We know that using the numbers from 1 to 25 (once each), we can build a magic square of order 5, being 65 the magic constant.

Your task is to build a magic square of order 5, using only the numbers from 1 to 20 (once each), leaving one cell empty in each row, in each column, in each main diagonal.

Obviously, the magic constant will be [(1 + 20)/2]*20/5 = 42.

Note: This type of magic square has a name.

With rotations/reflections aside, there are four basic possible arrangements for the holes:

x _ x x x
_ x x x x
x x _ x x
x x x x _
x x x _ x

x _ x x x
x x x x _
x x _ x x
_ x x x x
x x x _ x

_ x x x x
x x _ x x
x x x x _
x _ x x x
x x x _ x

_ x x x x
x x x x _
x x x _ x
x _ x x x
x x _ x x


brianjn has posted a solution for the third grid. I am curious as to how many of the four arrangements have solutions.

Posted by Dej Mar on 2008-07-28 23:00:28