With time for practice and to discuss the parameters and constraints, this activity takes at least two class periods. If you are pressed for time, that could be as little at 1.5 hours and you could probably fill 2 hours or more, if you allow time and materials for iterations and improvements.
Twenty sheets of paper is a good number to use. With 20 sheets, some students will create structures that will hold over 50 pounds, and in the past I have had structures support over 100 pounds. Copy paper is greater than 20cm on the short side, so let students know that they can use a sheet of paper to measure the height of their structure.
When it comes time to test the structures, have the students begin with their structure on a smooth floor, not carpeting. Do not test the structures on a table, as the stack of books can get very tall and heavy, and will pose a hazard. You do not need a scale to weigh the books, but it does help. It is interesting to weigh the structures as well.
There are several possible extension for this activity. You could assign costs to each of the materials and calculate the highest weight supported per dollar spent. You could have students work in groups and practice their collaboration skills. You could test the relative strengths of different papers (construction vs. copy paper), and you could load a structure with books and have students observe the effects of water sprayed onto it.
This activity works well on its own and as a part of an engineering curriculum. I have a second similar activity in which the challenge is to create the tallest free-standing structure. Either makes a decent activity for a substitute teacher, but you may not want to miss the fun.