23 Sep
2005
23 Sep
'05
1:27 p.m.
From dasimov@earthlink.net 1) Better here would be all rows & columns and broken diagonals (i.e., diagonals on the torus) multiply to the same product.
I do not know if it is possible, but our smallest 4x4 example with product 5040 has already (by construction with the 2 latin squares) 2 magic diagonals + 2 magic broken diagonals. 1 12 30 14 10 42 3 4 21 5 8 6 24 2 7 15 (broken 12*10*6*7 and 30*4*21*2) Another interesting example, magic product 14400: 1 6 40 60 20 120 2 3 24 4 15 10 30 5 12 8 Exchange columns 1 and 2, or columns 3 and 4, or idem for rows: the square remains magic!!! Because each diagonal of the four inside 2x2 squares have always the same magic product 120. Christian.