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2023 AMC 12A Question 20

AMC12 · 2023 AMC 12A

Question 20

Rows $1,$ $2,$ $3,$ $4,$ and $5$ of a triangular array of integers are shown below.

$$
\begin{array}{ccccccccc} &&&&1&&&&\\ &&&1&&1&&&\\ &&1&&3&&1&&\\ &1&&5&&5&&1&\\ 1&&7&&11&&7&&1 \end{array}
$$

Each row after the first row is formed by placing a $1$ at each end of the row, and each interior entry is $1$ greater than the sum of the two numbers diagonally above it in the previous row. What is the units digit of the sum of the $2023$ numbers in the $2023$rd row?
  1. $1$
  2. $3$
  3. $5$
  4. $7$
  5. $9$