Coincidence on our subjects! The additive-multiplicative magic squares n x n, mentioned in my previous email on multimagie.com, are sum-product matrices m x n ... of course with m = n... but with supplemental properties: -their n rows AND their n columns (and also their 2 diagonals) have the same sum S -their n rows AND their n columns (and also their 2 diagonals) have the same product P Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de David Wilson Envoyé : jeudi 21 janvier 2010 10:15 À : math-fun Objet : Re: [math-fun] sum-product matrices Erich, I should have known you would be all over this. My name was clearly original. I should never even have an idea without consulting you first. :-) ----- Original Message ----- From: "Erich Friedman" <efriedma@stetson.edu> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Wednesday, January 20, 2010 7:54 PM Subject: Re: [math-fun] sum-product matrices
I'm pretty sure that apart from 1 x 1 matrices, there are no square sum-product matrices.
1 10 15 12 6 8 20 4 2
But I was pleased to find that there are indeed sum-product matrices with equal row sum and column product. The following are (all?) "primitive" 14 x 2 sum-product matrices with sum = product = 1890.
there is a 10x2 sum-product matrix with equal row sum 840 and column product 840:
2 4 7 24 40 70 105 140 168 280 420 210 120 35 21 12 8 6 5 3
you can find more info on sum-product matrices here:
http://www2.stetson.edu/~efriedma/mathmagic/1102.html
erich
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