IMO Shortlist 1989 problem 22
Dodao/la:
arhiva2. travnja 2012. Prove that in the set
![\{1,2, \ldots, 1989\}](/media/m/9/0/c/90cc6abd2a2d0a80fb537fc62b71c06a.png)
can be expressed as the disjoint union of subsets
![A_i, \{i = 1,2, \ldots, 117\}](/media/m/e/c/3/ec3a05e95ca3f55cd3ffb729201fc446.png)
such that
i.) each
![A_i](/media/m/5/f/0/5f0935569a883b13bb70b83ea33eee14.png)
contains 17 elements
ii.) the sum of all the elements in each
![A_i](/media/m/5/f/0/5f0935569a883b13bb70b83ea33eee14.png)
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