The purpose of this publication is to bring attention to some physics problems whose answers seem to be paradoxical and, at first glance, do not agree with a limiting case check. Solving a problem on the motion of a system consisting of two masses and a spring, it is natural to examine the answer by considering a case when a spring constant is going to infinity. But how do you do it if there is no spring constant in the final formula? Three situations with paradoxical answers are considered in detail in this article. To solve these paradoxes we needed to look at the motion of each system more closely and to define more precisely the mathematical model of its motion. The results of our work could be used for educational research student's projects.