Pascal like Triangle

A Pascal-like triangle has $10$ as the top row and $10$ followed by $1$ as the second row. In each subsequent row, the first number is $10$, the last number is $1$, and, as in the standard Pascal triangle, each other number in the row is the sum of the two numbers directly above it. The first four rows are shown below.

\begin{tikzpicture}[x=1.15cm,y=0.7cm,every node/.style={inner sep=0pt}]
  \node at (0,0) {$10$};
  \node at (-0.5,-1) {$10$};
  \node at (0.5,-1) {$1$};
  \node at (-1,-2) {$10$};
  \node at (0,-2) {$11$};
  \node at (1,-2) {$1$};
  \node at (-1.5,-3) {$10$};
  \node at (-0.5,-3) {$21$};
  \node at (0.5,-3) {$12$};
  \node at (1.5,-3) {$1$};
\end{tikzpicture}

What is the sum of the digits of the sum of the numbers in the $11$th row?
\[
\textbf{(A)}\;11
\qquad
\textbf{(B)}\;13
\qquad
\textbf{(C)}\;14
\qquad
\textbf{(D)}\;16
\qquad
\textbf{(E)}\;17
\]

Solutions

• Solution 1