# 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?

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