IMO Shortlist 1978 problem 10

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2. travnja 2012.
An international society has its members from six different countries. The list of members contain 1978 names, numbered 1, 2, \dots, 1978. Prove that there is at least one member whose number is the sum of the numbers of two members from his own country, or twice as large as the number of one member from his own country.
Izvor: Međunarodna matematička olimpijada, shortlist 1978