  The study proves the existence of an algorithm to receive all elements of a
class of binary matrices without obtaining redundant elements, e. g. without
obtaining binary matrices that do not belong to the class. This makes it
possible to avoid checking whether each of the objects received possesses the
necessary properties. This significantly improves the efficiency of the
algorithm in terms of the criterion of time. Certain useful educational effects
related to the analysis of such problems in programming classes are also
pointed out.
