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The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers not because it is abstract, but because it is a representation of actual things.
In N. Rose, Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Loci: Convergence
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Euler Squares
Sudoku Skills
Skills learned in solving Sudoku puzzles can be applied to solving the Euler square. However, this is not an easy method, and is probably best applied after beginning with the two methods above. Randomly place pegs on diagonals or rows, and then continue by choosing a spot on the array and eliminating already used colors and shapes for that row and column. Now chose wisely from the remaining pegs, adjusting when necessary. At times the last color or last shape can be placed by checking which row or column does not yet have that attribute. This solution method was more random and did not evince diagonalization or symmetry (see Figure 7).
Figure 7: Using Sudoku skills to place the last red peg