IMO 2010 Shortlist C1
In a concert, 20 singers will perform. For each singer, there is a (possibly empty) set of other singers such that he wi...
Category: Combinatorics
Problem
In a concert, 20 singers will perform. For each singer, there is a (possibly empty) set of other singers such that he wishes to perform later than all the singers from that set. Can it happen that there are exactly 2010 orders of the singers such that all their wishes are satisfied? (Austria)