Consider a $n\times n$ table which is filled with numbers $1,2,3,...,n^2$ (in no particular order).We'd call such table "Special" if the sum of each column and each row and each diameter is a constant number.For what $n$s do we have a Special Table?
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1There are normal magic squares of all orders except $n=2$. – mjqxxxx Nov 04 '14 at 14:23
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@mjqxxxx I can't get what you mean by that can you make an example? – Minuano Nov 04 '14 at 14:25
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@FuriousMathematician: What mjqxxx is saying that the thing you call a "special table" is commonly known as a (normal) magic square, and it is well known that they exist for all $n\ge 3$. – hmakholm left over Monica Nov 04 '14 at 14:27
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@HenningMakholm I see... now how would you prove that? – Minuano Nov 04 '14 at 14:29
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What you call a "special table" is commonly known as a (normal) "magic square".
The Wikipedia article on magic squares links to various methods for constructing them explicitly for all side lenghts except $2$. (One easily sees that the $n=2$ case is impossible).
hmakholm left over Monica
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