To minimize the number of distinct values, we want to maximize the number of times they appear. So, we could have $223$ numbers appear $9$ times, $1$ number appear once, and the mode appear $10$ times, giving us a total of $223+1+1=$ (D) $225$. 
A list of $2018$ positive integers has a unique mode, which occurs exactly $10$ times. What is the least number of distinct values that can occur in the list? (2018 AMC 10B Problems, Question \#14) 
[a] $$202$$ 
[b] $$223$$ 
[c] $$224$$ 
[d] $$225$$ 
[e] $$234$$ 