magic constant

Given a magic square, magic cube, etc., the sum of any row, column or diagonal is called the magic constant of that magic square, cube, etc.

In the case of a standard n×n magic square that uses the integers from 1 to n2, the magic constant is


while that for a magic cube is


We can then generalize to higher dimensions d thus:


So, for dimension d the magic constant is n(nd+1)2. For instance, a Franklin magic square (n=8,d=2) has magic constant 8(82+1)2=260.

In a trivial sense, an n×n sudoku puzzle has a magic constant of n2.

Title magic constant
Canonical name MagicConstant
Date of creation 2013-03-22 16:24:57
Last modified on 2013-03-22 16:24:57
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 05B15