to bruteforce 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, easypeasy example...but there probably isn't.
Re: Sudoku Math Puzzle
Spoiler:
In the spirit of taking things too far  the 5x5x5x5x5 Rubik's Cube.
Re: Sudoku Math Puzzle
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?
Re: Sudoku Math Puzzle
Easy as Pi:
Spoiler:
Slay the living! Raise the dead! Paint the sky in crimson red!
Re: Sudoku Math Puzzle
+that also has digits 19 exactly once on the two diagonals?
Re: Sudoku Math Puzzle
Still kinda obvious...
Spoiler:
Slay the living! Raise the dead! Paint the sky in crimson red!
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