2n students at a "fair" math competition
Source: Romanian IMO Team Selection Test TST 2003, problem 6
September 24, 2005
algorithmcombinatorics proposedcombinatorics
Problem Statement
At a math contest there are students participating. Each of them submits a problem to the jury, which thereafter gives each students one of the problems submitted. One says that the contest is fair is there are participants which receive their problems from the other participants.
Prove that the number of distributions of the problems in order to obtain a fair contest is a perfect square.