Chim Tu has a large rectangular table. On it, there are ﬁnitely many pieces of paper with non-overlapping interiors, each one in the shape of a convex polygon. At each step, Chim Tu is allowed to slide one piece of paper in a straight line such that its interior does not touch any other piece of paper during the slide. Can Chim Tu always slide all the pieces of paper off the table in ﬁnitely many steps?
Please provide a full solution.
Note: this question is from HMMT, if this is the case