In columns-based intelligent systems, basic problems serve as the basis for solving all other problems. The article deals with the solution of basic problems for the pattern regions, which originally arose as a natural means of ensuring operation in the presence of interference. Basic concepts and definitions are given. The formulation of basic problems for pattern regions is described and their solution is given using a general universal method based on an element-by-element comparison of patterns. Further, the solution of basic problems for pattern regions using a more efficient intersection method is considered. The solution scheme and an explanatory example are described in detail. In conclusion, it is shown that memorizing pattern regions under certain names means memorizing the IF-THEN rules, in the conditional part of which connectives AND, OR, NOT and variables with a universal quantifier are used.