[seqfan] Re: Matrix puzzle
Jeremy Gardiner
jeremy.gardiner at btinternet.com
Mon Oct 27 22:27:32 CET 2014
Matrix puzzle
Example solution: 6 2 4
9 8 1
3 10 5
det A = 360
Considering an mxm matrix with all elements k or less
Then I conjecture:
m=2 has no solutions for k < 12
m=3 has no solutions for k < 10
m=4 has no solutions for k < 20
Jeremy
On 26/10/14 00:03, "Charles Greathouse" <charles.greathouse at case.edu> wrote:
> A friend of mine asks: Can you find a 3X3 matrix of distinct positive
integers
> with a nonzero determinant divisible by each of the nine
constituent
> elements?
It's easy to find a matrix with eight of the nine dividing the
> determinant
-- pick (almost) whatever you want for the first eight, then fit
> the last
to give a determinant equal to the product of the others.
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