2018 AMC 10B Problem 14

Every value other than the mode can appear at most $9$ times, to keep the mode unique

With $d$ distinct values the list holds at most $10 + 9(d-1)$ entries; make this at least $2018$

The mode shows up $10$ times. To keep the number of distinct values small, let every other value repeat as much as the rules allow, which is $9$ times each (any more would tie the mode). With $d$ distinct values the list holds at most $10 + 9(d-1)$ entries. We need $10 + 9(d-1) \ge 2018,$ so $d - 1 \ge 223.1,$ giving $d \ge 225.$ Therefore, the answer is D.