IMO Shortlist 2010 problem C1

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Dodao/la: arhiva
23. lipnja 2013.
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?

Proposed by Gerhard Wöginger, Austria
Izvor: Međunarodna matematička olimpijada, shortlist 2010