Magic squares
Task number: 3903
From orthogonal Latin squares \( A \) and \( B \) of order \( n \), composed of numbers \( 0,…, n-1 \), construct square \( C \) according to the rule \( c_{i, j} = na_{i,j} + b_{i, j} +1 \).
What are the special properties of the resulting square \(C\)?
Solution
The resulting square will contain the numbers \(1,…, n^2 \) and all row and column sums will be the same.
Such squares are sometimes called magic squares, although they are usually required to have the same sums also on both diagonals.
