Re^2: Sudoku for Saints

Dang it you are right! Mental mush today. My mind was stuck on fill-in-the-blank-ness and oneness inside the blocks (the 3x3 sub-blocks of a sudoku puzzle are magic squares) and I forgot about the repetition.

Magic squares are N items used only once within a single block as opposed to a 3x3 grid of blocks. To turn this into a sudoku one would need to do a bit more ... have to make dinner now, so I hope readers will be patient while I decide whether to amend the title and original post or amend the software to generate a true sudoku puzzles.

~~However, couldn't you create a 9x9 sudoku puzzle from a set of magic squares by properly rotating and transposing a magic square?~~

Best, beth

Update:Re-added line so that JavaFan's comment makes more sense. I realized was wrong and deleted the question while JavaFan was preparing his post below, not realizing that he was already preparing a response - Whoops! To further his point, since all magic squares have the same middle, the diagonal as well as any (3*N+1)%3 (where N=0..2) row or column of a 9x9 matrix would have the middle of the magic square three times.

Comment on Re^2: Sudoku for Saints

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Re^3: Sudoku for Saints by JavaFan (Canon) on Apr 06, 2009 at 15:42 UTC
However, couldn't you create a 9x9 sudoku puzzle from a set of magic squares by properly rotating and transposing a magic square? No. There's only one 3x3 magic square using the numbers 1 to 9 (excluding rotation and symmetry)¹. Which means that in any 3x3 magic square, regardless of how you rotate or mirror it, 5 will be in the middle. So you cannot have two magic 3x3 squares next to each other in a Sudoku. Now, making a Sudoku with semi-magic squares is of course trivial. ¹Magic Square	[reply]
Re^3: Sudoku for Saints by JavaFan (Canon) on Apr 06, 2009 at 16:51 UTC
Since there are 880 different 4x4 magic squares, not counting rotations and reflections, it may be possible to generate a Sudoku from 16 4x4 magic squares.	[reply]