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COMMENTS
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Definition for a magic border: imagine the border of a square matrix: E_1={a_{1,1},...,a_{1,n}} upper, E_2={a_{1,1},...,a_{n,1}} left, E_3={a_{n,1},...,a_{n,n}} lower, E_4={a_{1,n},...,a_{n,n}} right edge. Distribute the pairs of numbers (0,n^2-1),...,(2n-3,n^2-2n+2) (each once) on (a_{1,1},a_{n,n}), (a_{1,n},a_{n,1}) the pairs of corner elements and (a_{1,i},a_{n,i}), (a_{i,1},a_{i,n}) (i=2,...,n-1) the pairs of edges so that for k=1,...,4: sum_{a\in E_k) a = const. Reduced means that the pairs of corners, (a_{1,2},...,a_{1,n-1}) and (a_{2,1},...,a_{n-1,1}) are in ascending order.
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