Answer
1.7761 * 10^19 (5*5 magic square estimation)
Step-by-step explanation:
Excluding rotations and reflections, there is exactly one 3×3 magic square, exactly 880 4×4 magic squares, and exactly 275,305,224 5×5 magic squares. 778-783 gives the 880 4 X 4 squares.
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down vote
Given an n×nn×n magic square, write MnMn for its magic constant. There are nn rows, each of which has sum MnMn, so the sum of all the entries in the square is n⋅Mnn⋅Mn. Each whole number between 11 and n2n2 appears once, so
nMn=1+2+…+n2=n2(n2+1)2,Mn=n(n2+1)2.
nMn=1+2+…+n2=n2(n2+1)2,Mn=n(n2+1)2.
In particular, every n×nn×n magic square has the same constant.
