# Problem arises due overuse of magic - Part (1)

**Number Theory**Level 4

Ben plays a game: He writes the numbers from 1 to 2004 on a board, selects \(n\) numbers, then writes their sum \(s \bmod {11} \) on the board, casts a magic chant, so that the previous \(n\) selected numbers vanish from the board and starts over again with the numbers, which are left at the board.

- selecting \(n\) numbers,
- writing down the \(s \bmod { 11 } \),
- making the previous \(n\) numbers vanish.

At the end there were just two numbers left. One was 1000. What was the other one?