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Re^2: Not A Magic Square But Similar

by kennethk (Monsignor)
on Sep 06, 2013 at 20:04 UTC ( #1052761=note: print w/ replies, xml ) Need Help??


in reply to Re: Not A Magic Square But Similar
in thread Not A Magic Square But Similar

Also:

1 2 3 4 5 6 8 9 10 1 2 3 5 6 7 9 10 11 1 2 4 5 6 8 9 10 12
Any additive offset to a row or column from a valid state that doesn't cause a value collision also satisfies the permutation condition.
3 6 9 2 5 8 1 4 7 1 2 3 7 8 9 4 5 6 2 1 3 5 4 6 8 7 9
Rotations, row swaps and column swaps also yield valid results. Of course, these are actually a subset of the additive transformation. If you think about it, the 1 .. 9 square is just the all 1's square subjected to 9 row additions and 3 column additions; the minimum necessary number to achieve element uniqueness.

The real question for me is are there valid results which are not mappable via addition to the base square.


#11929 First ask yourself `How would I do this without a computer?' Then have the computer do it the same way.


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Re^3: Not A Magic Square But Similar
by Limbic~Region (Chancellor) on Sep 08, 2013 at 22:55 UTC
    kennethk,
    The real question for me is are there valid results which are not mappable via addition to the base square

    Yes and I am kicking myself for not including this in the list of trivial cases I had considered (as this is not my intent). In any event, if I had to make this work I could but I isn't what I was hoping for.

    Cheers - L~R

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