Paradoxes have played great instructive roles in many cultures. They provide an excellent paradigm for teaching concepts that require deep reflection. In this article, the authors present two different paradoxes related to the length contraction in special relativity and explain their resolution. They hope that these two Gedanken experiments and their explanations will help undergraduate students to develop a deeper understanding of the subject and train them to transfer this knowledge to other paradoxes in the area of relativity, or in other branches of learning. (Contains 6 figures.)