The above example explains why the "criss-cross" method for doubly even magic square works. Another possible 4×4 magic square, which is also pan-diagonal as well as most-perfect, is constructed below using the same rule. However, the diagonal sequence is chosen such that all four letters α, β, γ, δ appear inside the central 2×2 sub-square. Remaining cells are filled column wise such that each letter appears only once within a row. In the 1st column, the empty cells need to be filled with one of the letters selected from the complementary pair α and δ. Given the 1st column, the entry in the 2nd row can only be δ since α is already there in the 2nd row; while, in the 3rd row the entry can only be α since δ is already present in the 3rd row. We proceed similarly until all cells are filled. The Latin square given below has been obtained by flipping the Greek square along the main diagonal and replacing the Greek alphabets with corresponding Latin alphabets.
the above example explains why the "criss-cross" method for doubly even magic square works another possible 4×4 magic square which is also pan-diagonal as well as most-perfect is constructed below using the same rule however the diagonal sequence is chosen such that all four letters α β γ δ appear inside the central 2×2 sub-square remaining cells are filled column wise such that each letter appears only once within a row in the 1st column the empty cells need to be filled with one of the letters selected from the complementary pair α and δ given the 1st column the entry in the 2nd row can only be δ since α is already there in the 2nd row; while in the 3rd row the entry can only be α since δ is already present in the 3rd row we proceed similarly until all cells are filled the latin square given below has been obtained by flipping the greek square along the main diagonal and replacing the greek alphabets with corresponding latin alphabets