Question 9
Let us call a set of positive integers nice if the number of its elements equals to the average of its numbers. Call a positive integer $n$ an amazing number if the set $\{1, 2, \ldots, n\}$ can be partitioned into nice subsets.
**Part a.** Prove that every perfect square is amazing
**Part b.** Show that there are infinitely many positive integers which are not amazing.
**Part a.** Prove that every perfect square is amazing
**Part b.** Show that there are infinitely many positive integers which are not amazing.