000			01988nam a2200169Ia 4500
999			_c47159 _d47159
005			20200308073514.0
008			190927s9999 xx 000 0 und d
082			_aT C7683 2017
100			_aContreras, Mattheus Marcus B.
245		0	_aConstructing Magic Square Using Parity Map
260			_a3
260			_b602
260			_c2017
520			_aSince the discovery of the Lo Shu square around 2700 B.C. in China, the pursuit of constructing magic squares has been a fascination in recreational mathematics. Although there are many studies available, few of them could actually provide a unique and efficient solution for constructing magic squares of different order. In this paper, we define a normal magic square as a NxN square matrix whose entries are distinct positive integers from 1 to N^2 such that every row, column, and two main diagonals sums up to the same number, the magic constant. As a basis for constructing magic square of order N, we formulate constraints of normal magic square of order 3 by a collection of linear equations. We provide a well-known but computationally infeasible algorithm that uses exhaustive search method and produce eight normal magic square of 3. The we propose an efficient algorithm for constructing all normal magic squares of order 3. The algorithm makes use of parity map, Z={1,...,N}-Z={0,1} and define f(x)=0 if x is even, 1 if x is odd. Using this and other properties of an odd-ordered normal magic square, we prove that there exist only one parity magic square, a magic square with entries of 0 or 1, that satisfies the said constraints. From this f, we demonstrate that normal magic square of order 3 has four rotations and four reflections which show that normal magic square of order 3 is isomorphic to D. Using this fact, we proposed another algorithm which is more efficient and flexible than the other two, using also the parity map method to construct magic squares of order 3.
526			_a000-099
942			_cRB _2ddc