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1993 AMC 12 Question 16

AMC12 · 1993 AMC 12

Question 16

Consider the non-decreasing sequence of positive integers $$
\begin{aligned} &1,2,2,3,3,3,4,4,4,4,\\ &5,5,5,5,5,\ldots \end{aligned}
$$ in which the $n$th positive integer appears $n$ times. The remainder when the $1993$rd term is divided by $5$ is
  1. $0$
  2. $1$
  3. $2$
  4. $3$
  5. $4$