Nowadays there are many views related to the online testing systems. The importance of acquisition of the final result is considered to be the main disadvantage in the classic test system where the learner chooses the correct answer from the suggested set of answers; this does not motivate a person to define the answer themselves or to create a logical chain of problem solutions. The integration of the intellectual processes into the existing training systems will prevent the drawbacks of the existing knowledge assessment systems and will make it possible to assess the learners’ ability to make logical decisions, to clarify the answers using examples and to evaluate the method of achieving the result. The article describes the algorithm for creating the intellectual, user adapted questions; this algorithm uses the model of the learner from the set of questions and by fulfilling the modified Dijkstra's algorithm chooses the questions that help the learner reach the result that is most appropriate to their competence level.