MathDB

Let

N_{15}

be the answer to problem 15.
For a positive integer

x

expressed in base ten, let

x'

be the result of swapping its first and last digits (for example, if

x = 2024

, then

x' = 4022

). Let

C

be the number of

N_{15}

-digit positive integers

x

with a nonzero leading digit that satisfy the property that both

x

and

x'

are divisible by

11

(note:

x'

is allowed to have a leading digit of zero). Compute the sum of the digits of

C

when

C

is expressed in base ten.

Problem Statement