algorithm to find all values that occur more than n/10 times
Perhaps the hint was aiming at the following approach. Suppose that the array were sorted. If a value appears $m$ times and we divide the array into intervals of length $m$, then the value must appear at the end of one of the intervals. This suggests the following algorithm for finding all values that appear $n/C$ times: compute the $i \cdot n/C$-largest elements for $1 \leq i \leq C$, and for each of them, check whether the value appears at least $n/C$ times. Each iteration takes $O(n)$ time using Quickselect, for a total of $O(Cn)$ time.