AMC 10B 2025 (Problem 3)

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's 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{array}{ccccccc}&&&10&&&\\ &&10&&1&&\\ &10&&11&&1&\\ 10&&21&&12&&1\end{array}

What is the sum of the digits of the sum of the numbers in the

11

th row?

\text{(A)}\;11

\text{(B)}\;13

\text{(C)}\;14

\text{(D)}\;16

\text{(E)}\;17