TITLE: Finite sequence length before and after removing repetitions
QUESTION [0 upvotes]: I have a sequence $S$ of length $n^3+1$  where the elements are not necessarily distinct and every element appears at most $n$ times. Why does the sequence $S'$ where I remove all repetitions from $S$ have at least $n^2+1$ elements?

REPLY [3 votes]: Hint: If the length of sequence $S$ were $n^3$ and all terms were repeated exactly $n$ times, then you would have exactly $n^2$ distinct terms.
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