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The article presents a set of experimental-static models of the properties of fine-grained concretes on a cement–slag binder and quartz sand with the addition of a hardening accelerator made on a 3D printer. The influence of the factors of the composition of the mixture and the effects of their interaction on the studied properties of concrete was established. By analyzing the models, the influence of the factors of mixture composition on the studied properties was ranked. The nature and degree of interrelation of individual properties of concrete are shown. A method for calculating the optimal compositions of concrete for a 3D printer, providing the specified properties at a minimum cost, is proposed.