Several versions of the backtracking are known. In this paper, those versions are in focus which solve the problems whose problem space can be described with a special directed tree. The traversal strategies of this tree will be analyzed and they will be implemented in object-oriented style. In this way, the traversal is made by an enumerator object which iterates over all the paths (partial solutions) of the tree. Two different “acktracking enumerators” are going to be presented and the backtracking algorithm will be a linear search over one of these enumerators. Since these algorithms consist of independent objects (the enumerator, the linear search and the task which must be solved), it is very easy to exchange one component in order to solve another problem. Even the linear search could be substituted with another algorithm pattern, for example, with a counting or a maximum selection if the task had to be solved with a backtracking counting or a backtracking maximum selection.