Solution a87188a9-0857-4c32-ba2e-dfc7350a33ed

Points: 1 pt

Expanding the diagram and calculating the sum of each of the first five rows gives
\[
\setlength{\arraycolsep}{4pt}
\begin{array}{*{9}{c}@{\qquad}c@{\quad}r}
\multicolumn{9}{c}{} & & \text{Row sum} \\[4pt]
  &    &    &    & 10 &    &    &    &   & \longrightarrow & 10 \\[7pt]
  &    &    & 10 &    & 1  &    &    &   & \longrightarrow & 11 \\[7pt]
  &    & 10 &    & 11 &    & 1  &    &   & \longrightarrow & 22 \\[7pt]
  & 10 &    & 21 &    & 12 &    & 1  &   & \longrightarrow & 44 \\[7pt]
10&    & 31 &    & 33 &    & 13 &    & 1 & \longrightarrow & 88
\end{array}
\]
Starting with the second row, the sum doubles each time. We can clearly see that the sum of the $11$th row is
\[
11\cdot 2^9 = 5632.
\]
The sum of its digits is
\[
5+6+3+2=16.
\]

Final answer:
16