A Math circle leader assigned 20 problems as homework. At the next meeting, he found out that each student solved exactly 2 problems, and that each problem was solved by exactly 2 students.
A) How many students are in the circle?
B) Is it possible to set up a discussion of the problems so that
- a) each student explains one of the problems that he has solved and
- b) all the 20 problems get explained by the students?
From the book: Moscow math circle by Sergey Dorichenko