A base-N number formed by repeating the digit seven precisely (N-1) times is denoted by F(N). For example:

F(8) = 7,777,777 (base 8), F(9)= 77,777,777 (base 9) and, so on.

Determine the remainder when F(8)+ F(9)+ ....+ F(36) is divided by the base ten number 11.

*** For an extra challenge, solve this problem without using a computer program.