Question 116
Prove that the set $\{1,2, \ldots, 2007\}$ can be expressed as the union of disjoint subsets $A_{i}$ ($i=1,2, \ldots, 223$) such that
a. each $A_{i}$ contains 9 elements, and
b. the sum of all the elements in each $A_{i}$ is the same.
a. each $A_{i}$ contains 9 elements, and
b. the sum of all the elements in each $A_{i}$ is the same.