Mystery of numbers in a square matrix grid

Found On: December 2012

Recently, while playing with numbers I came across this strange mathematical property of numbers written in a square matrix grid with odd dimensions. When you add the numbers horizontally, vertically and across both diagonals, the numbers add up to the same sum. The following diagram illustrates this:


Turns out if you use a bigger square with dimensions 5×5, you get a common sum across these directions. What sorcery is this? If you can explain it, hit me a comment below.

P.S.: While making the above picture, I came across an optical illusion. If you look at points where the grey pixels intersect the black pixels, it looks like either they are brighter grey. This is not true. Only in your head! It is normal grey if you look closely.


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