Question 1
Prove that the set $\{1,2,\ldots,1989\}$ can be expressed as the disjoint union of 17 subsets $A_1,A_2,\ldots,A_{17}$ such that:
(i) each $A_i$ contains the same number of elements;
(ii) the sum of all elements of each $A_i$ is the same for $i=1,2,\ldots,17$.
(i) each $A_i$ contains the same number of elements;
(ii) the sum of all elements of each $A_i$ is the same for $i=1,2,\ldots,17$.