Placing a single color down a main diagonal of the pegboard begins this method. Then place another color on a parallel diagonal, noting this will leave a single peg of that color to be placed in the opposite corner. Continue to diagonalize by color. This is an eye-pleasing and symmetrical solution. Double diagonalization can be accomplished by placing color on one main diagonal and shape on the other second diagonal (see Figure 5).
Figure 5: Double diagonalization solution
Elaine Young, "Euler Squares - Diagonalization," Convergence (May 2011)