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.

Difficulty level: Easy task (using definitions and simple reasoning)
Reasoning task
Cs translation
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