kwh@bentley.UUCP (KW Heuer) (03/26/86)
Some definitions. An n x n array has 2n+2 _lines_: n rows, n columns, and two full diagonals. A square is _magic_ if the sum of the n elements in a line is constant (i.e. independent of the line). A square is _bimagic_ if it is magic and the sum of the squares of each line is also constant. A square is _normal_ if its elements are the first n^2 positive integers. (Since magic and bimagic squares preserved under affine transformations, you may substitute your favorite arithmetic progression. I often use [0,n) instead of (0,n].) What is the smallest normal bimagic square (after the trivial case n = 1)? More specifically, I've proved to my satisfaction that there are none for 2 <= n <= 6, and I have an example for n = 8. Is there a bimagic square of order 7? (The magic constant is 175 and the bimagic constant is 5775.) Karl W. Z. Heuer (ihnp4!bentley!kwh), The Walking Lint