IMO Shortlist 1989 problem 22
Dodao/la:
arhiva2. travnja 2012. Prove that in the set
can be expressed as the disjoint union of subsets
such that
i.) each
contains 17 elements
ii.) the sum of all the elements in each
is the same.
%V0
Prove that in the set $\{1,2, \ldots, 1989\}$ can be expressed as the disjoint union of subsets $A_i, \{i = 1,2, \ldots, 117\}$ such that
i.) each $A_i$ contains 17 elements
ii.) the sum of all the elements in each $A_i$ is the same.
Izvor: Međunarodna matematička olimpijada, shortlist 1989
Školjka 
