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In this paper we seek for an answer on Smarandache type question: may onecreate the theory of Magic squares 4x4 in size without using properties of someconcrete numerical sequences? As a main result of this theoretical investigationwe adduce the solution of the problem on decomposing the general algebraicformula of Magic squares 4x4 into two complete sets of structured and fourcomponent analytical formulae

ANALYTICAL FORLVIULAE Ai'll) ALGORITHMS FOR CONSTRUCTING MAGIC SQUARES FROM AN ARBITRARY SET OF 16 NUMBERS