Re: Prime Sums In A Grid

On Tue, 24 Feb 2009 09:07:02 +0200, Phil Carmody
<thefatphil_demunged@xxxxxxxxxxx> wrote:

quasi <quasi@xxxxxxxx> writes:
On Tue, 24 Feb 2009 12:54:46 +1100, Gerry Myerson
<gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

In article <p9h3q4dk6ldeipkieuqjf1vpcgsn8afnaa@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:

How about this variant ...

For which n in N is there an n x n matrix whose entries are 1, ...,
n^2, arranged so that every row and every column sums to a prime
number.

Note that the matrix entries must be distinct, but the row and column
sums need not be.

Remarks:

Clearly n = 1 fails. For n = 2 or n = 3, it's not hard to find
matrices which work. For n = 4, I'm not sure.

quasi

1 3 2 5
7 6 4 12
8 9 10 16
13 11 15 14

Cool.

n = 5 anyone?

This has almost certainly been done on Carlos Rivera's primepuzzles.net.

Then give the solution, if any, for n = 5.

quasi
.

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  • Re: Prime Sums In A Grid
    ... How about this variant ... ... arranged so that every row and every column sums to a prime ... Note that the matrix entries must be distinct, ...
    (sci.math)